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.
(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.
(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).