Summary. Recent literature in the theory of dynamic games addresses renegotiatioin-proof equilibria, For repeated games, I analyze the limit of renegotiation-proof equilibrium sets as discounting vanishes. The main result states that such limit sets must either be singletons or belong to the Pareto frontier of the convex hull of the feasible set of the stage game payoffs.
(with Rajiv Vohra), in Handbook of Game Theory Vol 4 (H.P. Young and S. Zamir, eds), Elsevier North Holland, 2014.
Summary. This chapter surveys a sizable and growing literature on coalition formation. We refer to theories in which one or more groups of agents (“coalitions”) deliberately get together to jointly determine within-group actions, while interacting noncooperatively across groups. The chapter describes a variety of solution concepts, using an umbrella model that adopts an explicit real-time approach. Players band together, perhaps disband later and re-form in shifting alliances, all the while receiving payoffs at each date according to the coalition structure prevailing at the time. We use this model to nest two broad approaches to coalition formation, one based on cooperative game theory, the other based on noncooperative bargaining. Three themes that receive explicit emphasis are agent farsightedness, the description of equilibrium coalition structures, and the efficiency implications of the various theories.
(with Doug Bernheim), Review of Economic Studies 54, 227-243, 1987.
Summary. We consider the properties of equilibrium behavior in an aggregative growth model with intergenerational altruism. Various positive properties such as the cyclicity of equilibrium programs, and the convergence of equilibrium stocks to a steady state, are analyzed. Among other normative properties, it is established that under certain natural conditions, Nash equilibrium programs are efficient and “modified Pareto optimal”, in a sense made clear in the paper, but never Pareto optimal in the traditional sense.