Unpublished and Working Papers

Displaying 13 Items

Maximality in the Farsighted Stable Set

(with Rajiv Vohra), December 2017, revised September 2018.

SummaryThe stable set of von Neumann and Morgenstern was 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. 

Games of Love and Hate

(with Rajiv Vohra), September 2018.

Dedicated to Tapan Mitra — advisor, colleague and dear friend. Tapanda, your sense of aesthetics, minimalism and rigor has been an inspiration to us. We hope you will find some reflection of it in these pages.

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.

 

 

Noisy Agents

(with Francisco Espinosa), July 2018. Supplementary Appendix.

SummaryAgents signal their type in a principal-agent model; the principal seeks to retain good agents. Types are signaled with some ambient noise. Agents can choose to add or remove additional noise at a cost. It is shown that monotone retention strategies, in which the principal keeps the agent if the signal crosses some threshold, are generically never equilibria. The main result identifies an equilibrium with a bounded retention zone, in which the principal is wary of both excessively good and excessively bad signals: she retains the agent if the signal is “moderate” and replaces him otherwise. 

Missing Unmarried Women

(with Siwan Anderson), February 2018, forthcoming, Journal of the European Economic Association.

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.

Hedonistic Altruism and Welfare Economics

August 2013, revised February 2018.

Summary. When future generations enter hedonistically into current welfare, a social planner should overweight the future relative to the individual, even if every individual has the same discount factor.

Groups in Conflict: Size Matters, But Not In The Way You Think

(with Laura Mayoral), December 2017.

Summary. This paper studies costly conflict over private and public goods. Oil is an example of the former, political power an example of the latter. Groups involved 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 an empirical setting

Capital and Inequality in the Long Run: Automation Without Technical Progress

(with Dilip Mookherjee), December 2017.

Summary. We present a theory of long run inequality and automation driven by capital accumulation rather than technical progress. At the heart of the theory is a singularity condition that guarantees automation in the production of automated technologies. If that condition is satisfied, the functional share of capital approaches 100% in the long run.

Backward Discounting

(with Nikhil Vellodi and Ruqu Wang), March 2018. Online Appendix.

SummaryWe study a model of time preferences in which agents discount both past and future payoffs to obtain their lifetime felicity. Agents derive utility from their current lifetime felicity, as well the anticipated felicity of a distinguished future self. These postulates permit an agent to anticipate future regret in current decisions, and generate a set of novel testable implications in line with empirical evidence. 

Information Aggregation with Heterogeneous Traders

(with Sahar Parsa), February 2017.

Summary. After the main theorem in this paper was proved, we came across Hellwig (1980), which is motivated by exactly the same considerations and proves the same result as our Theorem 2, except that our model allows for general signal structures with arbitrary covariances and asymmetries. Despite the significant additional generality, we fully appreciate Hellwig’s contribution and do not intend to publish these notes. We simply put up the results and proofs here in the hope that the approach here (which is quite distinct) will be useful to others working in the field. We intend to take these methods in other directions as well.

Apples and Oranges: Building a Better Dow

(with Rajiv Sethi), August 2012.

Summary. The Dow relies on price-weighting, which is decidedly an odd methodology. We propose a bridging process that generates convergence to a value-weighted index without compromising the historical continuity of the Dow.

Costly Conflict Under Complete Information

unpublished manuscript, June 2009.

Summary. This paper studies costly conflict in a world of complete information, in which society can commit to divisible transfers among all potentially warring groups. The difficulty in preventing conflict arises from the possibility that there may be several conflictual divisions of society, each based on a different marker, such as class, geography, religion, or ethnicity. It is shown that this diversity of societal markers is particularly conducive to social instability when potential conflict is over private, divisible resources. In contrast, when conflict is over public goods, such diversity promotes social stability.