Policy Research Working Paper 10600 Endogenous Institutions and Economic Policy James A. Robinson Alexander Vostroknutov Ekaterina Vostroknutova Macroeconomics, Trade and Investment Global Practice November 2023 Policy Research Working Paper 10600 Abstract This paper proposes a new framework to model institutions to conceptualize institutions as inclusive or extractive and and institutional change. It shows how moral agents, who model institutional change as a consequence of the choice strive to cooperate with others, can form institutions that of moral agents among available institutions as time unfolds. facilitate cooperation. The framework makes it possible With a series of examples of clientelistic networks, the paper to model informal as well as formal institutions as games shows that the framework can be useful for understand- played by moral agents: when the quality of the govern- ing how and why such networks form and persist. The ment is low and agents are not willing to use its services framework can be used to model any interactions among they will create informal institutions that allow them to moral agents, thus giving rise to a wide variety of possible cooperate outside the official channels. It is also possible institutional settings. This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at evostroknutova@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Endogenous Institutions and Economic Policy∗ James A. Robinson† Alexander Vostroknutov‡ Ekaterina Vostroknutova§ Topics: Institutions and Growth, Social Norms and Poverty, Economic Growth Policy. Keywords: endogenous institutions, social norms, inclusive/extractive institutions, growth, institutional policy. JEL Classification: E61, E71, H20, O11, O17, O43. ∗ All mistakes are our own. The findings expressed in this paper are those of the authors and do not necessarily represent the views of the World Bank or its member countries. We would like to thank Milan Brahmbhatt, Frederico Gil Sander, Norman Loayza, Stephen Ndegwa, Hannes Rusch, Gaute Solheim and the seminar participants in IMT Lucca, DECIG Seminar Series at the World Bank, and MBEES and MLSE at Maastricht University for valuable comments. † Harris School of Public Policy and Department of Political Science, University of Chicago. e-mail: jamesrobinson@uchicago.edu. ‡ Department of Microeconomics and Public Economics (MPE), Maastricht University, The Netherlands. e-mail: a.vostroknutov@maastrichtuniversity.nl. § The World Bank. e-mail: evostroknutova@worldbank.org. Corresponding author. 1 Introduction In the past decades, neoclassical economics has been rather successful in accounting for the process of economic growth in industrialized countries using the Solow-Swan model and its extensions [Solow, 1956, Swan, 1956, Aghion and Howitt, 2008]. However, it has failed to predict the slow catch up in income per capita by developing countries [North et al., 1993, Keefer and Knack, 1997, Caselli, 2005, Rodrik, 2013]. While recent methodological breakthroughs allow concluding that significant welfare gains from eliminating structural distortions can be achieved [Baqaee and Farhi, 2020], the literature does not explain the staggering proportions of these “distortions” or suggest policies to reduce them. For example, the informal sector employs the majority of workers and produces more than half of GDP in many parts of the world [Loayza, 2018, Perry et al., 2007], while political institutions in transplanted democracies are often overwhelmed with clientelism and corruption to the detriment of growth [Stokes, 2011]. The attempts to eliminate these distortions directly have failed [Floridi et al., 2020], suggesting that they are structural in the sense of being ”the way of life” in many developing countries [De Soto et al., 1989], and need to be taken into account in policy making. Chief among possible explanations of these failures has been the importance of economic institutions [North, 1990, Ostrom, 1990, Hall and Jones, 1999]. Historically, the formal institutions of the Western world (such as democratic political systems) have been shown to create long-term growth in income per capita [Fukuyama, 1995]. However, multiple studies have shown that transplanting Western institutions to other countries does not necessarily lead to a commensurate welfare improvement [Putnam et al., 1992, Raiser, 1997]. One potential reason is that institutional change is a long-term process, where institutions need to grow organically based on the existing economic system including the informal institutions and social norms already in place [Acemoglu and Robinson, 2020]. Indeed, Acemoglu and Robinson [2020] have argued that building and maintaining institutions con- ducive to economic growth requires enormous effort from governments and societies. Such inclusive institutions are located in the “narrow corridor” between a fully disorganized “state of nature,” or Warre, and an all-controlling Leviathan of a powerful government. Acemoglu and Robinson painstakingly col- lect evidence of institutional design and historical path-dependence that have led countries to or away from this narrow corridor. But while this analysis clarifies what features the desired inclusive institu- tions possess that makes them so effective in creating growth, in practice only a handful of developing countries have been able to properly engineer such institutions to create some convergence to the nar- row corridor. The majority of developing countries suffer through what Acemoglu and Robinson call extractive institutions, where a small proportion of the population enjoys the benefits that all workers of the economy create, and are not therefore conducive to long-term economic growth per capita. The general consensus across various literatures is that institutions arise to support cooperation of economic agents [e.g., Nee, 1998, Ostrom, 2000, Keefer and Knack, 2008, Henrich, 2015a]. Cooperation is also an important feature of inclusive institutions. As Acemoglu and Robinson [2020] note, “in the corridor [of inclusive institutions] the state and society do not just compete, they also cooperate. This 1 cooperation engenders greater capacity for the state to deliver the things that society wants and foments greater societal mobilization to monitor this capacity.” Yet, in neoclassical economics transactions are costless, agents are only interested in maximizing their own consumption utility, and firms—or collec- tives of agents who create surplus—are treated as exogenously given production functions. The fact that standard models do not account for cooperation is mainly the reason they are unable to model emergence of firms and other institutions [Coase, 1937]. Alternative approaches that tried to modify the neoclassical paradigm to incorporate institutions also did not produce a general, viable framework for policy applications. For example, according to views expressed in institutional economics, models of institutions have lagged the intuitive and histori- cal understanding of their importance [Williamson, 2000, Furubotn and Richter, 2010]. With a majority of models being at the country level and including exogenous variables to account for the quality of institutions, institutional economics has not yet arrived at the practicality of how to induce positive in- stitutional change or orchestrate a shift from extractive to inclusive institutions. To obtain a workable model of institutional change, there is a need for a more fundamental bottom-up approach to under- standing the formation and evolution of institutions that takes into account the motivation of individual agents to self-organize into cooperative “units” or firms [Sala-i Martin, 2002]. Such an approach can lead to a framework where institutions arise endogenously and where policies can be devised to change them. To our best knowledge, no such framework currently exists. Our study aims at filling this long-standing gap in the understanding of economic institutions and policies directed at changing them. We propose a parsimonious framework of how institutions arise and how they function within an economic environment defined by other institutions. In the version of the model described here, many of the “distortions” mentioned above (such as informality, clientelism, or corruption) appear organically and can be changed through appropriate policies suggested by the model. More importantly, the model can be adapted to various forms of institutions and economic environments, which can make it indispensable for applied and policy-oriented work related to institutional change. Conceptually, our framework is different from the neoclassical approach in only one small but funda- mental aspect. While neoclassical economic agents are assumed to have a single motivation, namely the desire to have more consumption utility, we assume that agents trade off two motivations: the standard preference to have more consumption and the desire to cooperate with others. While the introduction of the latter motivation in the utility function is novel, large swaths of literatures in various social sciences have been converging on the view that humans are a social species that has evolved special mental ca- pacity for cooperation.1 According to this view, the innate preference for cooperation is operationalized through the desire to adhere to social norms, or common beliefs about how things ought to be done. In economics, this second motivation is modeled as an additional term in the norm-dependent utility func- tion that was first introduced by Kessler and Leider [2012]: norm-following agents maximize the sum of their consumption utility and a measure of social appropriateness defined on outcomes (the agents 1 The reason this capacity has evolved is that cooperation is more profitable than no cooperation [e.g., Bicchieri, 2006, Henrich, 2015a, Fehr and Schurtenberger, 2018, Laland, 2018]. 2 prefer more socially appropriate outcomes to less socially appropriate ones). The introduction of the cooperative motivation dramatically changes the way agents behave and helps understand how institutions emerge. To be more specific, in neoclassics the concept of a cooper- ative enterprise (a firm) and the concept of an agent are necessarily separated because selfish agents by definition are unwilling to cooperate in social dilemmas and thus have no motivation to self-organize into firms. Firms however do exist in reality and therefore are simply brought in as production functions.2 In our framework, the norm-following agents care about the social appropriateness of their actions, which tends to be the highest when agents successfully cooperate with each other. This is the motivational force that pushes them to find ways to create new cooperative enterprises, and leads to the formation of institutions. We assume that the desire to cooperate is not negligible and has a tangible effect on preferences. Therefore, we should expect that norm-following agents are comparatively as willing to enter coopera- tive relationships and form institutions as they are willing to maximize their consumption utility. This implies that institutions for cooperation should emerge in all economic environments, even those in the “state of nature,” similarly to how we expect humans to strive for more consumption in all economic environments. In this view then, informality is not a distortion, but rather an attempt of norm-following agents to self-organize and cooperate in the absence of other means to do so [Perry et al., 2007]. This view also suggests that government plays a crucial role of a facilitator who helps agents to fulfill their desire to cooperate. With strong government that provides good and efficient services for doing business (e.g., in the form of enforceable laws), we should then expect that agents will prefer to cooperate legally through government rather than through informal institutions that are far less efficient given their inter- nal structure. This argument provides a flavor of institutional policy that comes out of our framework: agents are attracted to institutions that give them the best available options to cooperate; while this is happening, the less attractive institutions die out thus bringing about institutional change. The paper is structured as follows. In Section 2 we describe our general methodology based on the new framework to study the emergence of social norms by Kimbrough and Vostroknutov [2022a], further KV, and embed it in various literatures. This framework allows us to talk about social norms that emerge in individual interactions as building blocks of more complex institutions also termed “packages of social norms” [Henrich, 2015b]. In Section 3, we analyze the behavior of norm-following (or moral) agents in the Public Goods game. This game serves as an abstract representation of a cooperative enterprise (a “firm”) that can emerge or not depending on whether agents decide to cooperate. We relate the parameters coming from the framework of KV to the intuitive notion of trust that is considered by many authors to be the necessary ingredient of economic development [Keefer and Scartascini, 2022, Lederman et al., 2002]. We demon- strate that trust, operationalized by KV as having two dimensions, can account for a wide variety of 2 The neoclassical approach remains silent about how firms and institutions emerge. A vigorous attempt to fix this came in the form of New Institutional Economics that proposed a set of models of firm formation based on various principles [e.g., Hart, 1989, Holmstr¨om and Roberts, 1998]. 3 intuitive social constraints that prevent agents from successfully doing business with each other. In Section 4, we define institution for facilitation: the simplest form of institutional arrangement among three agents that allows two of them, who do not trust each other, to nevertheless cooperate with the facilitation from a common “acquaintance” whom both agents trust (the third agent called facilitator ). We show how the norm with respect to the amount of rent paid to the facilitator emerges endogenously from the parameters of the Public Goods game and trust weights. This in turn paves the way to natural definitions of inclusive (or norm-abiding) and extractive (or norm-breaking) institutions. In Section 5, we consider how agents choose between institutions. We give definitions of formal and informal institutions, and model the choice of a norm-following agent between them. Given that the agent intrinsically cares about the normative arrangement in the two types of institutions, her choice will depend not only on the consumption utility expected from the two institutions, but also on how “fair” (inclusive or extractive) these institutions are. We finish this section with a stylized model of the dynamics of trust in government, the size of the informal sector, institutional policy, and growth. This model suggests that increasing the quality of public services leads to higher trust in government, which then leads to the increase in the relative size of the formal sector. In Section 6 we consider arbitrary trust networks and discuss how and why some agents might prefer to work (participate in the Public Goods game) or facilitate (collect rent from facilitating cooperation of others). We show with an example that depending on the structure of the trust arrangements in the population, different forms of clientelistic networks may emerge. Sometimes, one or two large informal institutions like that take hold over the whole network (similar to a monopoly or a duopoly), which leads to high barriers to enter and elitism. In other cases, many facilitators compete for clients (similar to perfect competition), which creates the opposite situation where clients are paid for their attention to facilitators. In Section 7 we relate our framework to the theory of stages of development of historical and tradi- tional societies [Acemoglu and Robinson, 2020]. We add a punishment mechanism for norm violations which in different settings generates the Hobbesian ”state of nature” (Warre), cage of norms, the Despotic Leviathan, and the Shackled Leviathan. We discuss examples of currently existing traditional societies and societies that existed in the past and show how institutional change in these societies can be viewed from the perspective of our model. Finally, Sections 8 and 9 conclude with a discussion of further directions of research and the impli- cations of our framework for economic and institutional policy. 2 Literature and Methodology It has been noted in the literature that institutions—both economic and political—can be a major obstacle to development [North, 2008]. The policy dilemma of the century that can be succinctly formulated as “How to change institutions?” has attracted a lot of attention in the literature, but still remains unsolved. According to the long tradition of institutional economics, institutions can be good or bad for economic 4 development, and Western-style institutions have been shown to correlate with economic growth. How- ever, literature also documents many failed attempts at imposing them in developing countries [Putnam et al., 1992].3 Empirical analysis of the importance of institutions for development has traditionally treated insti- tutions as exogenous variables with evidence based on cross-country regressions that include proxies for “institutions” such as a democracy index, etc. The literature analyzing specific institutions, such as for example the legal regulations guiding financial market functioning, is not typically generalizable to other situations and takes the form of case studies. Other models do not take into account the context of economic interactions, rendering policy analysis impossible. It is no surprise that, similarly to Shirley [2005] and Knack and Keefer [1995], Rodrik et al. [2002] note that empirical studies show significant reg- ularities in how institutional variables tend to dominate others in explaining growth and social progress, “but these studies lack a theory that would transform regularities into causal explanations.” Not many formal models of institutions—with the purpose to shed some light on their role in eco- nomic activity—have been proposed in the literature. For example, Ostrom [2000] uses social dilemmas to reason about the nature of collective action and social norms in Common Pool Resource problems [see also Kimbrough and Vostroknutov, 2015]. Some other approaches appear in the literature on the emer- gence of firms [e.g., Hart, 1989, Holmstr¨om and Roberts, 1998]. Even though these models are capable of capturing certain elements of institutional influence on economic behavior, they cannot be used as the general models of institutional change or made more specific to arrive to more granular policy guidance. What has been lacking is a workhorse model of institutional change. Such a model needs to be gen- eral enough to be able to account for a wide range of institutions, but at the same time it should allow for specific adaptations to accommodate the impacts of specific policies. More importantly, in such a model institutions would need to enter endogenously [see also Engerman and Sokoloff, 2005], so that it is possible to consider the emergence and dynamic development of institutions depending on a set of parameters. This is needed for testing the model in practice as well as for policy implications and can only be achieved if institutions are introduced at the micro level, as social norms that aggregate into in- stitutional packages [Henrich, 2015b]. This bottom-up approach would allow to organically incorporate both formal and informal institutions [Keefer and Knack, 2008]. Moreover, apart from straightforward variables describing “institutional quality” or specific institutions, the model should directly account for the structural distortions that accompany them. For example, inclusive institutions would correlate with lower informality as they reduce exclusion [Perry et al., 2007]. Clientelism can also emerge organically and coexist with the existing, extractive political system [Munoz,˜ 2019]. 3 Acemoglu and Robinson [2020] provide many examples of “transplanted” formal institutions that have never taken root because they had been overwhelmed by pre-existing social norms and informal institutions. For example, the Peruvian pre-colonial mita system is among the origins of extractive institutions in Latin America. The political economy literature documents many cases of the failure of transplanted democratic institutions, leading to corruption and clientelism [Acemoglu and Robinson, 2006]. Among many cases when formal institutions have been unsuccessfully over-imposed on existing infor- mal institutions, the Latin American lettered city literature highlights the origins of modern widespread informality in the inconsistency of design of cities and reality of life for the poor, that has resulted in their continuous exclusion from the formal economy [Angel and Charles, 1996, Lazar, 2008]. 5 In this paper, we offer one such model. As was mentioned above, the main difference from the neo- classical approach is that agents are assumed to be moral (norm-following), or having an additional term in their norm-dependent utility that tracks social appropriateness of alternative outcomes they choose. This addition to selfish motivation makes agents want to cooperate and enter “business relationships” with each other. It is worth mentioning that this idea is not new and that the connection between norm-abiding behav- ior and business activity has been pointed out in economics for a long time [e.g., Arrow, 1972]. However, the traditional definitions that simply suggest this connection are not enough for policy and understand- ing institutional change. To have a workable model of institutions, the moral agents’ utility-maximizing behavior should be pinned down exactly, which means that the normative values (social appropriateness) of all outcomes should be specified. It may seem that in a given institution the values of social appropriateness of various actions and outcomes (what is considered appropriate to do within this institution) may heavily depend on the past history of the institution, local beliefs, and other specific cultural features. This is indeed true for many existing institutions. However, it is also true that people who consider entering a new business relation- ship face a new context (the set of feasible allocations) that depends on the specific business opportunities available to them at that time. So, it is plausible that there are no pre-specified norms from the past, cus- toms, or traditions that prescribe what is moral in this new context. KV propose that for such cases people have evolved moral psychology, or specific machinery in the brain that computes social appropri- ateness of outcomes solely from the information available in any current context (feasible allocations). Such computations, if done in the same way by all moral agents, should lead to formation of similar normative beliefs about social appropriateness and consequently to coordinated, cooperative behavior [see also Rusch and Vostroknutov, 2023]. KV describe a specific moral psychology of norm formation in any context that is based on the idea of aggregating dissatisfaction. Specifically, it is assumed that the social appropriateness of each given allocation is inversely proportional to the summed dissatisfactions of all agents in that allocation. The dissatisfaction of each agent in a given allocation is high when there are many other counterfactual allocations in the context that give the agent more consumption utility and low otherwise. Thus, dis- satisfactions express personal grievances of agents in a given allocation, and the normative value of the allocation is formed by aggregating all these dissatisfactions. In other words, the allocation is considered more socially appropriate, the less aggregated dissatisfaction it evokes. This construction may seem overly complex and unnecessary. However, tests of existing experimen- tal data have shown that the model of dissatisfaction-based norms can account for many puzzles in social behavior known to behavioral economists.4 Specifically, it resolves many issues pertaining to the exist- ing models of social preferences and reciprocal kindness [see Vostroknutov, 2020, for discussion] that are not context-dependent enough to accommodate certain stylized facts (e.g., radical context-dependence 4 Experiments by Merguei et al. [2022] and Panizza et al. [2021] perform direct and rather stringent tests of KV’s model and find a very good fit with the data. 6 of social behavior [List, 2007, Bardsley, 2008] or extreme switches of moral principles with small changes in payoffs [Galeotti et al., 2018]). Moreover, the model of KV allows to introduce social weights (aka trust weights) that measure the importance of dissatisfaction of each agent in the aggregation.5 This is an im- portant mechanism that accounts for various observations about social behavior within and without an in-group [Chen and Li, 2009], and that translates intuitively to one of the dimensions of trust. We base our model on the framework of KV exactly because it seems to fit well the moral intuitions used by people in new contexts and because it provides a way to determine what norms may emerge in these contexts without assuming some ad hoc social motives like, for example, inequality aversion [Fehr and Schmidt, 1999] or payoff efficiency maximization [Engelmann and Strobel, 2004] that may or may not play a role in a given institution. Most importantly though, the model of KV shows how norms—or rules of social conduct that define how to behave in certain situations—can emerge endogenously and later become the accepted rules of an emerging institution. The fact that norms are context-dependent and change with the environment provides the way to conceptualize institutional change that we follow in this paper. 3 Model 3.1 Public Goods Game Played by Moral Agents We start by describing the simplest possible incentive structure and the type of interaction among moral agents that will be used as a building block in applications presented later in the paper. Specifically, we assume that two moral (norm-following) agents desire to profit from mutual cooperation in the Public Goods game (PG), which is similar to game forms used by Ostrom [1990] to study common pool resource problems.6 This interaction can be seen as representing various forms of “doing business,” which can produce surplus and consequently growth of wealth through cooperation (or not). This assumption can be seen as an embodiment of the various views in institutional economics, where institutions facilitate interactions of economic agents and impact transaction costs [North, 2016]. Similarly to Ostrom [1990], we focus on a specific form of such costs related to trust and problems with cooperation as any form of economic activity requires a certain degree of trust and cooperation/coordination among the people involved. Notice also that we consider PG as a versatile example of a social dilemma that embodies potentially variable levels of productivity (through the PG multiplier). In applications, any other game with social dilemma flavor can be utilized. To describe how PG is played, suppose that before the game each player i ∈ {1, 2} has some endow- ment w ≥ 0.7 In the game, player i chooses an amount to contribute to the public good with some PG 5 In each allocation, the dissatisfaction is aggregated by summing up individual dissatisfactions of all agents. The weights multiplying these individual dissatisfactions act as measures of trust to individual agents. When an agent is not trusted (low weight), her dissatisfaction will count little in the aggregation, so that it may become socially appropriate to give her less than others (and vice versa for the agents with high trust weight). 6 The argument easily generalizes to more than two players. 7 A generalization to PG with unequal endowments is very interesting and easy to implement theoretically. However, for 7 multiplier p ∈ [ 1 2 , 1). Suppose that player i contributes xi ∈ [0, w], then her wealth after the game is wi = w − xi + p(xi + x−i ). (1) In other words, player i keeps the part of the endowment that was not contributed (w − xi ) and gains the return from the public good (the sum of contributions xi + x−i , where x−i stands for the contribution of the other player, times p). Notice that the multiplier p can be thought of as a measure of productivity and defines how profitable the cooperation is. It can be influenced by various factors (e.g., it is high when good-quality public services are provided and low otherwise). When agents are standard consumption utility maximizers, the unique Nash equilibrium of this game is to contribute nothing (x∗ i = 0 for all i). This represents the classic case of underprovision of public goods. When player i is assumed to be a moral agent, she chooses xi to maximize her norm-dependent utility [Kessler and Leider, 2012, Krupka and Weber, 2013] Ui (xi ; x−i ) = wi + ϕi ηi (wi , w−i ). (2) The utility function Ui consists of two terms: the standard linear consumption utility wi and the nor- mative term ϕi ηi (wi , w−i ) representing the desire to follow norms. Here we implicitly see wi as the function of xi and x−i as in (1); the coefficient ϕi ≥ 0 defines i’s propensity to follow norms; and ηi : C → R is the norm function of player i that defines the social appropriateness of each possible out- come (w1 , w2 ) in the game and arises endogenously from the set of all achievable wealth allocations defined by C = {(w1 , w2 ) | (x1 , x2 ) ∈ [0, w]2 }. Specifically, following KV we define ηi as ηi (wi , w−i ) = ηi (wi , w−i ; τ ) = −[Di (wi ) + τ D−i (w−i )] =− max{ci − wi , 0}dc + τ max{c−i − w−i , 0}dc . (3) c∈C c∈C Here, the notation ηi (wi , w−i ; τ ) emphasizes that the social appropriateness expressed by the norm func- tion depends on τ ≥ 0, the social weight that player i attaches to the other player (−i). Di (wi ) stands for the personal dissatisfaction that player i feels should she receive wealth wi after the game. This per- sonal dissatisfaction, in its turn, is the sum of dissatisfactions due to all possible other allocations in C where player i receives more consumption utility than wi (so, i is dissatisfied because she could have had more consumption). This is expressed with the max operator in the second line of (3), that measures dissatisfaction at wi due to some other possible consumption utility ci (we notate c = (ci , c−i ) since C is a subset of R2 ). Thus, the social appropriateness ηi (wi , w−i ) of outcome (wi , w−i ) from the perspective of player i is the negative of the weighted sum of the personal dissatisfactions of the two players (Di (wi ) and D−i (w−i )) with the latter weighted by the exogenously given social weight τ . The idea here is that player i feels that outcomes in C are more socially appropriate when they evoke less dissatisfaction from both the sake of expositional simplicity we choose to not introduce it in this paper and leave it for future research. 8 Wealth of player -i Wealth of player i Wealth of player i Wealth of player i Figure 1: Left. The set of allocations C with w = 1, p = 0.8, and τ = 0 (dark blue - the lowest social appropriate- ness; dark red - the highest social appropriateness). Middle. Same as the left panel only with τ = 1. Right. Same as the left panel only with τ = 0.2. players, though the dissatisfaction of the other player (−i) can be inflated or discounted in comparison to i’s own dissatisfaction (which has weight 1). For example, τ = 0 would imply that player i does not normatively care about player −i as a human being at all (e.g., slavery). From her perspective social appropriateness only increases when her own dissatisfaction goes down (regardless of what happens to the dissatisfaction of −i). The left panel on Figure 1 shows such norm function. When τ = 1 we get the case when player i treats the other player equally to herself. She cares about the dissatisfaction of the other player as much as she cares about her own (e.g., family). The norm function ηi for this case is shown in the middle panel of Figure 1. When τ ∈ (0, 1) we get the situation where i cares somewhat about the dissatisfaction of −i, but not as much as about her own. This is the case, for example, when −i belongs to another social group than i. Equal partners, who are not related through family ties, might have a τ above a certain threshold, but less than 1. The right panel of Figure 1 illustrates.8 Given these definitions, we can talk about the norm from the perspective of player i as an allocation ci = arg maxc∈C ηi (c) that has the highest social appropriateness. It is clear that in general, when τ ̸= 1, ∗ the two players will not “see eye to eye” with respect to what they consider as the norm in this game. However, when both players treat each other as equals (τ = 1 for both of them), they will agree on the norm, which should make cooperation easier to achieve (in this case c∗ i = c−i correspond to the ∗ outcome where both players contribute fully to the public good, see the middle panel of Figure 1). As we show formally in Appendix A.1, PG with moral agents has two possible Nash equilibria depending on the parameters. Given high enough ϕi and ϕ−i , so that players want to follow norms, and when τ ∈ (0, 1] is high enough for both players (they care a lot about each other), the unique equilibrium is to contribute full amounts (x∗i = x−i = w ). When ϕ’s are high and τ ’s are low, the unique equilibrium is to contribute ∗ nothing (x∗i = x−i = 0). For the case of low ϕ’s (when players do not care much about following norms ∗ in general), the unique Nash equilibrium is also to contribute nothing as in the case of selfish players who only maximize their own consumption utility. These possibilities are exhaustive. 8 It is important to emphasize at this point that this model has been tested against many experimental datasets (see KV) and shows a very good fit to actual human behavior. 9 3.2 Norms and Trust As described in the previous section, agents cooperate or do business more willingly with people whom they trust, so the concept of trust is important to understanding the behavior and beliefs of moral agents. A widely used definition of trust states that it is the belief that someone will not behave opportunistically, as in Keefer and Scartascini [2022]. A more general definition is that trust is a situation-specific expecta- tion about other agent’s behavior [Bauer and Freitag, 2018]. In other words, trust is context-dependent. In particular, trust can be linked to propensity to follow specific social norms. For example, agents ex- hibit higher trust towards people who belong to their social group [Chen and Li, 2009]. To reflect this, we add a second dimension to the commonly used definition of trust. The first dimension of trust corresponds directly to the definition of Keefer and Scartascini [2022]. This kind of trust is defined by the individual propensities to follow norms ϕi and ϕ−i (and players’ beliefs about them). Indeed, if player i believes, for example, that ϕ−i = 0, then she is sure that the other player is selfish and only maximizes his consumption utility. She does not trust him, because she believes that −i will disregard the norms (whatever they may be) and contribute nothing in PG, which is −i’s strictly dominant strategy. For the second dimension of trust (as we define it), notice that in our model i’s believing that −i has high ϕ−i is not enough for her to trust him. If i believes that ϕ−i is high but that −i does not care about her (low τ in η−i ), then she also will not trust −i. This happens not because i thinks that −i is selfish, but rather because −i has different norms that discount her, i’s, importance in the eyes of −i. For example, the members of two warring tribes might be absolutely sure that the opponent is a highly moral norm-following individual. However, they will still not cooperate with each other (contribute in the PG) because they know that both of them do not care about the dissatisfaction of the other. They do not trust each other due to different normative views [see e.g., Akerlof and Kranton, 2000, Chen and Li, 2009]. This is an important case of trust that we believe is the key to understanding the formation of institutions given that most human beings do follow norms of their—sometimes highly specific or imaginary—social groups most of the time.9 In the rest of the paper, we will assume therefore that all players are moral agents who, by definition, have some propensity to follow norms (ϕ’s are above zero), but that their normative views are different due to low social weights τ put on other players. Thus, we describe the world where all agents want to 9 Our terminology with regard to τ that we call the second dimension of trust might sound unfamiliar to some readers. The way τ enters norm-dependent utility is technically similar to models of altruism where agents directly care about the utility of other players. However, the similarity is only technical. What is important is the interpretation. In case of norm-dependent utility, τ is a parameter that determines normative views. In other words, τ determines whether an agent will consider some allocations involving other agents socially appropriate or not. Norms are social constructs that incentivize agents to act in the society, whereas altruism is a psychological construct that does not necessarily relate to social behavior. It can be easily imagined that there are agents who are not altruistic at all, but who follow norms nonetheless. Thus, if we consider utility representation (2) as just some utility function that involves utilities of other players, then τ can be interpreted as altruism. But when we consider it as a norm-dependent utility with norms that are supposed to be shared among many agents, then τ obtains a different meaning, it becomes related to whom we should trust and whom we should not trust. In the example with warring tribes, τ signifies how appropriate it is to be cooperative with the members of the other tribe and not how altruistic we should be towards them. 10 cooperate by following some norms (e.g., those of their social group), but might fail to cooperate with strangers because they think that they come from the out-group.10 4 Institutions for Facilitation Institutions are “humanly devised constraints that structure human interaction,” including formal con- straints such as constitutions and laws and informal constraints, such as norms, conventions and self- imposed codes of conduct [North, 1990]. Describing the incentives for “doing business,” Coase argued that “if the costs of making an exchange are greater than the gains which that exchange would bring, that exchange would not take place.” Institutions thus emerge to reduce transaction costs associated with production [Coase, 1937]. To understand the functioning of endogenous institutions in our model, we must understand their emergence and trace their development. We start from the Hobbes’ primordial “state of nature,” devoid of any institutions or social norms and observe the emergence of institutions to support cooperation. We eventually arrive at a model with endogenous institutions, where institutional change is possible between inclusive and extractive institutions, depending on personal characteristics of agents involved (ϕ) and their trust to each other (τ ). 4.1 The State of Nature To understand how and for what purpose institutions may emerge, we need to consider the motivation and incentives of agents in what moral philosophers call the state of nature or Warre [Hobbes, 1651, Acemoglu and Robinson, 2020]. This is a hypothetical world of unorganized individuals who do not hold any common views on how things should be done (social norms) and thus act mostly in their own self-interest in the absence of any shared norms, regulations, or laws. Translated to the language of our model in Section 3.1, this would correspond to the situation where moral agents, although willing to follow norms, are unable to cooperate because they do not trust anyone (high ϕ, low τ ; but see also Section 7). In this case, in equilibrium no two agents will contribute anything to the public good and thus there will be no growth of wealth. Such conditions are not inconceivable and existed for brief periods of time even in recent history [Leeson, 2007].11 Even though the state of nature precludes wide-spread cooperation with strangers due to generally low trust, some episodic cooperation and growth of wealth might exist among moral agents who know each other well and have high social weights τ attached to each other (e.g., family, friends). A pair of friends (or cousins) with high enough τ will contribute fully to the public good, thus benefiting them- selves. However, it is also reasonable to think that after some time they will exhaust all possibilities for 10 The case with low ϕ’s is not interesting anyway, as it is approximated well by standard players with selfish preferences. In this case, we know already that no cooperation can happen at all in any social dilemma. 11 Hobbes describes the state of nature as “war of all against all,” which can be likened to negative growth. In our model, such situation is also possible when social weights attached to other agents are negative (τ < 0). In this case, moral agents will find it socially appropriate to increase dissatisfaction of others (e.g., by appropriating or destroying their wealth). 11 profitable cooperation due to the fact that they most likely live in the same area and have access to the same resources. This will make the PG multiplier p, applicable to their interaction, low and the resulting growth will be negligible. From this we can argue that moral agents would strive to cooperate with others who have access to different resources and have potentially different skills and know-how (which makes the multiplier p in the potential PG high). However, such others will typically be strangers that cannot be trusted in the state of nature (low τ ). Thus, we have a situation where moral agents want to cooperate because it is profitable, but are unable to do so due to low trust. In this case, it is reasonable to believe that they will try to find some arrangements that will make cooperation possible. 4.2 Facilitation The simplest possible arrangement that can expand cooperation beyond what is possible in the state of nature is facilitation of cooperative relationship between two moral agents by a common friend, relative, or facilitator. It is possible, as we discuss in more detail in Section 7, that first facilitators emerging from the state of nature were extended family members related to agents through family ties (e.g., cousins, in- laws, or clan members). In later times and in societies that started to interact with strangers, facilitators were traders or other individuals (e.g., priests) who managed to gain trust of separate groups of people with different norms or social identities. This allowed them to act as intermediaries between them also facilitating economic relationships. Consider two moral agents in {1, 2} as in Section 3.1 with equal and low social weights τ2 < τ ∗ attached to each other, which is below the threshold τ ∗ above which the Nash equilibrium in the PG is to fully contribute (see Appendix A.1 for the values of τ ∗ as dependent on p).12 Thus, in the PG the agents will optimally choose to contribute nothing when their mutual social weights are τ2 (the meaning of subindex 2 will become clear in Section 6). Now suppose that there is a facilitator agent f with whom both agents maintain friendly relationships, so that the mutual social weights between any agent i ∈ {1, 2} and f are τ1 > τ ∗ . This means that agent i would cooperate with f if the opportunity arose. The left panel of Figure 2 illustrates: the dotted line emphasizes the impossibility of cooperation. Without facilitation With facilitation f f t en pa ym ym pa en τ1 τ1 τ1 τ1 t τ2 τ1 1 2 1 2 Figure 2: Left. Without facilitation players 1 and 2 cannot cooperate due to low social weights τ2 . Right. Players 1 and 2 can pay f for facilitation and cooperate with the same social weight τ1 that they have with the facilitator. 12 When p = 0.8, we have τ ∗ = 0.25. 12 Despite the possibility of cooperation with f , the agents want to cooperate with each other as this brings more profit than cooperation with f (see the argument above). Therefore, it is possible that the three agents agree on the following deal. Agent f facilitates the relationship between agents 1 and 2 by “vouching” for each agent as a good cooperative partner (since both are his friends). In the presence of such facilitation, agents 1 and 2 can cooperate with each other as if they share a friendly social weight τ1 that allows for an equilibrium with full contributions. Such deal is of course not free and agents also agree to pay the facilitator f some amount z for his services. Suppose that each agent pays f the amount z/2. The right panel of Figure 2 illustrates that now players 1 and 2 can cooperate if they pay the facilitator. It is clear that such deals can be profitable for all three agents as long as the payment z to facilitator is “reasonable.” In this case, the profit from cooperation for agents 1 and 2 minus the payment z/2 can exceed the profit from all other available options, of which there are not so many, and the deal will be made. This form of interaction can be thought of as the simplest form of institution for facilitation that allows for cooperation among strangers and that can emerge spontaneously due to its profitability to all parties involved. Of course, such an institution is not perfect as it cannot connect two agents who do not share a friend. However, with time more complex institutions can evolve from this simple interaction gradually involving more and more unrelated agents. 4.3 Norms in Institutions for Facilitation In Section 3.1 we analyzed how normativity and the notion of social appropriateness of outcomes emerges in a simple PG. The behavior of moral agents was consequently guided by these notions and allowed us to talk about morally “right” and “wrong” outcomes, or appropriate and inappropriate behavior (which leads to right or wrong outcomes). Using the same technique from KV, we can also analyze social appro- priateness of outcomes in the institution for facilitation that includes an additional player, the facilitator. This analysis will allow us to understand the behavior of moral agents as well as define norms that be- come the inalienable part of this institutional arrangement. Thus, we can calculate, for example, what would be considered reasonable amount of payment z to facilitator that agents 1 and 2 would find “fair.” This amount is the norm associated with the institution for facilitation. This is an important notion that leads to the extended welfare analysis for moral agents (with norm-dependent utility) that includes stan- dard consumption considerations as well as their utility losses or gains due to fairness or unfairness of the outcomes resulting from the institution for facilitation (see Section 5). To do this, we consider the set of all allocations to three players (agents 1, 2, and f ) that can be achieved in some (yet unspecified) non-cooperative game that represents how exactly agents interact in this institution.13 As in Section 3.1, suppose that players 1 and 2 have endowments w before the game 13 An important feature of the framework of KV is that norm functions or measures of social appropriateness are defined on the sets of allocations that ignore the non-cooperative game structure (who moves when, which actions are available, etc.). It allows us to analyze games in the style of cooperative game theory without specifying ex ante how the game unfolds. This property can be very useful for applications where the exact game structure is often unknown or changes depending on 13 (facilitator does not have or need an endowment since he is not playing the PG). Suppose as well that if each player i pays the amount z/2 to facilitator, then both of them have w − z/2 left to play the PG. Thus, we can say that the wealth of player i after the game where z was paid to the facilitator is given by wiz = w − z/2 − xz z z i + p(xi + x−i ) (4) where xz i ∈ [0, w − z/2] for both i ∈ {1, 2} is the amount contributed. We define the set of achievable allocations as CF = {(w1 z z , w2 1 , x2 ) ∈ [0, w − z/2] }. Here we assume that , z ) | z ∈ [0, 2w] and (xz z 2 all payments z are possible: from 0 (facilitator works for free) to full endowments of both players 2w (facilitator gets all the money and players 1 and 2 have nothing left). The set of allocations CF is a pyramid in R3 shown on the left panel of Figure 3. The definition of CF is all we need to specify the norm functions of the three players. For player i ∈ {1, 2}, we have z z z z ηi (wi , w− i , z ) = −[Di (wi ) + τ1 D−i (w−i ) + τ1 Df (z )] =− z max{ci − wi , 0}dc + τ1 z max{c−i − w− i , 0}dc + τ1 max{cf − z, 0}dc . (5) c∈CF c∈CF c∈CF Here we notate c = (ci , c−i , cf ) ∈ CF ⊆ R3 . In words, the social appropriateness of an outcome i , z ) ∈ CF from the perspective of player i is the weighted sum of personal dissatisfactions of z z (wi , w− the three players, with social weights τ1 for the other two players (as discussed in Section 4.2). The norm function for the facilitator f is z z z z ηf (w1 , w2 , z ) = −[Df (z ) + τ1 D1 (w1 ) + τ1 D2 (w2 )] =− max{cf − z, 0}dc + τ1 z max{c1 − w1 , 0}dc + τ1 z max{c2 − w2 , 0}dc . (6) c∈CF c∈CF c∈CF This is just the reshuffling of the same personal dissatisfactions as above, only with social weights τ1 applied to the players 1 and 2. We illustrate these functions in Figure 3. Specifically, the middle panel shows the unique norm func- tion for all three players that arises when τ1 = 1, or when both players 1 and 2 trust the facilitator as they trust themselves (e.g., family). This case represents the most cooperative situation achievable within the institution where all players treat each other as they treat themselves (of course, players 1 and 2 do not trust each other much outside the institution for facilitation, they have weight τ2 , see Section 4.2). Notice that in this case the norm (or the most appropriate allocation) obtained from maximization of (6) and marked on the graph in dark red gives 26% of 2w to the facilitator (z = 0.26 · 2w) and players 1 and 2 should choose to contribute the full amount of what is left after this payment. The right panel of Figure 3 shows the norm function of player 1 for the case when τ1 = 0.2. In this case, unsurprisingly, player 1 considers it socially appropriate to have more than both other players, which can be seen from the dark circumstances. See Kimbrough and Vostroknutov [2023a] for additional discussion. 14 2 0 0 0 2 2 Figure 3: Left. The set of allocations CF (with w = 1 and p = 0.8). The wealths of players 1 and 2 are on the x- and y -axes; the wealth of the facilitator on the z -axis. Middle. The Pareto frontier of the set of allocations CF in the PG with facilitation. The colors denote the norm function ηi with τ1 = 1 (dark blue - the lowest social appropriateness; dark red - the highest social appropriateness). Right. Same as the middle panel only with τ1 = 0.2. red spot being shifted to one side of the pyramid. The important implication of these calculations, especially that the payment to the facilitator in the most cooperative case is 26% of the players’ endowments, is that moral agents can use this as a bench- mark to judge how fair the payment to the facilitator is. For example, when the facilitator is an actual family member of players 1 and 2 (e.g., brother to one and son-in-law to the other) and demands the payment of, say, 30%, then both players will find it inappropriate and will think that the facilitator is breaking the norm. They might not agree to this arrangement on the basis of their moral convictions and might seek facilitation elsewhere. Similar arguments can be made about taxes and facilitation by the government or some informal institution. 4.4 Inclusive and Extractive Institutions Now that we know which norms emerge in institutions for facilitation, we can add the non-cooperative game structure to the institution (the explicit specification of the sequence of moves and available actions of the three players) and analyze the various types of equilibrium behavior that result depending on the parameters. In this section, we will assume that there is only one institution for facilitation available (this is relaxed in the next section) and that players 1 and 2 are “forced” to participate in it, given that without this institution they cannot make any profit at all (they do not trust each other enough to cooperate themselves).14 This analysis will allow us to discern two broad classes of equilibria (for different norm-dependent- utility parameters) that can be likened to what literature calls inclusive and extractive institutions [Robin- son and Acemoglu, 2012]. Note that the definitions used in the model are narrower and model-dependent than the broad concepts of inclusive and extractive institutions used in institutional economics. The key properties of these institutions remain the same however: the pluralistic nature of inclusive institutions, 14 The nature of this assumption is not that far-fetched as it may seem. It is often the case in developing countries that people are in such dire economic circumstances that they cling to any opportunity to make money. 15 where all can participate (at an affordable cost), that leads to more cooperation and production; and ex- clusive nature of extractive institutions that allow for a group of agents to extract rents above the ”fair” cost, from the rest of the population. Given that the state of nature does not provide players 1 and 2 with many outside options, it is not so hard to imagine that the facilitator can exercise power over them since without him players 1 and 2 cannot make any profits. Thus, we define the non-cooperative game as follows. First, the facilitator makes players 1 and 2 a take-it-or-leave-it offer of the payment z ∈ [0, 2w] that he wants for his services. Then, players 1 and 2 pay the requested amount z and play the PG with endowments w − z/2. As before, we assume that players 1 and 2 attach social weight τ1 > τ ∗ to the facilitator (and each other within the institution), so that they optimally cooperate in each subgame happening after any offer z . Notice that in the non-cooperative game all that matters is that players 1 and 2 believe that the social weight that they attach to the facilitator and guaranteed by him for their own relationship is τ1 (high enough for cooperation to be the Nash equilibrium in the subgames). This is important since, in principle, the facilitator does not have to respect or genuinely care about players 1 and 2 at all. All he needs to do for the institution to work (which leads to cooperation and payment of z to himself) is to convince the players that he can be trusted.15 The last ingredient of the non-cooperative game are the utilities that the players eventually receive. This is straightforward: the norm-dependent utility of player i ∈ {1, 2} is given by z Ui (xi ; x−i , z ) = wi z + ϕi ηi (wi z , w− i , z ), (7) and the norm-dependent utility of the facilitator is z Uf (z ; x1 , x2 ) = z + ϕf ηf (w1 z , w2 , z ). (8) The analysis of the equilibrium behavior proceeds by backward induction. Given that players 1 and 2 attach high social weight τ1 to each other within the institution and assuming that their propensities to follow norms ϕ1 and ϕ2 are high enough, they will choose full contributions x∗ i (z ) = w − z/2 given any offer z (see Appendix A.2 for details).16 In the next step of backward induction, the facilitator takes the equilibrium actions x∗i (z ) as given and solves the following maximization problem: max z + ϕf ηf (p(2w − z ), p(2w − z ), z ). z ∈[0,2w] Notice that here we use the wealth of player i given equilibrium play x∗ i (z ) and x−i (z ) determined as ∗ = w − z/2 − x∗ i (z ) + p(xi (z ) + x−i (z )) = p(2w − z ) for i ∈ {1, 2}. z ∗ ∗ wi What will determine optimal z ∗ that solves this maximization problem? As follows from the proof 15 In Section 6 we will show how this can lead to the emergence of clientelistic networks. 16 The case when ϕ1 and/or ϕ2 are low is uninteresting. Here players 1 and 2 will not contribute anything to the public good and cooperation will fail. Given that in our framework everyone strives to cooperate to make money, we assume that players 1 and 2 are norm-followers to a sufficient degree. 16 of Compromise Theorem [see Proposition 5 in Kimbrough and Vostroknutov, 2022a], in the vicinity of the optimum the maximand function is a downward sloping parabola such that limϕf →0 z ∗ = 2w and limϕf →∞ z ∗ = ηf ∗ (w, p, τ1 ), where ηf∗ (w, p, τ1 ) is the maximum of ηf given parameters w, p and τ1 .17 This means that selfish facilitator with ϕf = 0 will demand the highest possible payment of 2w thus leaving players 1 and 2 with nothing, and the most rule-following facilitator with ϕf → ∞ will ask for the payment that is the most socially appropriate from his perspective (the maximum of ηf ) given the optimal actions x∗i (z ) of players 1 and 2 in the subgames. This completely describes the Subgame-Perfect Nash equilibrium in this game. From the analysis above, it is clear that the “kind” of institution we get in equilibrium depends solely on the payment z ∗ demanded by the facilitator (since players 1 and 2 fully cooperate in all subgames). Thus, we can classify institutions depending on the value of z ∗ that also determines the resulting welfare of players 1 and 2. When the facilitator is selfish (ϕf = 0), he extracts everything from the two players (z ∗ = 2w), which leads to the wealth allocation (0, 0, 2w). This is the worst allocation from the perspec- tive of the welfare of the two players not only because they are left with nothing, but also because this allocation is considered highly inappropriate by both of them. Players 1 and 2 get the lowest possible level of normative part of their norm-dependent utility at (0, 0, 2w), see Figure 3. We formulate this as a definition. Definition 1. We call an institution for facilitation fully extractive when players 1 and 2 pay their full endowments to the facilitator, which gives them the lowest possible level of both consumption and normative utility, and the facilitator gets the highest possible payment. Fully extractive institutions can emerge for two different reasons that are related to the two dimen- sions of trust. The first possibility is when the facilitator is completely selfish (ϕf = 0) and thus disregards the norms: he will act as a standard consumption utility maximizer and extract all surplus from players 1 and 2. The second possibility, mentioned above, is that the facilitator is not selfish (ϕf > 0) but cares little for players 1 and 2 (e.g., his real trust weight towards them is very low). However, facilitator manages to convince players 1 and 2 that he can be trusted (τ1 > τ ∗ ). Then, players 1 and 2 may agree to participate in the institution, only to learn later that they lose all their endowments.18 Notice that fully extractive institutions can emerge for arbitrary levels of trust τ1 among agents in the institution. This is so because the other dimension of trust, namely the propensity to follow norms ϕf , is responsible for creating such conditions, which eliminates the dependency of the equilibrium on trust all together. In order to define the other extreme where the propensity to follow norms is high, we need therefore to take into account both dimensions of trust (ϕ’s and τ ’s). We formulate it as follows. Definition 2. We call an institution for facilitation fully inclusive when τ1 = 1, or when all players in the institution care about each other as they care for themselves, and when the payment to the facilitator is ∗ consistent with the norm and is equal to ηf (w, p, 1), or the payment that all three players find most socially 17 By the symmetric nature of ηf (with respect to players 1 and 2), its global maximum coincides with the maximum of ηf (p(2w − z ), p(2w − z ), z ) as a function of z . 18 An example of a fully extractive institution is slavery. 17 appropriate. These conditions are reached in equilibrium when ϕf → ∞, or when the facilitator only cares about social appropriateness and does not care about his own consumption (and when the trust in the institu- tion is the highest, τ1 = 1).19 In between fully extractive and fully inclusive institutions lies a continuum of possibilities that are characterized by non-extreme values of the two dimensions of trust: ϕf and τ1 . The problem with clas- sifying this continuum into some flavors of “extractiveness” and “inclusiveness” lies in the fact that for τ1 ∈ (0, 1) the norm functions η1 , η2 , and ηf will in general be different and have three different maxima (all players 1, 2, and f individually believe that they deserve more than the others). Thus, we need to pick a moral perspective from which to judge the welfare qualities of the institution. We propose to take the perspective of the players 1 and 2 since it is their welfare (and not that of the facilitator) that is important for economic policy. Moreover, the maxima of the norm functions η1 and η2 are reached at the same value z ¯(w, p, τ1 ) of payment to the facilitator (the functions are symmetric). So, players 1 and 2, although disagreeing on how much they themselves should get in the most socially appropriate allocation, nonetheless agree on the most socially appropriate payment to the facilitator. We use this fact in the definition. Definition 3. Suppose that τ1 ∈ (0, 1). Then call an institution for facilitation inclusive if the payment to the facilitator is consistent with the norms of players 1 and 2 and is equal to z¯(w, p, τ1 ). Such payment is considered fair by players 1 and 2. Else, call the institution for facilitation extractive. Notice that in the last definition we do not specify what parameters of the norm-dependent utility of the facilitator lead in equilibrium to inclusive or extractive institutions. The reason is that, in general, when τ1 ∈ (0, 1) the facilitator who maximizes his norm-dependent utility will always ask for strictly more payment than z ¯(w, p, τ1 ). This is so simply because the facilitator cares more about his own dissat- isfaction in the norm function ηf than he cares about the dissatisfactions of players 1 and 2. Thus, any informal relationship with τ1 ∈ (0, 1) will always lead to extractive institutions. Only government that, in principle, does not have to follow its own norm-dependent utility since it is not a human being can set the payment to itself to be equal to z ¯(w, p, τ1 ), thus creating an inclusive institution. 5 Choice of an Institution Today, most people live in developing countries, many of which have failed to create or sustain strong inclusive institutions [Acemoglu and Robinson, 2020]. As formal institutions are ineffective or not acces- sible, ”individuals enforce most bargains using informal institutions…and they have little trust in or trade with people not subject to these mechanisms” [Shirley, 2005]. We therefore assume that both formal and informal institutions exist, and that agents can choose between them. In the previous section, we have provided the analysis of the behavior of moral agents in a single 19 For example, family or a well-functioning democracy are inclusive institutions. 18 institution for facilitation in which players 1 and 2 were forced to participate. We now assume that agents can try to cooperate with others through an informal institution (and pay some amount to the informal facilitator) or they can do business through government (and pay taxes). In other words, people have outside options, and in this section we consider the implications of the availability of such options; their influence on the optimal demand of payment by the informal facilitator; and the resulting choice of institution by players 1 and 2. 5.1 Formal and Informal Institutions In our model, both informal institutions and government (formal institution) work using the same facil- itation mechanism described above. However, there are two tangible differences that we would like to emphasize. In the economy with players 1 and 2, an informal institution is an institution for facilitation where the facilitator is another player f with his specific norm-dependent utility as in (8). This means that such informal facilitator is a human being with some specific perspective on morality (as expressed by ηf ) who maximizes his norm-dependent utility. Moreover, the informal facilitator collects the pay- ment from the two players for himself and does not invest it in anything useful for them (e.g., public services). Thus, the informal institution is characterized by the norm-dependent utility of the informal facilitator Uf (as in (8)) and the trust in informal facilitator τ1 that determines the fairness of different levels of payments to him from the perspective of players 1 and 2. Government is a formal institution and another facilitator that also collects payment for its services, or taxes. But unlike the informal facilitator, government is not a human being, thus it does not have a specific morality described by the norm-dependent utility and consequently does not maximize it. Ideally, government’s job is to facilitate business transactions, collect taxes, and invest them into public services that enhance productivity p in the future (see Section 5.3). Though in reality, governments are steered by people who bring to them ideologies and values that might not be in the best interest of people. For example, in Section 7 we discuss the case of medieval states in the Middle East who acted as governments but mostly in their own interest (see also Ekeh [1975] on the two publics in Africa). Given this, an important parameter that defines government’s facilitation is the amount of trust in it determined by the social weight τg that enters players’ norm-dependent utilities (with τg instead of τ1 in (5)) and determines the fairness of tax payments from the perspective of players 1 and 2. 5.2 Model of Choice between Institutions To model the choice of institution by players 1 and 2, we consider the following parsimonious set-up that captures the main intuition of such choice. Suppose that the payment that government asks in taxes, in case players 1 and 2 use its facilitation services, is fixed before the game at zg and known to all players. We assume that zg is given and fixed since, realistically, government cannot adjust taxes quickly at any desired moment in time. Though, we can still work out the consequences of different choices of zg by comparing the optimal responses of other players in the game (comparative statics). Suppose as well 19 that other parameters, namely, w, p, τ1 , and τg are known and fixed. The game proceeds as follows. First, the informal facilitator makes an offer for payment z to him from players 1 and 2. Then players 1 and 2 compute the norm-dependent utilities they would get in both possible institutions (informal and formal) and choose an institution that brings them the highest utility. To avoid coordination problems (when the two players want to choose different institutions), we assume for the sake of the argument that ϕ1 = ϕ2 , so that both players 1 and 2 will prefer the same institution. We also assume as above that ϕ1 and ϕ2 are high enough for players to be able to cooperate. These assumptions will be relaxed in the network economies with more than two players that we consider in later sections. To analyze the game resulting from the above description, we again use backward induction and consider the choices of players 1 and 2 between institutions (the choices within institutions are already computed in Section 4). Player i ∈ {1, 2} chooses formal institution when in the corresponding subgame her equilibrium norm-dependent utility in it is higher than that in the informal institution. This can be expressed using (7) as z z z z z z wi g + ϕi ηi (wi g , w−gi , zg ; τg ) ≥ wi + ϕi ηi (wi , w− i , z ; τ1 ). i = w − z/2 (and the same for zg ), we Plugging equilibrium choices corresponding to full cooperation xz obtain p(2w − zg ) + ϕi ηi (p(2w − zg ), p(2w − zg ), zg ; τg ) ≥ p(2w − z ) + ϕi ηi (p(2w − z ), p(2w − z ), z ; τ1 ) or ϕi [ηi (p(2w − zg ), p(2w − zg ), zg ; τg ) − ηi (p(2w − z ), p(2w − z ), z ; τ1 )] ≥ p(zg − z ). Notice that now ηi is a function of zg and τg or z and τ1 , so we simplify the notation and rewrite the above as ϕi [ηi (zg ; τg ) − ηi (z ; τ1 )] ≥ p(zg − z ). (9) Inequality (9) is the condition under which player i will choose the formal institution (government) for facilitation over the informal one (remember, player −i has exactly the same condition, since by assumption ϕ1 = ϕ2 ). For player i with high ϕi , who cares about norms enough to be able to cooperate (an assumption made above that is also necessary for the full contributions in the subgames), this inequality represents a trade-off between the social appropriateness of participating in the two institutions (which is important for player i) and the payments that should be made in them. Going up the game tree, we now consider the choice of offer z by the informal facilitator f , who understands that he can only make profit z when (9) is not satisfied (otherwise f gets nothing).20 In general, this choice of z depends on zg , τg , τ1 in potentially non-trivial way. However, it is not hard to see what the choice of z will be for the realistic case when 1) player i considers the tax zg too high and 20 Technically, the informal facilitator compares his norm-dependent utility Uf as in (8) in case z is accepted to his Uf when the players choose the formal institution, in which case we assume the informal facilitator’s normative part of the utility is the lowest: the deal that could have been made was not made, which creates dissatisfaction. 20 inappropriate given the level of trust τg that player i has for the government; and 2) when τg = τ1 = τ . The latter condition is not too restrictive as the most socially appropriate level of taxes (or payments to informal facilitator) is not very sensitive to changes in τ when it is higher than the minimum level of trust τ ∗ necessary for cooperation. approp. social z'g z zg z payment to facilitator Figure 4: The graph of ηi (z ; τ ). Amount zg is the realistic, inappropriate level of taxation by the government and ′ is the appropriate level of taxation. The choices of z by informal facilitator either make player i choose the zg government (z to the right of zg ) or the informal institution (z to the left of zg ). For this case, as Figure 4 illustrates, the choice of z is straightforward. If the informal facilitator chooses z > zg , the inequality (9) will be trivially satisfied as zg − z < 0 and ηi (zg ; τ ) − ηi (z ; τ ) > 0. In this case players 1 and 2 will prefer the government. Thus, the informal facilitator will choose some z < zg to guarantee the opposite. The optimal value of z will be just below zg if the informal facilitator is selfish (ϕf = 0) and potentially something lower if he cares about norms (ϕf > 0). Either way, by choosing z smaller than zg the informal facilitator can always lure players 1 and 2 to use his institution instead of the government. This situation is often observed in reality. For example, the informal sector in some developing coun- tries employs more than 80% of the labor force and produces well over half of GDP. Following the seminal review in Perry et al. [2007], we can recognize two mechanisms that are at play. First, informal workers and firms are excluded from the formal economy in the sense that while they may not be paying taxes they also cannot enjoy the benefits provided by formality, such as contract enforcement or pensions. Second, economic agents and organizations (firms) in the informal sector have likely opted out of the formal sector based on a cost-benefit analysis weighing taxes and regulations against state’s enforcement effort and capability [following Hirschman, 1970]. How can the government avoid such an unappealing situation? The model suggests that the only way to do that is to make sure that zg is as socially appropriate as possible from the perspective of player i with trust τg (e.g., zg ′ on Figure 4). In this case, ηi (zg ; τg ) will be the highest and the undercutting by informal facilitator will be problematic, because now he will have to compromise the social appropriateness of his 21 institution. This suggests that in order to make players prefer the government to informal institutions, the gov- ernment should try to align the level of taxes with their perceived social appropriateness. In the model, this can be achieved in two ways. First, the government can lower the taxes. This option is, however, very limited. Leaving aside the very inefficiency that prompts the use of informal institutions, the govern- ment (unlike the informal facilitator) is a complex institution that has costs and obligations to provide public services, so the taxes cannot be too low. The second way is to increase trust in government τg that will then make the existing level of taxes seem more socially appropriate. This latter strategy would be consistent with reducing the main driver of informality: “a massive opting out of formal institutions by firms and individuals […] implies a blunt societal indictment of the quality of the state’s service provision and its enforcement capability” [Perry et al., 2007, p. 2]. 5.3 Dynamics of Trust in Government and Policy How can the trust in government τg be increased? The classic view is based on its interconnection to the quality of institutions, where high quality of institutions can compensate for mistrust; for example Keefer and Scartascini [2022] emphasize prosecutors and audit agencies, dispute resolution systems, and electoral processes. Other approaches focus on the role of the social contract, citizenship, and collective action [Keefer et al., 2021]. In the latter vein, a policy that can increase collective action also increases trust in government. For example, Falconi and Robinson [2021] suggest promoting collective identities, ideas that have a unifying effect on the population (e.g., Peruvian cuisine). In theory, such a unifying national idea can spill over to the government and make people believe that it represents their national interests thus increasing τg . In this section, we take a more traditional view and propose one intuition using a reduced-form dynamic model of public service provision. We link trust to the relative appro- priateness of formal and informal institutions, and to quality of public services. In doing so, we also shed some light on the relationship between the size of formal and informal sectors and growth that is stimulated through the connection between the amount of public services and the quality of cooperation in PG or productivity (represented by the multiplier p). For this exercise, we make several simplifying assumptions that do not compromise the main intu- ition, but make things more tractable. First, we assume that the informal facilitator is selfish (ϕf = 0). This assumption has one implication that will simplify the analysis. Selfish informal facilitator in the settings described above will always optimally choose z = zg − ε, where ε is some small number, to barely undercut the government and attract players to his institution (the logic of this is similar to the standard Bertrand competition). This makes the right-hand side of inequality (9) equal to 0. Thus, the condition for the players to use the formal institution becomes ϕi [ηi (zg ; τg ) − ηi (z ; τ1 )] ≥ 0. (10) Given this, we assume that there is a continuum of players on [0, 1], who in each discrete time period 22 t = 1, 2, ... choose whether to join the formal or informal institution. We make a reduced-form assump- tion that, given the quantity dt = ηi (zg ; τgt ) − ηi (zg ; τ1 ), the measure R(dt ) of players joins the formal institution. We assume that: R(0) = 0 (when the appropriateness of formal and informal institutions is the same everyone joins the informal one) and R() is an increasing function (the more appropriate the formal institution is, relatively to the informal one, the more players join it). The latter assumption is not that unrealistic, as heterogeneity in ϕi in the population will generate optimal solutions of this sort anyway. Next, we assume that the more players join the formal institution, the more taxes they pay, so the amount of total tax collected in period t is equal to Zt = R(dt )zg . The quantity Zt is spent by the government on public services that influence productivity, or multiplier p in the PG. Suppose that in period t we have productivity pt = pt−1 + π (Zt−1 ), where π () is an increasing function with π (0) = −π < 0. The idea here is that without constant provision of public services, the productivity can decrease due to depreciation of the existing ones. Finally, assume that trust in government τgt in period t is related to the amount of public services that it provided in the previous period. When people see that the government is doing what it is supposed to do (provide public services), they start trusting it more. So, τgt = τgt−1 + g (Zt−1 ), where g (Zt−1 ) = g ¯>0 when Zt−1 is higher than some fixed threshold Z and g (Zt−1 ) = −g ¯ ¯ < 0 otherwise (we proxy the amount of public services by the amount of taxes collected). The idea here is that people’s trust in government increases by a constant when they see that enough public services is provided and decreases otherwise. Thus, we have the system of equations dt = ηi (zg ; τgt ) − ηi (zg ; τ1 ) τgt = τgt−1 + g (R(dt−1 )zg ) pt = pt−1 + π (R(dt−1 )zg ) The first two equations determine the joint dynamics of trust τgt , the difference in the appropriateness of the two institutions dt , and other related variables. Growth in represented by the third equation and expressed in terms of productivity of the PG. To understand how this system evolves, notice first that if the government does not pay specific attention to dt , then the situation in the economy will deteriorate with time. Suppose that d1 = 0, which happens when τg1 = τ1 , or the trust in the formal and informal institutions is the same. In this case, the informal sector constitutes 100% of the economy, trust in government decreases with time (because no new public services are provided), and productivity deteriorates due to depreciation for the same reason, which leads to negative growth. As time unfolds, the situation will get worse and worse and the economy will get to the state where no public services are provided at all. If however, we start from a good initial conditions where d1 is positive enough so that enough people join the formal sector, pay taxes, and R(dt )zg > Z ¯ , then the positive feedback loop in the first two equations will start. High tax revenues will generate a lot of public services that will increase trust. 23 That in its turn will increase dt even more. This will increase the proportion of the formal sector R(dt ), which will consequently lead to more taxes and more public services. This in its turn will increase trust even further, etc. On this path, the informal sector will shrink with time and disappear, with all agents choosing the formal sector for their transactions. All this will be accompanied by increasing productivity pt , which will lead to economic growth. In this model, the opting out of the formal sector happens because taxes are considered too high for the public services that are provided, and trust in government is low. As a result, a vicious cycle of high informality and low trust ensues. According to our dynamic system, a way to start a virtuous cycle would be to create a positive shock to public services provision. If the government could improve public services consistently (for a number of periods), trust τgt will gradually increase. As trust increases, a threshold will be reached at some point after which dt will become positive. At this moment, some players will join the formal sector, which will then be able to increase taxes and provide more public services. This will feed back into growing trust and more people joining the formal sector until at some point we will have R(dt )zg > Z ¯ . Once in this positive feedback loop, the economy will be growing, the formal sector will expand, and the informal sector will shrink. 6 General Trust Network Up to this point, our arguments were built on a micro-level interactions between four agents: players 1 and 2, the informal facilitator f , and the government. The relationship between the two players and the informal facilitator was based on a small trust network (see Figure 2) where nodes represent people and the links are the social weights between them. Also, the roles of the players were fixed: players 1 and 2 were those who tried to cooperate and the informal facilitator always facilitated and did not participate in any cooperative activities. In this section, we expand this idea to a general trust network covering an arbitrary number of agents that can represent the whole economy. In such a general network, moral agents have a choice between cooperation (doing business with each other) or facilitation (collecting rent). We will provide some ideas about what determines the choice of becoming cooperator or facilitator, which will consequently shed some light on the emergence and evolution of informal institutions under various conditions. Then we apply these ideas to understanding the economics of clientelistic networks ˜ [Stokes, 2011, Munoz, 2019]. Suppose that there is a set of players N with connections defined by cij ∈ {0, 1} for i, j ∈ N . If i and j “know each other” then cij = cji = 1, else cij = cji = 0. The weights cij describe the “network of friends.” Let us define nij ∈ N as the minimal number of links that connect players i and j . If they are direct friends with cij = 1, or 1-friends, then nij = 1. If i and j share a friend but themselves are not friends, then they are 2-friends with nij = 2, etc.21 The network described above not only defines the structure of friendship connections but also the levels of trust among them. If two players are 1-friends (nij = 1) then when they play some game with 21 In the previous sections, players 1 and 2 are 2-friends. 24 Government 6 7 τ1 5 9 τ1 τ1 τ1 τ1 τ1 11 8 τ1 1 τ1 10 4 τ1 τ1 2 3 Figure 5: An example of a trust network (informal, in black) and the government network (formal, in orange). each other they use equal social weights τ1 in their norm-dependent utilities (as in (3)) and trust each other to the degree τnij = τ1 ∈ [0, 1]. In general, we assume that the level of trust is weakly decreasing in nij , so the further away the players are on the network, the less they trust each other. In other words τ1 ≥ τ2 ≥ τ3 ≥ ... This definition takes into account possible “parochial tendencies” of the players [Kimbrough and Vostroknutov, 2022b] when the weights quickly decrease to 0 (e.g., if τ2 = 0, then players only trust their friends and no one else), but at the same time leaves room for some trust towards strangers τ > 0 when limk→∞ τk = τ . For convenience, let us define the level of trust between players i and j as τij = τnij and assume that τii = τ0 ≡ 1 for all i ∈ N (any player trusts herself at least as much as her 1-friends, τ0 ≥ τ1 ). Figure 5 shows an example of a trust network with links (in black) representing 1-friendships. The trust network is the foundation on which informal institutions are built: as time unfolds, informal facilitation will generate some cooperation between 2-friends (and in more complex settings possibly between 3-friends, etc.). However, formal institutions, or government, are based on a slightly different idea. Government is modeled here as an agent to whom all agents in the economy are connected by a direct link (in orange in Figure 5). This means that—through laws, regulations, and public services— government can act as a facilitator for any two agents, thus overcoming the parochial nature of informal facilitation. This makes formal institutions a potentially much more powerful mechanism for enhancing cooperation and eventually growth. Given these definitions, we can now think about what makes agents want to cooperate or facilitate on the trust network. Simply from the structure of the network it is clear that some agents are better suited for cooperation and some for facilitation. Consider agent 1 on Figure 5. He is connected to many other agents, who in their turn are only connected to him. Thus, agent 1 is in perfect position for facilitation. He can make a lot of money by simply connecting his friends to each other, who might not be able to cooperate without him due to low trust. At the same time, agents with only one connection 25 cannot be facilitators, because they have only one friend, so they are best suited for cooperation. Thus, it is reasonable to expect that for agents with many friends facilitation will be more profitable than cooperation and vice versa. Well-connected agents will choose facilitation as their primary source of income, whereas agents with few friends will choose cooperation. Another way to think about who should facilitate and who should cooperate is by imagining that new friendships can be forged at a cost. New friendships create opportunities for facilitation and thus profit, but constitute an investment. Thus, the question is Which agents would be willing to invest in finding new friends? To answer this, notice that in the previous sections we always assumed that players 1 and 2 have high propensities to follow norms ϕ1 and ϕ2 , which made them able to cooperate with each other in principle. Even if the agents do not originally trust each other, they can use facilitation to enter a successful cooperative relationship and make profit. However, experimental estimates of propensities to follow norms [e.g., Kimbrough and Vostroknutov, 2016, 2018] suggest that the distribution of ϕ’s is bimodal: around 20% of people have very high ϕ’s, around 20% very low ϕ’s, and the rest is spread somewhere in between, which is more or less the same across countries (see Figure 10 in Appendix B). This evidence suggests that around 20% of the population with high ϕ’s are able to cooperate, thus they might prefer that to investing into finding new friends. The other 20% with low ϕ’s are not able to cooperate at all, because in PG or any other social dilemma, they would always free ride. Given this, it is reasonable to think that selfish agents like that would invest in collecting new friends with the purpose of making money through facilitation. This argument suggests that the number of friendship links on a network might not be random, but rather modulated by agents’ propensity to follow norms: selfish agents in trust networks are motivated to invest into new connections with the purpose of facilitation, whereas norm-following agents might prefer to benefit from cooperation. 6.1 Clientelistic Networks In this section, we use the idea about the motivation of selfish and norm-following agents explained above to understand the nature and purpose of clientelistic networks. The literature on this topic [Stokes, 2011, Acemoglu, 2005] has catalogued many instances of this phenomenon that is reflected in the attempts of businessmen and politicians to “collect” clients through various forms of gifts, bribes, lobbying, public political events, etc. with the purpose of increasing their own power (through votes, increased political influence, rent, etc.). The literature has described the typologies and even network nature of clientelism ˜ [Munoz, 2019]. A new understanding of clientelism proposes that it arises organically to fill in the vac- uum created by the weak state [Acemoglu, 2005, Lazar, 2008]. More specifically, Falconi and Robinson [2021] suggest that clientelism and state weakness in Latin America inhibit provision of basic public goods. Raiser [1997] highlights the role of informal institutions in fostering trust in third-party enforce- ment through the state during transition from a planned to a market economy in Eastern Europe; he describes how, if trust is eroded by persistent fiscal crises, the control over institutional change can be taken over by competing informal agents (”roving bandits”). But the literature stops short of an expla- 26 nation as to why this is happening, why this phenomenon takes so many different forms, and how to counteract it. The model of trust network and facilitation provides some new ideas in that regard. One example of a clientelistic network is reported in Falconi and Robinson [2021], where the story of Jhon “Calzones,” a Colombian businessman turned politician, is analyzed. Calzones used his connections to provide public services to (illegal) plots of land, 10,000 of which he then sold to the poorest people in the area with a subsidy for constructing a house, before he ran for mayor. Falconi and Robinson note that through his “philanthropic work [Calzones] formed a clientele, a political base, by using his wealth [and connections] to provide services that the Colombian government does not provide, and this allowed him to fill a niche intermediating between the people and the state.” To this day, the people of Yopal, or the ‘Ciudadela la Bendici´ on’ exist as a society independent of the state. Dramatically, this is not a stand-alone case in Colombia (or several other countries in Latin America). In fact, these arrangements are viewed as a legitimate political process. When the state underprovides public goods, it often legalizes the local elites having emerged in similar way, and distributes resources and jobs through their networks. Other examples of structures parallel to the state exist and are some- times described by the concept of the ”lettered city” [Lazar, 2008]. In this set-up, clientelism is no longer dismissed as undemocratic or inefficient. On the contrary, it provides a solid alternative to the weak for- mal political and economic institutions, and can even include competition between patrons for clients, who decide which network to support [Lazar, 2008, Falconi and Robinson, 2021]. The connection to the political system and parallel provision of public goods are important for un- derstanding the nature of clientelistic networks and their impact on institutions. Fergusson et al. [2022] show that tax evasion, as a measure of state weakness, and vote buying, as a measure of clientelism, are highly correlated at individual level. Other studies have drawn parallels between the strength and degree of fragmentation of the political system and the level of clientelism [e.g., Levitsky and Zavaleta, 2016]. In another set of studies, Munoz˜ [2019] analyzes the political system in Peru, where candidates employ clientelistic strategies in the absence of political machines or other means of bargain enforce- ment. She stresses that approaches focused on monitoring, reciprocity, and conditional loyalty cannot account for the widespread electoral clientelism. The absence of political machinery, Munoz ˜ claims, gives rise to clientelism as a means of determining candidates viability and election. Similar ideas have been expressed in the context of other countries with better organized political systems, which nevertheless are plagued with clientelism. One puzzling feature of Peruvian clientelism is that many “facilitators” distribute gifts to populations in various ways seemingly without any means to guarantee that they get something in return (in form of votes or political influence), which puzzled many a political economist [Munoz, ˜ 2019]. Our network model provides an interesting account of this phenomenon. For clients living in remote areas or working in the informal sector, joining a patron network might be the only means to cooperate or “do business,” as they do not have access to formal networks. Figure 6 illustrates. In such circumstances, selfish agents who are not constrained by the political system try to collect rent by enticing the unconnected individuals with promises of becoming connected to a trust network. 27 Government Agents not connected to any trust network 6 7 8 τ1 5 9 2 4 τ1 3 τ1 τ1 τ1 11 1 10 Figure 6: An example of a network that has agents who are not connected to anything and do not have means to cooperate with others. At the same time, such individuals desperately want to be connected to any trust network, since they realize that such connections can potentially bring them profitable opportunities for cooperation through facilitation. Thus, both sides of this “market” want something from the other. On the one side we have selfish agents who compete for the connections with poor people. On the other side of the market, we have poor people who want to be connected to some trust networks. As a result, we obtain a situation similar to perfect competition among selfish facilitators, who are ready to do anything to obtain new connections. This competition decreases the price for facilitation services and also makes facilitators seek any new connections even if they cannot guarantee any tangible returns from the clients. Clientelistic networks express themselves differently in countries where the political system is more established than in Peru (e.g., Brazil or the US). To continue the analogy with market organization, imag- ine that one clientelistic network manages to create a monopoly in the form of an elite that facilitates cooperation of the whole country. Such a network will create the conditions where people who need to join the trust network have to pay high rents to enter, since there is only one network that they can use (the government is weak and does not provide good facilitation services). At the same time, the net- work will actively fight any attempts by outside facilitators to lure clients on their own, thus keeping the monopoly power and not allowing more “wild” forms of clientelism as in Peru. In this case, the network can spread to all strata of the society and become entrenched in the political system. Yet other “market structures” for clientelistic networks are possible. The constant switch of govern- ments from left to right in many Latin American countries can be accounted for as the system with two large clientelistic networks that constantly battle for political power and influence. Such duopoly can have negative consequences for the economy and growth as the two networks have to reorient govern- ment organizations towards themselves after each election. 28 7 Perspective on Historical and Traditional Societies The analysis of institutional change and the model presented in this paper have so far assumed that 1) agents have a possibility to walk away from a deal with a facilitator if they do not like it and 2) agents cannot impose punishment for norm violation. These assumptions reflect modern conditions where there is considerable freedom of movement and many economic alternatives available in large, densely populated areas where multiple institutions exist and allow agents the choice between them. However, in many traditional societies or societies that existed in the past these assumptions do not always hold.22 Indeed, Acemoglu and Robinson [2020] describe many cases where lives of agents, to use Hobbes’ expression, are “poore, nasty, brutish, and short.” This can happen for many reasons. For example, some societies might be in the state of nature (or Warre) as was the case in the Democratic Republic of Congo in the 1990s or in the Dark Ages of Ancient Greece. Life in small, traditional societies like the Tiv of Nigeria might be very close to subsistence level and heavily depend on social security nets provided by extended kin or tribal affiliates. In such societies, agents cannot walk away from a deal because they have nowhere to go and will die without the support of their clan. The possibility of punishment and control by more powerful agents is very real and constitutes a large part of agents’ incentive structure. This can also go the other way round. The Red Queen effect [Acemoglu and Robinson, 2020], or the constant state of bargaining between the people and their Leviathan that propels societies to liberty and economic prosperity by keeping them in the Narrow Corridor, critically depends on the ability of the people to impose punishment on their rulers. For example in Athens during Antiquity, people could ostracize their Archons by banishing them from the city for ten years. In reality, this did not actually happen too often. However, the possibility of ostracism incentivized many a ruler to behave in the ways that allowed people more freedoms and thus stimulated the Red Queen effect. The Founding Fathers also (though grudgingly) admitted that the power of the people over government is crucial for maintaining liberty. Thomas Jefferson once asked: “What country can preserve its liberties if their rulers are not warned from time to time that their people preserve the spirit of resistance?” and answered: “Let them take arms.” To incorporate these considerations into our framework and thus to cover historical and traditional institutions in our analysis, we need to introduce one additional ingredient, namely, a punishment tech- nology. As noted by Henrich [2015a], punishment is a mechanism that is necessary to maintain the proper functioning of social norms. Without punishment (under a common assumption that people are selfish to some degree) norms disintegrate and cannot perform their primary function – that of main- taining cooperation and curbing violence. Mathematically, punishment technology can be introduced into our framework using, for example, the model proposed by Kimbrough and Vostroknutov [2023b]. This is straightforward, so we will not go into much detail and will propose only a brief sketch of what the model with punishment can tell us for different choices of other parameters like the propensity to 22 Examples of such societies also exist today, for example in communities that are remote or in other ways cut off from alternative institutions, such as in gang-controlled neighborhoods, see for example Khanna et al. [2019]. 29 follow norms ϕ and the social weights τ . To describe how punishment technology works, consider a network of agents with trust weights as discussed in Section 6. Suppose that each agent in the network can punish any other agent and that for each agent i there is a cost of punishing any other agent j , denoted by cij . Also, let us assume that i can punish j by some maximal amount kij . For example, some agents are powerless and cannot exert much punishment over other agents (or only subset of other agents). This happens when agents have high cij and/or low kij . Agents can be powerful, because they can punish others due to low cij and/or high kij . With this simple setup, we can imagine how our framework can incorporate various institutional arrangements singled out by Acemoglu and Robinson [2020]. For example, Warre, the chaotic state of affairs with rampant violence, can be thought of as a network where all agents can be powerful with respect to all other agents and have ϕ = 0 and τ = 0 (in the most extreme case). In such a world, mostly selfish agents will take away from others what they want by force and without hesitation since norms are non-existent or weak. This is what happens in many African countries where various warring groups (e.g., RCD and Mai-Mai in Congo) attack villagers and fight with each other for resources. Notice that in the world of Warre, the institution for facilitation cannot take hold, because no one trusts anyone else (a prerequisite for facilitation is high trust in facilitator), so facilitation does not emerge spontaneously. Another interesting case is the cage of norms defined as a (seemingly) non-violent institution in which any attempt at grabbing power or control over others is quickly dealt with with severe punishments. Even though such institutions may sound like a great idea, in reality the extreme norms, traditions, and customs against anyone holding power or “unnecessary” wealth disincentivize independent thinking and make doing any business or accumulation of wealth practically impossible, thus leading to a meager existence of the population. We can think of such institution as a collection of networks of agents divided by clan affiliation (high τ for the agents in the own clan and low τ for everyone else). Even though agents trust others in their clan, their ϕ is low, so they are not very keen on following norms in general. However, the cost of punishment is also low for all agents with respect to all other agents, while the losses for those being punished can be very high (all agents are powerful). This leads to a seemingly contradictory situation where agents are mostly selfish (low ϕ), but are still willing to punish others for not sharing within a clan (low cost of punishment and high τ for the clan members). This is the case of the Tiv and their concept of tsav (power). Among the Tiv, any activity that goes beyond growing food for the needs of own family (accumulation of wealth included) can be interpreted by others as witchcraft with the intention to obtain tsav. Punishments can be easily meted upon others by spreading rumors that such and such is a witch (low cost) or secretly urinating on someone’s grain storage (evil spirits are accused of doing it). The losses from being punished can be high because people accused of witchcraft can be banished, suffer violence, or lose their food supplies. As a result, the Tiv always share food when asked by other clan members. But this is done not because they follow some strong norms of caring about others, but rather because they try to avoid punishment being overall selfish (low ϕ). 30 It is interesting to notice that, within our framework, the cage of norms is almost identical to Warre in terms of parameters. Specifically, the only difference between Warre and the cage of norms is a barely positive ϕ (so that people realize that norms exist) and high trust to the clan members τ . Thus, our framework suggests how cage of norms could have evolved from Warre. This happens when clans take a more definite shape and promulgate some general idea of reciprocal duties towards other clan members. Notice as well that, similarly to Warre, the institution for facilitation cannot spontaneously emerge in this case either but for a different reason. Facilitation implies that agents who work together accumulate more wealth in the PG game than they would otherwise, which constitutes the violation of the norm against holding too much power (or wealth) and thus can be punished. Even though there is some trust in the system (towards other clan members), the low ϕ and, more importantly, the norms against accumulation of power prevent facilitation from emerging and preclude the Tiv and other similar societies from increasing their production efficiency and developing markets and other institutions that promote economic growth. The next example is the Despotic Leviathan. Medieval Arab writer Ibn Khaldun describes the rise and fall of Arab empires after conquest of the territories, roughly corresponding to what is now Middle East, by nomadic, desert tribes of the Bedouin. Khaldun proposed the general pattern of the evolution of these empires starting from the first generation rulers, who still retained cultural and economic connections to the Bedouin, and through second and third generations that lost these connections and turned to despotism passing the stage of some economic growth. In our framework, the Despotic Leviathan in these stories can be seen as an extractive institution as defined above, where the population cannot escape and has to submit to the rule of the Caliph. How- ever, what is interesting is the economic and institutional progression from the stateless Bedouin setup of tribal allegiance similar to the Tiv (all agents are powerful, low ϕ, high τ within each tribe) to the orderly imperial power asymmetry where the Caliph is the single supremely powerful agent among the powerless population. When the Bedouin first created their empires through conquest, they needed to assert some rule over the culturally diverse populations of the conquered territories. This was done by the imposition of (some sort of) unified imperial law that applied on the whole territory together with a common language. The necessities of ruling the Caliphate, the need for taxation, and the laws that maintained this structure created a situation where the institutions for facilitation could and did emerge. Khaldun reports the de- velopment of trade within the Caliphates and consequent increase in productivity from the new types of crops brought from the tropics (like rice, sorghum, hard wheat, and coconut palms) together with better investment climate and rise in private enterprise. Despite the fact that culturally the first-generation Bedouin Caliphs remained the same barely norm-following individuals (low ϕ) who only answered to their tribe (high τ ), as facilitators for the now vast territory, they did their job well in order to generate profits. They maintained the rule of law and reasonable taxes, which created a good environment for the development of institutions for facilitation. Common language gave people of the empire the ability to cooperate with each other on a broader scale and produce wealth by using the facilitation possibilities 31 for doing business within the new order, which generated economic growth. However, their second- and third-generation descendants, who never changed their cultural atti- tudes (low ϕ) while losing their affinity with the tribes (now low τ ) needed new alliances to maintain order. Given that they were selfish facilitators with a lot of power to punish, they used it profusely thus suppressing the environment where institutions for facilitation could thrive and destroying the achieve- ments of the previous generation. This led to despotism, decrease in growth, and eventually fall of these empires as Khaldun colorfully depicts. All these observations can be reconciled theoretically within our framework that proposes a perspective on the institutional change that took place in this time period. Finally, we turn to the Shackled Leviathan, the Red Queen effect, and the story of Solon, the Archon of Athens. When Solon came to power, he inherited the city state in economic crisis that was precipitated by the rich elites who consolidated a lot of power and enserfed many citizens of Athens with the help of then wide-spread debt peonage norms among other standard economic means. These were extractive institutions at their extreme, where agents willing to do business used their own self as a collateral and lost their freedoms when their enterprise did not work out. Debt peonage was a big hurdle on the way of development of institutions for facilitation simply because more and more agents lost their freedom and were forced to do their owner’s bidding instead of exploring business opportunities. On top of that, Athenian society at the time had very little rule of law and economically deprived citizens had no way to protect themselves from the predatory practices of the wealthy elite. This was the hallmark of the Dark Ages of Ancient Greece, the Despotic Leviathan. In only a single year while Solon was in power, he managed to change the path of Athens with his reforms towards the “shackling” of the Leviathan. He cancelled all peonage debts thus freeing all enserfed citizens, democratized Athenian institutions, which dramatically increased public participation in state affairs, and introduced the Hubris Law that protected everyone including slaves from being assaulted by the wealthy. Anyone now could file a complaint to court that often led to punishments of the perpetrators of hubris, the acts of intimidation. These measures decreased the influence of the elites and gave citizens of Athens much more power over how to live their lives. In the terminology of our framework, Athens transited from the state with few powerful agents and powerless population to the state where the elites and the population had power over each other (both had means to punish the other side). Moreover, the Hubris Law and the total ban on debt peonage have gradually changed the norms that now required Athenians to respect each other, which can be interpreted as an increase in both ϕ and τ (towards other Athenians). As a result, the institutions for facilitation could take off and the economy of Athens started to grow. Solon’s reforms started the Red Queen effect: the new system, though not without troubles, managed to maintain the balance of power between elites and population and with time Athens became a wealthy city state. As we can see from this example, the balance of power and the adjusting norms created the environment where it was not worthwhile for either side to abuse the other. These conditions fit into our model without punishment described in the sections above. Moreover, such balance naturally promulgated the norms of mutual respect among the new citizens who were born into this new order, 32 which increased trust. Thus, the facilitation relationships similar to modern conditions have emerged and developed. In this section, we connected some examples of institutions in traditional societies and institutional change in historical perspective to our formal framework. A defining feature of these examples (e.g., Arab empires and Athens) is that institutions change mostly without specifically engineered interference. Even though Solon’s reforms in Athens were deliberately directed at shackling the Leviathan, his example is rare in history, and it leaves us with no additional understanding of how to replicate his success in modern societies. However, relating these examples to the model presented in this paper does propose a path to systematic policy that can change this situation. One theory that encompasses both economic and social factors of institutional arrangements like the state of nature, cage of norms, the Despotic, and Shackled Leviathans allows to analyze existing institutions, to estimate model parameters for them (e.g., taxes and trust), and to provide quantitative instruments to guide institutional change into the Narrow Corridor. 8 Discussion In this paper, we show how introducing an additional motivation to the economic agent—namely, the motivation to cooperate with others that works through the innate desire to adhere to social norms— can give rise to a theory of institution formation and institutional change. Moral agents strive to follow norms and have good cooperative relationships with others, which incentivizes them to seek business opportunities in any economic environment. This implies that when the quality of the government is low and agents are not willing to use its services they will create informal institutions that allow them to cooperate outside the official channels. Various forms of informality ranging from elite capture to “wild” clientelistic networks can emerge depending on the political landscape and current economic situation. It is important to note that the models presented above are just an illustration of this general approach and do not constitute some final word on how specifically institutions should be modeled. For example, we use the Public Goods game to represent a small business arrangement in which various agents may choose to cooperate with each other or not. However, given the specific context of some country or industry that needs to be modeled, other more tailored games might be used. Also, the way agents change their trust weights towards others in an institution for facilitation can be adapted to specific cases. What we try to present in this paper is the general style of modeling institutions that, similarly to game-theoretic Industrial Organization, can be flexible in treating specific details. Given all this, we believe that our approach contributes to the understanding of institutional change and can help develop new institutional policy. Although the models of institutions with moral agents can get arbitrarily specific, we think that the value of our framework lies in its ability to model institutional change and to make general predictions about a variety of institutional arrangements. For example, the idea that moral agents choose whether to work in formal or informal sectors, and do so depending on the two institutions’ comparative economic 33 and normative characteristics, shows how easily standard economic policy can go awry. Imagine that the government decides to increase taxes expecting more tax revenue. However, in reality the revenues might fall because after the tax increase agents may leave the formal institution and join the informal one. This process will take place regardless of the specifics of the informal institutions. This example shows that taking institutions into account in a structural way within the model can have tangible and important policy implications. Another important lesson to be learned from our framework is that moral agents, who have two motivations (selfish and moral), can be heterogeneous in how they mix them.23 Some agents may be very selfish and disregard the norms, whereas others may be extremely norm-abiding. This fact implies that a policy may have differential effect on different agents and can fail because not all of them react to it in the desired way. For example, introducing a lower speed limit on a highway might make norm- abiding agents drive slower, which will decrease their utility. However, it may not decrease the number of accidents, because selfish agents who do not follow rules will keep driving very fast regardless of the change in the speed limit. This shows how a seemingly benign policy can have adverse effects in the world with moral agents. Our framework can be used to take situations like this into account. The value of the model with endogenous institutions for applications, as well as empirical and policy work lies in the possibility to calibrate it to specific country or circumstances, existing interest groups, etc. For example, the version of the model as it is presented in this paper can be calibrated to a case of specific country where the estimates for trust weights (τ ), propensities to follow norms (ϕ); choice context; and actual rents to facilitators can be obtained from surveys. Then, conclusions can be drawn regarding the “fairness” of the institutions, or how extractive they are, as well as on the effectiveness of specific policies. For example, having estimated the parameters pertaining to moral agents, it would be possible to say how effective a policy to increase tax rate would be in increasing revenue: it would be possible to estimate how many agents will leave for the informal sector, thus providing estimates for the revenue reduction through this channel. On a final note, we would like to point out that our framework can be used not only for studying “current” institutional change in a given country, but also for understanding the broader historical pro- cesses of economic development that start with the emergence of informal institutions in the original state of nature, then proceed to more complex institutions like tribes, and finally lead to the formation of larger arrangements like kingdoms or states. Indeed, in the current version of the model we assume, for example, that government simply exists. However, we do not explicitly describe how it came to be. We believe that this is possible. The versatility of our framework that can be essentially seen as an upgrade of game theory with norms should in principle allow to model institutions of any complexity. 23 Notice that this problem does not arise in the neoclassical world where agents have only one motivation. 34 9 Conclusion In this paper, we propose a new framework to model institutions and institutional change based on Acemoglu and Robinson [2020] and the theory of norms by Kimbrough and Vostroknutov [2022a]. We show how moral agents, who care about following social norms and thus strive to cooperate with others, can form institutions that facilitate cooperation. Similarly to game-theoretic Industrial Organization, the framework allows to model informal as well as formal institutions as games played by moral agents. It is possible to conceptualize institutions as inclusive or extractive and model institutional change as a consequence of choice of moral agents among available institutions as time unfolds. We demonstrate how the framework can be used to understand the origins of informal institutions. With a series of examples of clientelistic networks, we show that our framework can be useful for understanding how and why such networks form and persist. While in the paper we show how our framework is able to account for some interesting phenom- ena related to institutions in developing countries, these models are just mere illustrations of the full power of the framework that can be used to model any interactions among moral agents, thus giving rise to a wide variety of possible institutional settings. This opens new possibilities to model institutional change; devise new types of policies that take into account normative considerations of the agents; and understand informal and formal institutions in greater detail. We use the example of clientelistic networks to show how the framework can be applied to specific types of institutions. In principle, one direction for future research could be to create more specific and applied models of clientelistic networks or other types of institutions. However, we believe that the power of the framework lies in its ability to produce general conclusions about broader classes of institutions. For that, more theoretical research is needed that could explore the general game-theoretic properties of institutions with moral agents. Another important direction for future research is to make the framework more practical; to test it with real or experimental/survey data; and to see how to calibrate the model’s parameters from surveys or specifically designed tasks. In the next step, policy implications can be considered and estimated, and cost-benefit analysis of impact could be performed. 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Journal of economic literature, 38(3):595–613, 2000. 39 Robinson, Vostroknutov, Vostroknutova “Endogenous Institutions and Economic Policy” Appendix A Additional Analyses A.1 Best Responses in the Public Goods Game In this appendix we analyze the Nash Equilibria (NE) of the Public Goods game considered in Section 3.1. We assume that the propensities to follow norms ϕ1 and ϕ2 are high enough so that the consumption part of the norm-dependent utility (2) is negligible. Thus, we analyze the Public Goods game where the payoffs are equal to the norm function ηi (wi , wj ; τ ) = −Di (wi ) − τ Dj (wj ) for player i (we will call j the player who is not i, or j = −i). Our main goal is to prove that there is a threshold value τ ∗ of trust to the other player such that the Public Goods game with utilities defined by ηi (wi , w−i ; τ ) has either 1) unique NE where both players contribute fully (for all τ > τ ∗ ); 2) unique NE where both players contribute nothing (for all τ < τ ∗ ); and 3) all pairs of choices of equal contributions are NE (when τ = τ ∗ ). We prove this by construction. First, notice that from the proof of the Compromise Theorem [Proposition 5 in Kimbrough and Vostroknutov, 2022a] we know that on convex polytopes of allocations—to which class the set of allocations C in the Public Goods game belongs—we can write Di (wi ) = ai i 2 i k (bk − wi ) + ck , k∈Ωwi where Ωwi is the set of vertices of the polytope that have player i’s consumption utility higher than wi and aik , bk , ck ∈ R are some coefficients (they cover all possible quadratic equations). Notice as well that Di (wi ) is i i a piece-wise parabola with fixed coefficients for three ranges of wi . When wi is high there is only one vertex with higher wealth than that (one set of coefficients). When wi is lower, there are two vertices with wealth of player i higher than wi , so the coefficients change. For even lower wi there are three vertices with higher wealth, so the coefficients change yet again. What is important for us though is the fact that for two players i and j the personal dissatisfaction functions are the same, or that Di (w) = Dj (w). This comes from the symmetry of the game. Also, since Di are quadratic, so is ηi , which is a collection of piece-wise-stitched concave quadratic forms. Now, we want to focus on the allocations that are obtained when both players i and j choose the same con- tributions x = xi = xj that result in some symmetric allocation (w, w). In this case, using Lemma 1 in Appendix A.3, we have Di (w) = Dj (w) = a(b − w)2 + c, where a, b, c ∈ R are some coefficients common for both players. These coefficients are also common for all allocations (w, w) because all such allocations have two vertices with wealth larger or same as w (for either player). Now that this fact is established, we can use it to show that there is a specific value of the trust weight τ = τ ∗ such that the best response of both players with this τ ∗ is to choose the same contribution as the other player, no matter what that contribution is. We show that such τ ∗ indeed exists and that it also satisfies the first order condition: the derivative at (w, w) along the choices of one player having the other player’s action fixed is zero (this guarantees that it is a best response). Let us write down the derivative. Notice that by definition ηi (wi , wj ; τ ) = −Di (wi ) − τ Dj (wj ), which can be rewritten in terms of contribution choices as ηi (xi , xj ) = −Di (w − xi + p(xi + xj )) − τ Dj (w − xj + p(xi + xj )). Suppose that xj is considered fixed and we look at the maximization problem of player i, who chooses xi to 1 maximize the above (best response). Using the fact that Di (w) = Dj (w) = a(b − w)2 + c, we can write the first order condition (the derivative of the above with respect to xi equal to zero) as −2a(1 − p)(b − (w − xi + p(xi + xj ))) + 2apτ (b − (w − xj + p(xi + xj ))) = 0. Notice that when xi = xj , or when the players choose equal allocations we are interested in, the big parentheses cancel out and we get the condition −(1 − p) + pτ = 0 (11) or 1−p τ= = τ ∗. p This means that the first order condition above is satisfied for all xi = xj only when τ = τ ∗ = (1 − p)/p. The left panel on Figure 7 illustrates. Here we show the representation of the set of allocations in the Public Goods game (the set of points within the polytope ABCD) together with allocations that give both players equal wealth (all in magenta lines). Suppose that xj is fixed and that player i chooses xi . Then her choices fall along the lines parallel to AB and DC depending on the value of xj (AB when xj = w and DC when xj = 0). The result above means that when τ = τ ∗ the derivatives of ηi are zero for all points (w, w) on the diagonal. This is shown graphically by the dashed black lines (along the edges AB and DC ) and little grey dashed lines in between. A A A B B B D D D C C C Figure 7: Illustration of best responses in the Public Goods game. This is also true for the other player. Thus, all this together implies that when τ = τ ∗ the derivatives on the diagonal are zero and are best responses of both players (symmetry). Given that these are mutual best responses, we have a continuum of NE on the diagonal when τ = τ ∗ . This argument demonstrates that there is τ ∗ = (1 − p)/p such that when the two players with trust τ ∗ to each other play the Public Goods game, they have a continuum of NE on the diagonal (when they choose the same contributions). This is also a unique τ ∗ because only it can satisfy the first order condition (11) on the diagonal. The next thing we need to show is that there is a unique NE for all other values of τ , below and above τ ∗ . To do that, notice that the condition (11), the left-hand side of which defines the derivative at all diagonal allocations (with equal wealth), tells us that these derivatives are always the same for all such allocations: they are all either positive, negative, or zero depending on the value of τ . For example, the middle panel of Figure 7 shows the case when the derivatives are negative. This means the following. Given that ηi is concave, the negative derivative at point D on the figure implies that it is the maximum on the edge DC (the range of choices of player i given fixed xj = 0) and thus the best response (marked by a black circle). To the contrary, negative derivative at point B means that B cannot be the best response on the edge AB , because the function then grows in the direction of point A. So, the best response is somewhere on the edge AB , but not at B . This last observation also holds in the same way for all points on the diagonal between B and D. Thus, except for the point D, all best 2 responses of player i lie to the left of the diagonal. Similarly, we can work out that for positive derivatives (the right panel of Figure 7), we have best response at point B and not in D (all best responses in this case are on the right side of the diagonal). We can use these findings when looking for mutual best responses for the two players. Indeed, when τ < τ ∗ we have the case of negative derivatives. This means that the best responses of the two players are symmetrically situated on the opposite sides of the diagonal except for the point D, where the best responses coincide. They do not coincide anywhere else, since they are divided by the diagonal in all other places. Thus, we can conclude that when τ < τ ∗ , we have a unique NE of the game with zero contributions (point D, xi = xj = 0). Similarly, when τ > τ ∗ the best responses of the two players coincide at point B , but not anywhere else, since for all other actions the best responses again lie on the opposite sides of the diagonal. Thus, for τ > τ ∗ the unique NE is to contribute fully (point B , xi = xj = w). w τ = 0.15 τ = 0.20 Contribution of player 2 0 0 w 0 w Contribution of player 1 Contribution of player 1 w τ* = 0.25 Contribution of player 2 0 0 w Contribution of player 1 w τ = 0.50 τ = 0.75 Contribution of player 2 0 0 w 0 w Contribution of player 1 Contribution of player 1 Figure 8: Best response correspondences in Public Goods game with p = 0.8 and different levels of τ . Figure 8 shows numerically computed best response correspondences and Nash equilibria in the Public Goods with p = 0.8 for different levels of trust τ of the players to each other. The black lines correspond to the best response of player 1 and grey lines to those of player 2. Equilibria are marked with red circles and dashed lines denote the continuum of equilibria. One can see that for low τ , the unique NE is to contribute nothing as is demonstrated on the top two graphs of Figure 8. For high τ , the NE is to contribute full amounts (the bottom graphs). Finally, when τ = τ ∗ = 0.25 we have an intermediate case where any choice of equal contributions constitutes a NE (the middle graph). This same structure of best responses and NE is present for any value of p ∈ [0.5, 1) when τ ∗ = (1 − p)/p. To illustrate, we plot the values of τ ∗ as dependent on p in Figure 9. Notice that the values on the graph were 3 1 .8 .6 tau* .4 .2 0 .5 .55 .6 .65 .7 .75 .8 .85 .9 .95 p Figure 9: The relationship between productivity p and the cooperation threshold τ ∗ . obtained from the numerical computations of best responses and the resulting values of τ ∗ are in perfect alignment with the function (1 − p)/p, which validates our computations. A.2 Best Responses in the Public Goods Game with Facilitation In this appendix, we show that the threshold property of NE holds also in the Public Goods with facilitation (three players). The logic of this is exactly the same as in the previous section where we considered a simple Public Goods game with two players. To see this notice first that after the facilitator chooses the payment z , the two players find themselves in a subgame, which is essentially a Public Goods game with endowments w − z/2 instead of w (z is a given constant). However, we cannot treat this subgame as a simple instance of the Public Goods because the norm function is computed differently using all the allocations in the set CF (the 3D pyramid on Figure 3). Despite the complication with the norm function, the logic of the proof of the threshold property stays the same. Indeed, by the results in the proof of Compromise Theorem in Kimbrough and Vostroknutov [2022a], we know that for any game with any number of players as long as the allocations are represented by a convex polytope, we have personal dissatisfactions Di represented by piece-wise connected quadratic functions as in Appendix A.1. Moreover, by symmetry these functions are the same for players i and j on the diagonal allocations because again they are defined only by the vertices with higher consumption utility and on the diagonal such vertices are always the same for both players (they may differ for different points (w, w), but are the same for a given point (w, w)). This observation—together with the fact that the dissatisfaction of the facilitator in any subgame is constant and can be ignored—allows us to do the same reasoning as in Appendix A.1 and conclude that there is a unique threshold τ ∗ = (1 − p)/p such that for any τ > τ ∗ the unique NE in all subgames is to contribute fully and for τ < τ ∗ the unique NE in all subgames is to contribute nothing. This result suggests the optimal behavior of the facilitator as described in the main text. 4 A.3 Lemmata Lemma 1. Any non-constant function f (x) = k ak (bk − x)2 + ck with some coefficients ak , bk , ck ∈ R can be represented as f (x) = a(b − x)2 + c where a, b, c ∈ R are also some coefficients. Proof. When we open up the squared terms in f , we get f (x) = (a1 + ... + ak )x2 − 2(a1 b1 + ... + ak bk )x + d, where d is some constant. Then 2 a1 b1 + ... + ak bk a1 b1 + ... + ak bk f (x) = (a1 + ... + ak ) x2 − 2 x+ + e, a1 + ... + ak a1 + ... + ak where e is some constant. This can be rewritten as 2 a1 b1 + ... + ak bk f (x) = a −x + c, a1 + ... + ak where a = a1 + ... + ak and c is some constant. From the above we have b = a1 +...+ak . a1 b1 +...+ak bk □ B Additional Graphs The Netherlands USA Canada 30 20 10 Percent 0 Turkey Italy All Data 30 20 10 0 0 .5 1 0 .5 1 0 .5 1 Rule-Following Figure 10: The graph from Kimbrough and Vostroknutov [2018] showing the distributions of ϕ’s in five countries and overall. All distributions (except Turkey) are bimodal with a large measure of experimental subjects complying fully with an artificial but costly rule (rule-following = 1), and a large measure of subjects not complying with the rule at all (rule-following = 0). 5