Random – DEBRAJ RAY

Contracts with Interdependent Preferences

(with Marek Weretka), March 2024.

Summary. This paper studies contracting between a principal and multiple agents. The setup is classical except for the assumption that agents have interdependent preferences. We characterize cost effective contracts, and relate the direction of co-movement in rewards — “joint liability” (positive) or “tournaments” (negative) — to the assumed structure of preference interdependence. We identify two asymmetries. First, the optimal contract leans towards joint liability rather than tournaments, especially in larger teams, in a sense made precise in the paper. Second, when the mechanism-design problem is augmented by robustness constraints designed to eliminate multiple equilibria, the principal may prefer teams linked via adversarial rather than altruistic preferences.

Nash Bargaining with Coalitional Threats

(with Rajiv Vohra). March 2024.

Summary. We axiomatically characterize bargaining outcomes in the presence of coalitional threats. As in Nash’s solution, these involve the product of payoffs net of disagreement points, but coalitional threats appear as conventional constraints, and are not netted out from payoffs as disagreement points are. This basic property is implied by a new “expansion axiom” that is automatically satisfied in the standard bargaining problem. We then endogenize coalitional threats using internal consistency. For games with convex feasible sets of payoffs, the internally consistent solution coincides with one in which the only threat from each coalition is the use of their “standard” Nash solution, unconstrained by subcoalitions. For transferable-utility games, this observation uncovers a connection between the coalitional bargaining solution and the egalitarian solution of Dutta and Ray (1989, 1991).

Measuring Upward Mobility

(with Garance Genicot). This version February 2023. Forthcoming, American Economic Review. [Slides]

Summary. We develop a measure of upward mobility that distills central features of the relative and absolute approaches to measuring mobility. The former is embodied in the Growth Progressivity axiom: transfers of instantaneous growth rates from relatively rich to poor individuals increases upward mobility. The absolute approach is embodied in the Growth Alignment axiom: mobility increases with higher growth for all individuals. These axioms, along with standard auxiliary restrictions, identify a simple one-parameter family of upward mobility measures, linear in individual growth rates and exhibiting geometrically declining weights on baseline incomes. A serendipitous implication of our measure is that it does not rely on panel data, which greatly expands our analytical scope to data-poor settings.

The Social Equilibrium of Relational Arrangements

(with Parikshit Ghosh), forthcoming, Journal of Institutional and Theoretical Economics, Special Issue on Relational Contracts.

Summary. Building on Ghosh and Ray (1996), we study norms within partnerships that exhibit gradually increasing cooperation, thus serving to deter deviations. But socially beneficial gradualism may be undermined by partners renegotiating to greater cooperation from the outset. We show that incomplete information regard- ing partner patience ameliorates this tension even as it adds to the anonymity of the environment.

Groups in Conflict: Private and Public Prizes

(with Laura Mayoral), Journal of Development Economics 154, https://doi.org/10.1016/j.jdeveco.2021.102759 (2022).

Supplementary Appendix.

Summary. This paper studies costly conflict over private and public goods. Oil is an example of the former, political and civil rights an example of the latter. Our theory predicts that groups in conflict are likely to be small when the prize is private, and large when the prize is public. We examine these implications empirically by constructing a global dataset at the ethnic group level and studying conflict along ethnic lines. Our theoretical predictions find significant confirmation in this setting, and the analysis sheds new light on group size and collective action in the context of violent conflict.

Conveying Value Via Categories

(with Paula Onuchic), October 2019, revised December 2022. Forthcoming, Theoretical Economics.

A sender is about to come into possession of an object of heterogeneous quality. Prior to knowing that quality, she commits to a categorization. That is, she partitions the set of qualities into subsets — some possibly singletons — and verifiably commits to reveal the element in which the quality belongs. The categories must be monotone. Our main results fully describe the profit-maximizing categorization for any pair of priors over object quality held by sender and receiver. We apply these results to the design of educational grades.

Too Good To Be True? Retention Rules for Noisy Agents

(with Francisco Espinosa), revised January 2022, forthcoming American Economic Journal: Microeconomics. Supplementary Appendix.

Summary. An agent who privately knows his type (good or bad) seeks to be retained by a principal. A principal seeks to retain good agents. Agents signal their type with some ambient noise, but can alter this noise, perhaps at some cost. Our main finding, that we examine in several extensions, is that in equilibrium, the principal treats extreme signals in either direction with suspicion, and retains the agent if and only if the signal falls in some intermediate bounded set. In short, she follows the maxim: “if it seems too good to be true, it probably is.”

Decoding India’s Low Covid-19 Case Fatality Rate

(with Minu Philip and S. Subramanian), Journal of Human Development and Capabilities 22, 27-51 (2021).

Summary. India’s case fatality rate (CFR) under covid-19 is strikingly low, trending from 3% or more, to a current level of under 1.8%. The world average rate is far higher. Several observers have noted that this difference is at least partly due to India’s younger age distribution. In this paper, we use age-specific fatality rates from comparison countries, coupled with India’s distribution of covid-19 cases to “predict” what India’s CFR would be with those age-specific rates. In most cases, those predictions are lower than India’s actual performance, suggesting that India’s CFR is, if anything, too high rather than too low.

India’s Lockdown: An Interim Report

(with S. Subramanian), May 2020, Indian Economic Review, https://doi.org/10.1007/s41775-020-00094-2

Summary. The world has continued to change rapidly since the last version of this article was written on May 20, 2020. Yet, as this article goes to press, we are aware of two realities; first, that we cannot perennially chase a moving target, but second, that nothing about the fundamental trends that we have identified appear to have changed. India is firmly in the throes of a vicious pandemic that we can only hope will abate with the development of an effective vaccine. Our plea for the widespread provision of adequate health and medical facilities, adequate protection for the elderly, and transfers to those severely affected by the lockdown are absolutely unchanged in the face of the latest data. In contrast, the brutal enforcement of a lockdown with none of these accompanying measures can only worsen outcomes for the poorest and most vulnerable among the population.

Aspirations and Economic Behavior

(with Garance Genicot), Annual Review of Economics 12, 715-746 (2020). [Slides from a 2023 review lecture]

This paper reviews the literature on aspirations in economics, with a particular focus on socially determined aspirations. The core theory builds on two fundamental principles: (a) aspirations can serve to inspire, but still higher aspirations can lead to frustration and resentment; and (b) aspirations are largely determined by an individual’s social environment. We discuss the implications of this framework for the study of interpersonal inequality, social conflict, fertility choices, risk taking and goal-setting.

Information Aggregation in a Financial Market with General Signal Structure

(with Youcheng Lou, Sahar Parsa, Duan Li and Shouyang Wang), Journal of Economic Theory 183, 594–624 (2019).

Summary. We study a financial market with asymmetric, multidimensional trader signals that have general correlation structure. Each of a continuum of traders belongs to one of finitely many “information groups.” There is a multidimensional aggregate signal for each group. Each trader observes an idiosyncratic signal about the fundamental, built from this group signal. Correlations across group signals are arbitrary. Several existing models serve as special cases, and new applications become possible. We establish existence and regularity of linear equilibrium, and demonstrate that the equilibrium price aggregates information perfectly as noise trade vanishes. Combines and extends results in Parsa and Ray (2017) and Lou, Li and Wang (2017), both mimeo. Online Appendix.

Games of Love and Hate

(with Rajiv Vohra), Journal of Political Economy 128, 1789-1825 (2020).

Dedicated to Tapan Mitra — advisor, colleague and dear friend, whose sense of aesthetics, minimalism and rigor has been an inspiration to us. Tapan Mitra died on February 3, 2019.

Summary. A strategic situation with payoff-based externalities is one in which a player’s payoff is a function of her own action and the payoffs of other players. Every action profile therefore induces an interdependent utility system. A strategic situation is continuous if each such utility system is continuous. If each utility system is bounded, with a unique payoff solution for every action profile, we call the strategic situation coherent, and if the same condition also applies to every subset of players, we call the situation sub-coherent. A coherent, sub-coherent and continuous situation generates a standard normal form, referred to as a game of love and hate. Our central theorem states that every equilibrium of a game of love and hate is Pareto optimal, in sharp contrast to the general prevalence of inefficient equilibria in the presence of externalities. While externalities are restricted to flow only through payoffs there are no other constraints: they could be positive or negative, or of varying sign. We further show that our coherence, sub-coherence and continuity requirements are tight.

Maximality in the Farsighted Stable Set

(with Rajiv Vohra) Econometrica 87(5), 1763–1779 Online Appendix.

Summary. The stable set of von Neumann and Morgenstern can be extended to cover farsighted coalitional deviations, as proposed by Harsanyi (1974), and more recently reformulated by Ray and Vohra (2015). However, while coalitional deviations improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable, and easily verifiable, properties is unaffected by the imposition of this stringent maximality requirement.

Hindu-Muslim Violence in India: A Postscript from the 21st Century

(with Anirban Mitra), in Advances in the Economics of Religion (J-P Carvalho, S. Iyer and J. Rubin, eds.) Volume 158, International Economic Association Series, Palgrave Macmillan (2019).

Summary. We revisit and extend the core issues studied in Mitra and Ray (2014). The main reason behind this retrospection is to check if the robust empirical patterns recorded there persist once we consider a longer time frame extending into the 21st century. We make three observations: (i) There is a clear economic component to violence, roughly along the lines of our earlier paper; (ii) There is a new aspect which is assuming salience now — namely, a strong political component which is manifesting itself through the presence of BJP legislators; (iii) Ahmedabad exemplifies the ascendancy of this political component.

Missing Unmarried Women

(with Siwan Anderson), Journal of the European Economic Association 2019 17(5), 1585–1616; jvy027, https://doi.org/10.1093/jeea/jvy027

Summary. We provide systematic estimates of the excess female mortality faced by older unmarried women in developing regions. We place these estimates in the context of the missing women phenomenon. There are approximately 1.5 million missing women between the ages of 30 and 60 years old each year. We find that 35% of these missing women of adult age can be attributed to not being married. These estimates vary by region. India has the largest proportion of missing adult women who are without a husband, followed by the countries in East Africa. By contrast, China has almost no missing unmarried women. We show that 70% of missing unmarried women are of reproductive age and that it is the relatively high mortality rates of these young unmarried women (compared to their married counterparts) that drive this phenomenon.

Certified Random: A New Order for Co-Authorship

(with Arthur Robson), American Economic Review 108, 489–520 (2018).

Summary. Certified random order (a) distributes the gain from first authorship evenly over the alphabet, (b) allows either author to signal when contributions are extremely unequal, (c) will invade an environment where alphabetical order is dominant, (d) is robust to deviations, (e) may be ex-ante more efficient than alphabetical order, and (f) is no more complex than the existing alphabetical system modified by occasional reversal of name order.

Conflict and Development

(with Joan Esteban) Annual Reviews of Economics 9, 263-293, 2017.

Summary. In this review, we examine the links between economic development and social conflict. By economic development, we refer broadly to aggregate changes in per capita income and wealth or in the distribution of that wealth. By social conflict, we refer to within-country unrest, ranging from peaceful demonstrations, processions, and strikes to violent riots and civil war. We organize our review by critically examining three common perceptions: that conflict declines with ongoing economic growth; that conflict is principally organized along economic differences rather than similarities; and that conflict, most especially in developing countries, is driven by ethnic motives.

Aspirations and Inequality

(with Garance Genicot) Econometrica 85, 485-519, 2017. Online Appendix. 2009 version.

Summary. This paper develops a theory of socially determined aspirations, and the interaction of those aspirations with growth and inequality. The interaction is bidirectional: economy-wide outcomes determine individual aspirations, which in turn determine investment incentives and social outcomes. Thus aspirations, income, and the distribution of income evolve jointly.

Information and Enforcement in Informal Credit Markets

(with Parikshit Ghosh), Economica 83, 59–90, 2016.

Summary. We study loan enforcement in informal credit markets with multiple lenders but no sharing of credit histories, and derive the dynamics of loan size and interest rates for relational lending. In the presence of a sufficient fraction of ‘natural defaulters’, the rest of the market can be incentivized against default by micro-rationing—sharper credit limits and possibly higher interest rates that serve as gateways into new borrowing relationships. When there are too few natural defaulters in the market, this can be supplemented by macro-rationing—random exclusion of some borrowers. When information collection is endogenized, multiple equilibria may arise. (Published version of unpublished notes from 2001.)

Aspirations And The Development Treadmill

Journal of Human Development and Capabilities 17, 309–323, 2016.

Summary. I describe a positive theory of socially determined aspirations, and some implications of that theory for the study of economic inequality and social conflict. The main contribution of the theory is that it attempts to describe, in the same explanatory arc, how a change in aspirations can be inspirational in some circumstances, or a source of frustration and resentment in others. These different reactions arise from the aspirational gap: the difference between socially generated aspirations and the current socio-economic standard that the individual enjoys. Ever-accelerating economic development can cut both ways in terms of inspiration and frustration.

Anatomy of a Contract Change

with Rajshri Jayaraman and Francis de Vericourt, American Economic Review 106, 316-358, 2016. Online Appendix.

Summary. We study a contract change for tea pluckers. Base wages increased while incentive piece rates were lowered or kept unchanged. Yet, in the following month, output increased by 20–80%. This response contradicts the standard model, is only partly explicable by greater supervision, and appears to be “behavioral.” But in subsequent months, the increase is comprehensively reversed. Our findings suggest that behavioral responses may be ephemeral, and should ideally be tracked over an extended period.

Poverty and Self-Control

(with Doug Bernheim and Sevin Yeltekin), Econometrica 83 (5), 1877-1911, 2015. Online Appendix. A link to the 1999 version, which only had numerical results.

Summary. Poverty can perpetuate itself by undermining the capacity for self-control. Our main result demonstrates that low initial assets can limit self-control, trapping people in poverty, while those with high initial assets can accumulate indefinitely.

Nit-Piketty

CesIfo Economic Studies 2015.

Summary. Yes, capital must displace labor, but not because r > g. This article is based on this blog post, Branko Milanovic objected here; I replied. Piketty replies to some of his critics here.

The Farsighted Stable Set

(with Rajiv Vohra), Econometrica 83, 977–1011, 2015. Online Appendix.

Summary. We propose a definition of farsighted stability in coalitional games, in the spirit of von Neumann-Morgenstern stability and its modification by Harsanyi. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single-payoff allocation. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games.

Coalition Formation

(with Rajiv Vohra), in Handbook of Game Theory Vol 4 (H.P. Young and S. Zamir, eds), Elsevier North Holland, 2014.

Summary. This chapter surveys a sizable and growing literature on coalition formation. We refer to theories in which one or more groups of agents (“coalitions”) deliberately get together to jointly determine within-group actions, while interacting noncooperatively across groups. The chapter describes a variety of solution concepts, using an umbrella model that adopts an explicit real-time approach. Players band together, perhaps disband later and re-form in shifting alliances, all the while receiving payoffs at each date according to the coalition structure prevailing at the time. We use this model to nest two broad approaches to coalition formation, one based on cooperative game theory, the other based on noncooperative bargaining. Three themes that receive explicit emphasis are agent farsightedness, the description of equilibrium coalition structures, and the efficiency implications of the various theories.

Implications of an Economic Theory of Conflict: Hindu-Muslim Violence in India

(with Anirban Mitra), Journal of Political Economy 122, 719-765, 2014.

Summary. We model intergroup conflict driven by economic changes within groups. We show that if group incomes are low, increasing group incomes raises violence against that group and lowers violence generated by it. We then apply the model to data on Hindu-Muslim violence in India. Our main result is that an increase in per capita Muslim expenditures generates a large and significant increase in future religious conflict. An increase in Hindu expenditures has a negative or no effect. These findings speak to the origins of Hindu-Muslim violence in post-Independence India. Online Appendix. Sequel.

Gender Differentials in Eye Care: Access and Treatment

(with Rajshri Jayaraman and Shing-Yi Wang), Economic and Political Weekly 49 No. 25, June 21, 2014.

Summary. Two potential sources of gender bias in health care are (a) females access treatment later than males and (b) they receive differential care at the medical facility. We explore both of these for eye care at a large Indian medical facility. At presentation, women have worse diagnoses than men for indicators of symptomatic illness, such as myopia and cataract. There is no difference in treatment.

Inefficiency and the Golden Rule: Phelps-Koopmans Revisited

(with Tapan Mitra), in Sugata Marjit and Meenakshi Rajeev (eds), Emerging Issues in Economic Development: A Contemporary Theoretical Perspective: Essays in Honour of Dipankar Dasgupta & Amitava Bose, Oxford University Press, 2012.

Summary. We study the celebrated Phelps-Koopmans theorem in environments with nonconvex production technologies. We argue that a robust failure of the theorem occurs in such environments. Specifically, we prove that the Phelps-Koopmans theorem must fail whenever the net output of the aggregate production function f(x), given by f(x) − x, is increasing in any region between the golden rule and the maximum sustainable capital stock.

The Age Distribution of Missing Women in India

(with Siwan Anderson), Economic & Political Weekly 47, No. 47-48, December, 2012.

Summary. Relative to developed countries, there are far fewer women than men in India. Estimates suggest that among the stock of women who could potentially be alive today, over 25 million are “missing”. Sex selection at birth and the mistreatment of young girls are widely regarded as key explanations. We provide a decomposition of missing women by age across the states. While we do not dispute the existence of severe gender bias at young ages, our computations yield some striking findings. First, the vast majority of missing women in India are of adult age. Second, there is significant variation in the distribution of missing women by age across different states. Missing girls at birth are most pervasive in some north-western states, but excess female mortality at older ages is relatively low. In contrast, some north-eastern states have the highest excess female mortality in adulthood but the lowest number of missing women at birth.

Ethnicity and Conflict: An Empirical Study

(with Joan Esteban and Laura. Mayoral), American Economic Review 102, 1310-1342, 2012. Online Appendix.

Summary. We examine empirically the impact of ethnic divisions on conflict, by using a specification based on Esteban and Ray (2011). That theory links conflict intensity to three indices of ethnic distribution: polarization, fractionalization, and the Gini-Greenberg index. The empirical analysis verifies that these distributional measures are significant correlates of conflict. These effects persist as we introduce country-specific measures of group cohesion and of the importance of public goods, and combine them with the distributional measures exactly as described by the theory.

A Theory of Occupational Choice with Endogenous Fertility

(with Dilip Mookherjee and Silvia Prina), American Economic Journal: Microeconomics 4, 1–34, 2012.

Summary. Theories based on partial equilibrium reasoning alone cannot explain the widespread negative cross-sectional correlation between parental wages and fertility, without restrictive assumptions on preferences and childcare costs. We argue that incorporating a dynamic general equilibrium analysis of returns to human capital can help explain observed empirical patterns.

On the Phelps–Koopmans Theorem

(with Tapan Mitra), Journal of Economic Theory 147, 833–849, 2012.

Summary. We examine whether the Phelps–Koopmans theorem is valid in models with nonconvex production technologies. Dedicated to the memory of David Cass: mentor, friend and an extraordinary economic theorist.

Status, Intertemporal Choice, and Risk-Taking

(with Arthur Robson), Econometrica 80, 1505–1531 (2012). Online Appendix.

Summary. This paper studies endogenous risk-taking by embedding a concern for status (relative consumption) into an otherwise conventional model of economic growth. We prove that if the intertemporal production function is strictly concave, an equilibrium must converge to a unique steady state in which there is recurrent endogenous risk taking.

Ethnicity and Conflict: Theory and Facts

(with Joan Esteban and Laura Mayoral), Science 336, 858 – 865, 2012.

Summary. Over the second half of the 20th century, conflicts within national boundaries became increasingly dominant. Many (if not most) such conflicts involved violence along ethnic lines. On the basis of recent theoretical and empirical research, we provide evidence that preexisting ethnic divisions do influence social conflict. Our analysis also points to particular channels of influence. Specifically, we show that two different measures of ethnic division—polarization and fractionalization—jointly influence conflict, the former more so when the winners enjoy a “public” prize (such as political power or religious hegemony), the latter more so when the prize is “private” (such as looted resources, government subsidies, or infrastructures).

Linking Conflict to Inequality and Polarization

(with Joan Esteban), American Economic Review 101, 1345–1374, 2011.

Summary. In this paper we study a behavioral model of conflict that provides a basis for choosing certain indices of dispersion as indicators for conflict. We show that a suitable monotone transform of the equilibrium level of conflict can be proxied by a linear function of the Gini coefficient, the Herfindahl-Hirschman fractionalization index, and a specific measure of polarization due to Esteban and Ray.

Missing Women: Age and Disease

(with Siwan Anderson), Review of Economic Studies 77, 1262-1300, 2010. Online Appendix,

Summary. Relative to developed countries and some parts of the developing world, most notably sub-Saharan Africa, there are far fewer women than men in India and China. It has been argued that as many as a 100 million women could be missing. The possibility of gender bias at birth and the mistreatment of young girls are widely regarded as key explanations. We provide a decomposition of these missing women by age and cause of death. While we do not dispute the existence of severe gender bias at young ages, our computations yield some striking new findings: (1) the vast majority of missing women in India and a significant proportion of those in China are of adult age; (2) as a proportion of the total female population, the number of missing women is largest in sub-Saharan Africa, and the absolute numbers are comparable to those for India and China; (3) almost all the missing women stem from disease-by-disease comparisons and not from the changing composition of disease, as described by the epidemiological transition.

Uneven Growth: A Framework for Research in Development Economics

Journal of Economic Perspectives 24 (3), Summer, 45-60, 2010.

Summary. In many developing countries, economic growth has been fundamentally uneven. This article takes the reality of “uneven growth” seriously, and uses it as an organizing device for a research program in Development Economics.

A Remark on Color-Blind Affirmative Action

(with Rajiv Sethi), Journal of Public Economic Theory 12, 399-406, 2010.

Summary. Elite educational institutions have turned to criteria that meet diversity goals without being formally contingent on applicant identity. Under weak and generic conditions, such color-blind affirmative action policies must be nonmonotone in student test scores.

Inequality and Markets: Some Implications of Occupational Diversity

(with Dilip Mookherjee), American Economic Journal Microeconomics 2 38–76, 2010.

Summary. This paper studies income distribution in an economy with borrowing constraints. If the span of occupational investments is large, long-run wealth distributions display persistent inequality. With a “rich” set of occupations, so that training costs form an interval, the distribution is unique and the average return to education must rise with educational investment.

The Phelps–Koopmans Theorem and Potential Optimality

International Journal of Economic Theory 6 11–28, 2010.

Summary. The Phelps–Koopmans theorem states that if every limit point of a path of capital stocks exceeds the “golden rule,” then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false in a strong sense. Not only can there be efficient paths with capital stocks forever above and bounded away from a unique golden rule, such paths can also be optimal under the infinite discounted sum of a one-period utility function.

Informal Insurance in Social Networks

(with Francis Bloch and Garance Genicot), Journal of Economic Theory 143, 36-58, 2008.

Summary. This paper studies bilateral insurance schemes across networks of individuals. We investigate the structure of self-enforcing insurance networks. Network links play two distinct and possibly conflictual roles. They act as conduits for both transfers and information; affecting the scope for insurance and the severity of punishments upon noncompliance. Their interaction leads to a characterization of stable networks as suitably “sparse” networks. Thickly and thinly connected networks tend to be stable, whereas intermediate degrees of connectedness jeopardize stability.

On the Salience of Ethnic Conflict

(with Joan Esteban), American Economic Review 98:5, 2185–2202, 2008. Online Appendix.

Summary. “In much of Asia and Africa, it is only modest hyperbole to assert that the Marxian prophecy has had an ethnic fulfillment.” — Donald Horowitz (1985).

Group Decision-Making in the Shadow of Disagreement

(with Kfir Eliaz and Ronny Razin), Journal of Economic Theory 132, 236–273, 2007.

Summary. A model of group decision-making is studied, in which one of two alternatives must be chosen. Our model is distinguished by three features: private information regarding valuations, differing intensities in preferences, and the option to declare neutrality to avoid disagreement. There is always an equilibrium in which the majority is more aggressive in pushing its alternative, thus enforcing their will via both numbers and voice. However, under general conditions an aggressive minority equilibrium inevitably makes an appearance, provided that the group is large enough. Such equilibria invariably display a “tyranny of the minority”: the increased aggression of the minority always outweighs their smaller number, leading to the minority outcome being implemented with larger probability than the majority alternative.

Coalition Formation with Binding Agreements

(with Kyle Hyndman), Review of Economic Studies 74, 1125–1147, 2007.

Summary. We study coalition formation in “real time”, a situation in which coalition formation is intertwined with the ongoing receipt of payoffs. Agreements are assumed to be permanently binding: They can only be altered with the full consent of existing signatories. For characteristic function games we prove that equilibrium processes—whether or not these are history dependent—must converge to efficient absorbing states. For three-player games with externalities each player has enough veto power that a general efficiency result can be established. However, there exist four-player games in which all Markov equilibria are inefficient from every initial condition, despite the ability to write permanently binding agreements. Online Appendix.

Inequality and Inefficiency in Joint Projects

(with Jean-Marie Baland and Olivier Dagnelie), Economic Journal 117, 922-935, 2007.

Summary. A group of agents voluntarily participates in a joint project, in which efforts are not perfectly substitutable. The output is divided according to some given vector of shares. A share vector is unimprovable if no other share vector yields a higher sum of payoffs. We describe unimprovable share vectors.

Bargaining Power and Enforcement in Credit Markets

(with Garance Genicot), Journal of Development Economics 79, 398-412, 2006.

Summary. In a credit market with enforcement constraints, we study the effects of a change in the outside options of a potential defaulter on the terms of the credit contract, as well as on borrower payoffs. The results crucially depend on the allocation of “bargaining power” between the borrower and the lender. We prove that there is a crucial threshold of relative weights such that if the borrower has power that exceeds this threshold, her expected utility must go up whenever her outside options come down. But if the borrower has less power than this threshold, her expected payoff must come down with her outside options. These disparate findings within a single model permit us to interpret existing literature on credit markets in a unified way.

A Decision-Theoretic Basis for Choice Shifts in Groups

(with Kfir Eliaz and Ronny Razin), American Economic Review 96, 1321-1332, 2006.

Summary. The phenomenon of choice shifts in group decision-making has received much attention in the social psychology literature. Faced with a choice between a “safe” and “risky” decision, group members appear to move to one extreme or the other, relative to the choices each member might have made on her own. Both risky and cautious shifts have been identified in different situations. This paper demonstrates that from an individual decision-making perspective, choice shifts may be viewed as a systematic violation of expected utility theory. We propose a model in which a well-known failure of expected utility — captured by the Allais paradox — is equivalent to a particular configuration of choice shifts. Thus, our results imply a connection between two well-known behavioral regularities, one in individual decision theory and another in the social psychology of groups.

Inequality, Lobbying, and Resource Allocation

(with J. Esteban), American Economic Review 96, 257–279 (2006). Supplementary Notes.

Summary. This paper describes how wealth inequality may distort public resource allocation. A government seeks to allocate limited resources to productive sectors, but sectoral productivity is privately known by agents with vested interests in those sectors. They lobby the government for preferential treatment. The government—even if it honestly seeks to maximize economic efficiency—may be confounded by the possibility that both high wealth and true economic desirability create loud lobbies. Broadly speaking, both poorer economies and unequal economies display greater public misallocation. The paper warns against the conventional wisdom that this is so because such governments are more “corrupt.”

On the Dynamics of Inequality

Economic Theory 29, 291–306, 2006.

Summary. The dynamics of inequality are studied in a model of human capital accumulation with credit constraints. This model admits a multiplicity of steady state skill ratios that exhibit varying degrees of inequality across households. The main result studies nonstationary equilibrium paths, and shows that an equilibrium sequence of skill ratios must converge monotonically to the smallest steady state that exceeds the initial ratio for that sequence. This paper, in honor of Mukul Majumdar, publishes notes from 1990, which contain a different proof of the main result.

Aspirations, Poverty and Economic Change

in Abhijit Banerjee, Roland Benabou and Dilip Mookherjee, What Have We Learned About Poverty?, Oxford University Press, 2006.

Summary. Introduces the idea of aspirations as a socially determined reference point. The paper argues that reachable aspirations serve to inspire, while still higher aspirations could lead to frustration.

Farsighted Network Formation

(with Bhaskar Dutta and Sayantan Ghosal), Journal of Economic Theory 122, 143 – 164, 2005.

Summary. This paper studies a model of dynamic network formation when individuals are farsighted: players evaluate the desirability of a “current” move in terms of its consequences on the entire discounted stream of payoffs. We define a concept of equilibrium which takes into account farsighted behavior of agents and allows for limited cooperation amongst agents.

Polarization: Concepts, Measurement, Estimation

(with Jean-Yves Duclos and Joan Esteban), Econometrica 72, 1737–1772, 2004.

Summary. We develop the measurement theory of polarization for the case in which income distributions can be described using density functions. The main theorem uniquely characterizes a class of polarization measures that fits into what we call the “identity-alienation” framework, and simultaneously satisfies a set of axioms. Here is a link to a somewhat expanded version, which was published in C. Barrett (ed), The Social Economics of Poverty: Identities, Groups, Communities and Networks, London: Routledge (2005).

Persistent Inequality

(with Dilip Mookherjee), Review of Economic Studies 70, 369-393, 2003.

Summary. When human capital accumulation generates pecuniary externalities across professions, and capital markets are imperfect, persistent inequality in utility and consumption is inevitable in any steady state.

Group Formation in Risk-Sharing Arrangements

(with Garance Genicot), Review of Economic Studies 70, 87-113, 2003.

Summary. We study informal insurance within communities, explicitly recognizing the possibility that subgroups of individuals may destabilize insurance arrangements among the larger group. We therefore consider self-enforcing risk-sharing agreements that are robust not only to single-person deviations but also to potential deviations by subgroups. Variant on an Example in the paper. A conjecture related to the paper.

Coalition Formation as a Dynamic Process

(with Hideo Konishi), Journal of Economic Theory 110, 1–41, 2003.

Summary. We study coalition formation as an ongoing, dynamic process, with payoffs generated as coalitions form, disintegrate, or regroup.

Contractual Structure and Wealth Accumulation

(with Dilip Mookherjee), American Economic Review 92, 818–849, 2002. Online Appendix.

Summary. Can historical wealth distributions affect long-run output and inequality despite “rational” saving, convex technology and no externalities? We consider a model of equilibrium short-period financial contracts, where poor agents face credit constraints owing to moral hazard and limited liability. If agents have no bargaining power, poor agents have no incentive to save: poverty traps emerge and agents are polarized into two classes, with no interclass mobility. If instead agents have all the bargaining power, strong saving incentives are generated: the wealth of poor and rich agents alike drift upward indefinitely and “history” does not matter eventually.

Is Equality Stable?

(with Dilip Mookherjee), American Economic Review (Papers and Proceedings) 92, 253–259, 2002.

Summary. We explore the view, further developed in our other work, that inequality is an inevitable consequence of the market mechanism.

The Time Structure of Self-Enforcing Agreements

Econometrica 70, 547–582, 2002.

Summary. A principal and an agent enter into a sequence of agreements. The principal faces an interim participation constraint at each date, but can commit to the current agreement; in contrast, the agent has the opportunity to renege on the current agreement. We show that every constrained efficient sequence must, after a finite number of dates, exhibit a continuation that maximizes the agent’s payoff over all such sequences.

Reinforcement Learning in Repeated Interaction Games

(with Jon Bendor and Dilip Mookherjee), Advances in Theoretical Economics 1, Issue 1, Article 3. Additional notes on extending the model to the probabilistic choice framework of Luce.

Summary. We study long run implications of reinforcement learning when two players repeatedly interact with one another over multiple rounds to play a finite action game. Within each round, the players play the game many successive times with a fixed set of aspirations used to evaluate payoff experiences as successes or failures. The probability weight on successful actions is increased, while failures result in players trying alternative actions in subsequent rounds. The learning rule is supplemented by small amounts of inertia and random perturbations to the states of players. Aspirations are adjusted across successive rounds on the basis of the discrepancy between the average payoff and aspirations in the most recently concluded round. We define and characterize pure steady states of this model, and establish convergence to these under appropriate conditions.

Collective Action and the Group Size Paradox

(with Joan Esteban), American Political Science Review 95, 663–672, 2001.

Summary. According to the Olson paradox, larger groups may be less successful than smaller groups in furthering their interests. We address the issue in a model with three distinctive features: explicit intergroup interaction, collective prizes with a varying mix of public and private characteristics, and nonlinear lobbying costs. The interplay of these features leads to new results. When the cost of lobbying has the elasticity of a quadratic function, or higher, larger groups are more effective no matter how private the prize. With smaller elasticities, a threshold degree of publicness is enough to overturn the Olson argument, and this threshold tends to zero as the elasticity approaches the value for a quadratic function.

Coalitional Power and Public Goods

(with Rajiv Vohra), Journal of Political Economy 109, 1355-1384, 2001.

Summary. We study the provision of public goods when all agents have complete information and can write binding agreements. The focus is on coalition formation as a potential source of inefficiency.

Inequality, Control Rights, and Rent Seeking: Sugar Cooperatives in Maharashtra

(with Abhijit Banerjee, Dilip Mookherjee and Kaivan Munshi), Journal of Political Economy 109, 138-190, 2001.

Summary. This paper presents a theory of rent seeking within farmer cooperatives in which inequality of asset ownership affects relative control rights of different groups of members. . Predictions concerning the effect of the distribution of local landownership on sugarcane price, capacity levels, and participation rates of different classes of farmers are confirmed by data from nearly 100 sugar cooperatives in the Indian state of Maharashtra over the period 1971–93.

What’s New in Development Economics?

The American Economist 44, 3-16, 2000.

Summary. This essay is meant to describe the current frontiers of development economics, as I see them. I might as well throw my hands up at the beginning and say there are too many frontiers. In recent years, the subject has made excellent use of economic theory, econometric methods, sociology, anthropology, political science and demography and has burgeoned into one of the liveliest areas of research in all the social sciences.

Conflict and Distribution

(with Joan Esteban), Journal of Economic Theory 87, 379-415, 1999.

Summary. We develop a behavioral model that links the level and pattern of social conflict to the society-wide distribution of individual characteristics. The model can be applied to groups that differ in characteristics such as wealth, ethnicity, religion, and political ideology. We settle questions of existence and uniqueness of conflict equilibrium. Conflict is seen to be closely connected with the bimodality of the underlying distribution of characteristics. However, in general, the conflictdistribution relationship is nonlinear and surprisingly complex. Our results on conflict patterns also throw light on the phenomena of extremism and moderation.

A Theory of Endogenous Coalition Structures

(with Rajiv Vohra), Games and Economic Behavior 26, 286–336, 1999.

Summary. Consider an environment with widespread externalities, and suppose that binding agreements can be written. We study coalition formation in such a setting. Our analysis proceeds by defining on a partition function an extensive-form bargaining game. We establish the existence of a stationary subgame perfect equilibrium. Our main results are concerned with the characterization of equilibrium coalition structures. We develop an algorithm that generates such a structure. Our characterization results are especially sharp for symmetric partition functions.

Evolving Aspirations and Cooperation

(with Rajeeva Karandikar, Dilip Mookherjee, and Fernando Vega-Redondo), Journal of Economic Theory 80, 292-331, 1998.

Summary. A 2×2 game is played repeatedly by two satisficing players. The game considered includes the Prisoner’s Dilemma, as well as games of coordination and common interest. Each player has an aspiration at each date, and takes an action. The action is switched at the subsequent period only if the achieved payoff falls below aspirations; the switching probability depends on the shortfall. Aspirations are periodically updated according to payoff experience, but are occasionally subject to trembles. For sufficiently slow updating of aspirations and small tremble probability, it is shown that both players must ultimately cooperate most of the time.

Equilibrium Binding Agreements

(with Rajiv Vohra), Journal of Economic Theory 73, 30-78, 1997.

Summary. We study equilibrium binding agreements, the coalition structures that form under such agreements, and the efficiency of the outcomes that result. We analyze such agreements in a context where the payoff to each player depends on the actions of all other players. Thus a game in strategic form is a natural starting point. Unlike the device of a characteristic function, explicit attention is paid to the behavior of the complementary set of players when a coalition blocks a proposed agreement. A solution concept and its applications are discussed.

Egalitarianism and Incentives

(with Kaoru Ueda), Journal of Economic Theory 71, 324-348, 1996.

Summary. A group of agents is collectively engaged in a joint productive activity. Each agent supplies an observable input, and output is then collectively shared among the members according a social welfare function. However, individual actions are taken on a selfish basis, and the collective decision is only made after inputs are chosen. This leads to inefficiency. The aim of this paper is to show formally that, contrary to popular belief, the degree of inefficiency decreases in the extent of egalitarianism embodied in the social welfare function.

Cooperation in Community Interaction without Information Flows

(with Parikshit Ghosh), Review of Economic Studies 63, 491–519, 1996.

Summary. We study cooperative behavior in communities where the flow of information regarding past conduct is limited or missing. Players are initially randomly matched with no knowledge of each other’s past actions; they endogenously decide whether or not to continue
the repeated relationship. We define social equilibrium in such communities. Such equilibria
are characterized by an initial testing phase, followed by cooperation if the test is successful. It is precisely the presence of myopic types that permit cooperation, by raising barriers to entry into new relationships.

Labor Tying

(with Anindita Mukherjee), Journal of Development Economics 47, 207-239, 1995.

Summary. The co-existence of seasonal fluctuations in income and imperfect credit markets suggests that tied contracts should dominate rural labor markets. However, empirical observation from India suggests that this is far from being the case, and indeed, that there is a declining trend in labor tying. In our model, casual labor markets are always active despite the presence of seasonality, and a variety of implications are derived that link economic growth, changing information flows, and the decline of labor tying over time.

On the Measurement of Polarization

(with Joan Esteban), Econometrica 62, 819–851, 1994.

Summary. This paper is concerned with the conceptualization and measurement of polarization. Suppose that a population is grouped into significantly-sized “clusters’,” such that each cluster is “similar” in terms of the attributes of its members, but different clusters have “dissimilar” attributes. In that case we would say that the society is “polarized.” We study these intuitive criteria carefully, and provide a theory of measurement.

Internally-Negotiation-Proof Equilibrium Sets: Limit Behavior for Low Discounting

Games and Economic Behavior 6, 162-177, 1994.

Summary. Recent literature in the theory of dynamic games addresses renegotiatioin-proof equilibria, For repeated games, I analyze the limit of renegotiation-proof equilibrium sets as discounting vanishes. The main result states that such limit sets must either be singletons or belong to the Pareto frontier of the convex hull of the feasible set of the stage game payoffs.

A Non-Cooperative Theory of Coalitional Bargaining

(with Kalyan Chatterjee, Bhaskar Dutta and Kunal Sengupta), Review of Economic Studies 60, 463-477, 1993.

Summary. We explore a sequential-offers model of n-person coalitional bargaining with transferable utility and with time discounting. Our focus is on stationary equilibria of the resulting non-cooperative game. Efficient stationary equilibria converge to a point in the core as the discount factor approaches 1. For strictly convex games, this is the egalitarian solution of Dutta and Ray (Econometrica 1989).

Wages and Involuntary Unemployment in the Slack Season of a Village Economy

(with Anindita Mukherjee), Journal of Development Economics 37, 227-264, 1992.

Summary. We model slack season wages in a village economy, in the presence of involuntary unemployment. Our model draws its inspiration from sociological notions of ‘everyday peasant resistance’. A continuum of equilibrium wage configurations is obtained. These configurations, barring one, involve wages exceeding reservation wages, despite the presence of involuntary unemployment.

Why Does Asset Inequality Affect Unemployment? A Study of the Demand Composition Problem

(with Jean-Marie Baland), Journal of Development Economics 35, 69-92, 1991.

Summary. This paper is devoted to a general equilibrium analysis of the relationship between the inequality in asset holdings and the aggregate levels of output and employment in a developing economy. Since luxuries and basic goods compete for the use of the same scarce resources, unemployment is conceived as a mechanism whereby the market demand for basic goods can be limited to a sufficiently low level so that the high demand for luxuries can be met. The ambiguous effects of capital accumulation on employment are also examined.

On the Competitive Pressure Induced by the Diffusion of Innovations

(with Dilip Mookherjee), Journal of Economic Theory 54, 124-147, 1991.

Summary. We consider the decision of a dominant firm to adopt a sequence of potential cost-reducing innovations, where the latest technology adopted diffuses to a competitive fringe at an exogenous rate. With price competition on the product market, the leader optimally spaces apart the adoption dates of successive innovations, so the industry is characterized by cycles of alternating innovation and diffusion. These results may, however, be reversed in the case of quantity competition.

The Economics of Orchards: An Exercise in Point-Input, Flow-Output Capital Theory

(with Tapan Mitra and Rahul Roy), Journal of Economic Theory 53, 12-50, 1991.

Summary. This paper is concerned with the qualitative properties of optimal intertemporal programs in a model of point-input flow-output capital theory, when future utilities are discounted. Under a mild condition on the flow-output vector, we establish that optimal programs for every discount factor and every initial state (other than a unique stationary optimal state) will exhibit non-convergence.

Collective Dynamic Consistency in Repeated Games

Games and Economic Behavior 1, 295-326, 1989

We formalize the notion of collective dynamic consistency for noncooperative repeated games. Intuitively, we require that an equilibrium not prescribe any course of action in any subgame that players would jointly wish to renegotiate, given the restriction that any alternative must itself be invulnerable to subsequent deviations and renegotiation. While the appropriate definition of collective dynamic consistency is clear for finitely repeated games, serious conceptual difficulties arise when games are infinitely repeated.

A Concept of Egalitarianism Under Participation Constraints

(with Bhaskar Dutta), Econometrica 57, 615-635, 1989.

Summary. We introduce a new solution concept for transferable-utility games in characteristic function form, when individuals collectively believe in equality as a desirable social goal, although in their private actions they behave selfishly. This latter consideration implies that an “egalitarian solution” must satisfy core-like participation constraints, while the former implies that such a solution is also a Lorenz-maximal element of the constrained set. Despite the well-known fact that the Lorenz ordering is incomplete, we show that the egalitarian solution is unique whenever it exists.

Credible Coalitions and the Core

International Journal of Game Theory 18, 185-187, 1989.

Summary. A problem with the concept of the core is that it does not explicitly capture the credibility of blocking coalitions, This notion is defined, and the concept of a modified core introduced, consisting of allocations not blocked by any credible coalition. The core and modified core are then shown to be identical. The concept of credibility is thus implicit in the definition of the core.

Economic Growth With Intergenerational Altruism

(with Doug Bernheim), Review of Economic Studies 54, 227-243, 1987.

Summary. We consider the properties of equilibrium behavior in an aggregative growth model with intergenerational altruism. Various positive properties such as the cyclicity of equilibrium programs, and the convergence of equilibrium stocks to a steady state, are analyzed. Among other normative properties, it is established that under certain natural conditions, Nash equilibrium programs are efficient and “modified Pareto optimal”, in a sense made clear in the paper, but never Pareto optimal in the traditional sense.

Inequality as a Determinant of Malnutrition and Unemployment, II. Policy

(with Partha Dasgupta), Economic Journal 97, 177-188, 1987.

Summary. This is the second part of a two-part article which develops a theory of involuntary unemployment and the incidence of undernourishment, relates these in turn to the production and distribution of income, and ultimately to the distribution of productive assets. In this part, we study policy options such as land reform.

Nonpaternalistic Intergenerational Altruism

Journal of Economic Theory 41, 112-132, 1987.

Summary. The paper develops a concept of equilibrium behaviour in a model of nonpaternalistic intergenerational altruism. When each generation’s utility depends on that of at least two successors, equilibria may be inefficient.

Inequality as a Determinant of Malnutrition and Unemployment, I. Theory

(with Partha Dasgupta), Economic Journal 96, 1011-1034, 1986.

Summary. This is the first part of a two-part article which develops a theory of involuntary unemployment and the incidence of undernourishment, relates these in turn to the production and distribution of income, and ultimately to the distribution of productive assets. In this part, we study the general equilibrium of such a framework and describe its properties.