(with Jon Bendor and Dilip Mookherjee), Advances in Theoretical Economics1, 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.
(with Parikshit Ghosh), Review of Economic Studies63, 491–519, 1996.
Summary. We study cooperative behavior in communities where the flow of information regarding past conduct is limited or missing. Players are initially randomly matched with no knowledge of each other’s past actions; they endogenously decide whether or not to continue
the repeated relationship. We define social equilibrium in such communities. Such equilibria
are characterized by an initial testing phase, followed by cooperation if the test is successful. It is precisely the presence of myopic types that permit cooperation, by raising barriers to entry into new relationships.
(with Tapan Mitra), Journal of Economic Theory147, 833–849, 2012.
Summary. We examine whether the Phelps–Koopmans theorem is valid in models with nonconvex production technologies. Dedicated to the memory of David Cass: mentor, friend and an extraordinary economic theorist.
