Publication: Nash on a Rotary: Two Theorems with Implications for Electoral Politics
Loading...
Published
2016-06
ISSN
Date
2016-06-14
Author(s)
Editor(s)
Abstract
The paper provides a complete characterization of Nash equilibria for games in which n candidates choose a strategy in the form of a platform, each from a circle of feasible platforms, with the aim of maximizing the stretch of the circle from where the candidate’s platform will receive support from the voters. Using this characterization, it is shown that if the sum of all players’ payoffs is 1, the Nash equilibrium payoff of each player in an arbitrary Nash equilibrium must be restricted to the interval [1/2(n − 1), 2/(n + 1)]. This implies that in an election with four candidates, a candidate who is attracting less than one-sixth of the voters can do better by changing his or her strategy.
Link to Data Set
Citation
“Basu, Kaushik; Mitra, Tapan. 2016. Nash on a Rotary: Two Theorems with Implications for Electoral Politics. Policy Research Working Paper;No. 7701. © World Bank. http://hdl.handle.net/10986/24538 License: CC BY 3.0 IGO.”
Digital Object Identifier
Associated URLs
Associated content
Other publications in this report series
Publication The Macroeconomic Implications of Climate Change Impacts and Adaptation Options(Washington, DC: World Bank, 2025-05-29)Estimating the macroeconomic implications of climate change impacts and adaptation options is a topic of intense research. This paper presents a framework in the World Bank's macrostructural model to assess climate-related damages. This approach has been used in many Country Climate and Development Reports, a World Bank diagnostic that identifies priorities to ensure continued development in spite of climate change and climate policy objectives. The methodology captures a set of impact channels through which climate change affects the economy by (1) connecting a set of biophysical models to the macroeconomic model and (2) exploring a set of development and climate scenarios. The paper summarizes the results for five countries, highlighting the sources and magnitudes of their vulnerability --- with estimated gross domestic product losses in 2050 exceeding 10 percent of gross domestic product in some countries and scenarios, although only a small set of impact channels is included. The paper also presents estimates of the macroeconomic gains from sector-level adaptation interventions, considering their upfront costs and avoided climate impacts and finding significant net gross domestic product gains from adaptation opportunities identified in the Country Climate and Development Reports. Finally, the paper discusses the limits of current modeling approaches, and their complementarity with empirical approaches based on historical data series. The integrated modeling approach proposed in this paper can inform policymakers as they make proactive decisions on climate change adaptation and resilience.Publication South Africa’s Fragmented Cities: The Unequal Burden of Labor Market Frictions(Washington, DC: World Bank, 2026-01-08)Using high-resolution administrative, census, and satellite data, this paper shows that South African cities are characterized by spatial mismatches between where people live and where jobs are located, relative to 20 global peers. Areas within 5 kilometers of commercial centers have 9,300 fewer residents per square kilometer than expected, which is 60 percent below the global median. Poor, dense neighborhoods are most affected. In Johannesburg, a 10-percentile increase in distance from the nearest business hub corresponds to a 3.7-percentile drop in asset wealth (a proxy of household wellbeing) and 4.9-percentile drop in employment. In Cape Town, the declines are 4.0 and 3.7 percentiles, respectively. Employment is 87 percent lower in the poorest decile than the richest in Johannesburg and 61 percent lower in Cape Town. These findings suggest that South Africa’s spatial organization of people and economic activity constrains agglomeration and reinforces inequality. This methodology provides a scalable and standardized data-driven framework to analyze spatial accessibility and agglomeration frictions in complex, data-constrained urban systems.Publication The Evolution of Local Participatory Democracy in Nepal(Washington, DC: World Bank, 2025-11-05)Nepal is, according to its constitution, among the world’s most decentralized countries, with a long and complex tradition of local-level public participation. This paper traces the evolution of Nepal’s modern participatory institutions, examining the extent to which they are “induced” by external interventions versus being “organically” rooted in indigenous practices. The paper identifies three broad phases: an initial focus on participation in project implementation; a subsequent phase that expanded citizen engagement; and a third phase of citizen empowerment, culminating in the 2015 federal constitution, which granted unprecedented local autonomy. The analysis yields five key findings. First, over the past 50 years, successive reforms have progressively expanded opportunities for citizens to influence local decision-making. Second, these reforms have integrated traditional participatory mechanisms into formal institutions of local government. Third, although central-level initiatives exist, most participatory platforms continue to operate at the local level. Fourth, the federal constitution has created a new landscape of local democracy, embedding autonomy and accountability. Fifth, although they are still valued in many ethnic and territorial communities, traditional participatory practices are gradually disappearing. The paper concludes by offering policy recommendations to help donor agencies and governments strengthen Nepal’s democratic trajectory. It argues that effective interventions should build on Nepal’s deep participatory traditions while recognizing the constitutional reality of far-reaching local autonomy.Publication Institutional Capacity for Policy Implementation: An Analytical Framework(Washington, DC: World Bank, 2026-01-07)State capacity is an important prerequisite for policy implementation, yet at the country level it is difficult to measure, assess, and reform. This paper proposes a focus on institutional capacity: the ability of public institutions to implement the specific policy mandates for which they are responsible. Based on a review of existing literature, the paper defines the different dimensions that compose institutional capacity and groups them into two cross-cutting categories: organizational dimensions (personnel, financial resources, information systems, and management practices) and governance dimensions (transparency, independence, and accountability). The paper proposes measures for organizational and governance dimensions using existing data, shows intra-institutional variation of these measures within countries, and discusses how new data could be collected for better measurement of these concepts. Finally, the paper illustrates how the framework can be used to diagnose the sources of common problems related to weak policy implementation.Publication Closing the Gender Gap in Entrepreneurship: Overcoming Challenges in Law and Practice for Female Entrepreneurs(Washington, DC: World Bank, 2026-01-07)Despite significant strides toward gender equality, women around the world continue to encounter systemic obstacles that hinder their entrepreneurial success. This paper systematically reviews the literature on the barriers female entrepreneurs face and the solutions proposed to overcome these challenges. It discusses institutional factors, financial factors, human capital factors, and social and cultural factors. The literature overview is complemented by a series of stylized facts that illustrate how overcoming some of these existing barriers is correlated with improved women’s entrepreneurship and female labor force participation, drawing on the World Bank’s Women, Business and the Law database as well as the World Bank’s Enterprise Surveys. The findings underscore the need for creating an enabling environment where women can thrive as entrepreneurs.
Journal
Journal Volume
Journal Issue
Collections
Related items
Showing items related by metadata.
Publication Markets and Manipulation(World Bank, Washington, DC, 2016-04)There is a growing appreciation in economics that people have emotional vulnerabilities, commitments to social norms, and systematic irrationalities, which impact their decision making and choice in the marketplace. The flip side of this is that human beings are susceptible to being manipulated by unscrupulous agents who are single-minded about marketing their services and wares. This paper reviews George Akerlof and Robert Shiller's book, Phishing for Phools: The Economics of Manipulation and Deception, alongside other writings in the field, and discusses how this research agenda can be taken forward. The paper shows how this new research can shed light on the ubiquity of corruption in so many societies, and proposes ideas for controlling corruption.Publication Joseph E. Stiglitz(World Bank, Washington, DC, 2008-01)Joseph E. Stiglitz, 2001 Nobel Laureate in Economics, helped create the theory of markets with asymmetric information and was one of the founders of modern development economics. He played a leading role in an intellectual revolution that changed the characterization of a market economy. In the new paradigm, the price system only imperfectly solves the information problem of scarcity because of the many other information problems that arise in the economy: the selection over hidden characteristics, the provision of incentives for hidden behaviors and for innovation, and the coordination of choices over institutions.Publication The Art of Currency Manipulation : How to Profiteer by Deliberately Distorting Exchange Rates(World Bank, Washington, DC, 2013-09)A frequent charge in foreign exchange markets in developing countries is that of manipulators being at work. Since to buy is to raise prices and to sell is to lower prices, the question that naturally arises is whether the widespread charge of market manipulation is valid. The paper shows that (whether or not "widespreadness" has any merit) it is possible for a player to manipulate and profiteer. By using some simple principles of game theory, the paper outlines a strategy that a manipulator may use. The aim of this paper is not to provide a manual for the manipulator but to enable the regulator to understand the art and develop policies to curb manipulation.Publication Private Cities(Washington, DC: World Bank, 2022-02-10)Institutional weaknesses limit the capacity of local governments to support efficient urbanization in developing countries. They also lead to the emergence of large developers with the clout to build entire cities. This paper analyzes the urbanization process when local governments are weak and large developers are powerful. Results from a non-cooperative game setting with minimal assumptions show that multiple equilibria can emerge depending on key institutional parameters of the model and the nature of the game, but all of them are inefficient. In this simple setting, increasing the capacity of the local government may not lead to better outcomes, because it may crowd out urban land development by the more effective private investor. Subsidizing the large investor can ensure efficiency, but it makes the rest of society worse off. Selling the rights to the city can be Pareto efficient, but only provided that the price at which the rights are sold are sufficiently high. However, more analytical and empirical work is needed before these analyses can be deemed relevant in practice. Competition among jurisdictions, time consistency challenges, and the social implications of private cities deserve special attention.Publication International Lending, Sovereign Debt and Joint Liability : An Economic Theory Model for Amending the Treaty of Lisbon(World Bank, Washington, DC, 2013-08)As the Eurozone crisis drags on, it is evident that a part of the problem lies in the architecture of debt and its liabilities within the Eurozone and, more generally, the European Union. This paper argues that a large part of the problem can be mitigated by permitting appropriately-structured cross-country liability for sovereign debt incurred by individual nations within the European Union. In brief, the paper makes a case for amending the Treaty of Lisbon. The case is established by constructing a game-theoretic model and demonstrating that there exist self-fulfilling equilibria, which would come into existence if cross-country debt liability were permitted and which are Pareto superior to the existing outcome.
Users also downloaded
Showing related downloaded files
Publication Perils of Simulation : Parallel Streams and the Case of Stata’s Rnormal Command(World Bank, Washington, D.C., 2012-11)Large-scale simulation-based studies rely on at least three properties of pseudorandom number sequences. Since they behave like random numbers, they can be replicated and generated in parallel. However, there has been some divergence between empirical techniques employing random numbers and the standard battery of tests used to validate them. A random number generator that passes tests for any single stream of random numbers may fail the same tests when it is used to generate multiple streams in parallel. The lack of systematic testing of parallel streams leaves statistical software with important potential vulnerabilities. This paper reveals one such vulnerability in Stata's rnormal function which went unnoticed for almost four years and how this error was detected. Furthermore, the paper discusses practical implications for the use of parallel streams in existing software.Publication Adaptation to a Changing Climate in the Arab Countries : A Case for Adaptation Governance and Leadership in Building Climate Resilience(Washington, DC: World Bank, 2012-12-01)Adapting to climate change is not a new phenomenon for the Arab world. For thousands of years, the people in Arab countries have coped with the challenges of climate variability by adapting their survival strategies to changes in rainfall and temperature. Their experience has contributed significantly to the global knowledge on climate change and adaptation. But over the next century global climatic variability is predicted to increase, and Arab countries may well experience unprecedented extremes in climate. Temperatures may reach new highs, and in most places there may be a risk of less rainfall. Under these circumstances, Arab countries and their citizens will once again need to draw on their long experience of adapting to the environment to address the new challenges posed by climate change. This report prepared through a consultative process with Government and other stakeholders in the Arab world assesses the potential effects of climate change on the Arab region and outlines possible approaches and measures to prepare for its consequences. It offers ideas and suggestions for Arab policy makers as to what mitigating actions may be needed in rural and urban settings to safeguard key areas such as health, water, agriculture, and tourism. The report also analyzes the differing impacts of climate change, with special attention paid to gender, as a means of tailoring strategies to address specific vulnerabilities. The socioeconomic impact of climate change will likely vary from country to country, reflecting a country's coping capacity and its level of development. Countries that are wealthier and more economically diverse are generally expected to be more resilient. The report suggests that countries and households will need to diversify their production and income generation, integrate adaptation into all policy making and activities, and ensure a sustained national commitment to address the social, economic, and environmental consequences of climate variability. With these coordinated efforts, the Arab world can, as it has for centuries, successfully adapt and adjust to the challenges of a changing climate.Publication Reducing Poverty, Protecting Livelihoods, and Building Assets in a Changing Climate : Social Implications of Climate Change for Latin America and the Caribbean(World Bank, 2010)This book provides a much needed look at the impact of climate change on the poor. It convincingly demonstrates that issues of poverty and livelihoods must be integrated into climate change policies to help achieve sustainable development gains. The high incidence of natural disasters, growing urbanization, and increased water scarcity combined with the acute impact of these phenomena on the poor and vulnerable complicates the already enormous challenge of reducing poverty and inequality in Latin America and the Caribbean. This publication lays bare the social implications of climate change and equips the reader with a framework for understanding how climate change and climate variability affect livelihoods, poverty, income, health, and migration. These scenarios call for greater efforts to incorporate poverty, livelihood, and social considerations into climate change adaptation and mitigation policies. Purposefully targeted policies and investments can support economic growth and poverty reduction efforts and help achieve sustainable development goals. In other words, good climate change adaptation policies can also be good development policies. This book will change the way the author think about the relationship between poverty, social development, and climate change. It provides climate-smart policy options to help reduce vulnerability, protect livelihoods, and build communities that are resilient to changing climate conditions.Publication East Asia and Pacific Update, November 2007(World Bank, Washington, DC, 2007-11)Growth in Emerging East Asia is expected to exceed 8 percent in 2007 for a second year in succession and to moderate only slightly in 2008. Our projections for regional growth in 2007 and 2008 have been substantially increased compared to six months ago, mainly due to the unexpected and large domestic demand-led acceleration of growth in China. Growth also picked up in most of the other larger economies of the region, again a result of more buoyant investment and consumption spending. Concerns about the impact of the US sub-prime crisis and the renewed surge in oil prices have clearly increased downside risks. Nevertheless we expect that the stronger growth momentum in the region will carry through 2008. There are as yet few signs of a significant pick-up in underlying core inflation pressures or of other domestic constraints or imbalances that would require a marked slowing of growth.Publication Digital Africa(Washington, DC: World Bank, 2023-03-13)All African countries need better and more jobs for their growing populations. "Digital Africa: Technological Transformation for Jobs" shows that broader use of productivity-enhancing, digital technologies by enterprises and households is imperative to generate such jobs, including for lower-skilled people. At the same time, it can support not only countries’ short-term objective of postpandemic economic recovery but also their vision of economic transformation with more inclusive growth. These outcomes are not automatic, however. Mobile internet availability has increased throughout the continent in recent years, but Africa’s uptake gap is the highest in the world. Areas with at least 3G mobile internet service now cover 84 percent of Africa’s population, but only 22 percent uses such services. And the average African business lags in the use of smartphones and computers as well as more sophisticated digital technologies that catalyze further productivity gains. Two issues explain the usage gap: affordability of these new technologies and willingness to use them. For the 40 percent of Africans below the extreme poverty line, mobile data plans alone would cost one-third of their incomes—in addition to the price of access devices, apps, and electricity. Data plans for small- and medium-size businesses are also more expensive than in other regions. Moreover, shortcomings in the quality of internet services—and in the supply of attractive, skills-appropriate apps that promote entrepreneurship and raise earnings—dampen people’s willingness to use them. For those countries already using these technologies, the development payoffs are significant. New empirical studies for this report add to the rapidly growing evidence that mobile internet availability directly raises enterprise productivity, increases jobs, and reduces poverty throughout Africa. To realize these and other benefits more widely, Africa’s countries must implement complementary and mutually reinforcing policies to strengthen both consumers’ ability to pay and willingness to use digital technologies. These interventions must prioritize productive use to generate large numbers of inclusive jobs in a region poised to benefit from a massive, youthful workforce—one projected to become the world’s largest by the end of this century.