Julius Silver Professor, Faculty of Arts and Science, and
Professor of Economics, New York University
Research Associate, NBER
Part-Time Professor, University of Warwick
Council Member, Game Theory Society
Research Fellow, CESifo
Board Member, BREAD and ThReD
Researcher in Residence, ESOP

Department of Economics, NYU, 19 West 4th Street
New York, NY 10012, U.S.A.
debraj.ray@nyu.edu, +1 (212)-998-8906.

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Oxford University Press, 2008. This book is now open-access; feel free to download a copy, and to buy the print version if you like the book.
≋ Three Randomly Selected Papers
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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.

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.

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.