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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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.

Nash Bargaining with Coalitional Threats

(with Rajiv Vohra). March 2024. Supplementary Notes.

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).

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.