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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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.

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.

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.