(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.
Summary. We revisit Nash’s axiomatic bargaining solution when coalitions employ threats that must be consistent with their solutions. As in Nash, our solution maximizes a (possibly weighted) product of payoffs for each coalition, but subcoalitional threats appear as conventional constraints that are not netted out when maximizing the Nash product. We study different aspects of this coalitional solution, including its connections to a notion of “pragmatic egalitarianism”. We then embed the solution into a setting with externalities, and define viable coalitional structures, under which every coalition follows its coalitional solution but interacts noncooperatively with other coalitions. We discuss applications to public goods, R&D coalitions, oligopoly cartels, and hospital networks.
(with Joan Esteban), American Economic Review 98:5, 2185–2202, 2008. Online Appendix.
Summary. “In much of Asia and Africa, it is only modest hyperbole to assert that the Marxian prophecy has had an ethnic fulfillment.” — Donald Horowitz (1985).
