Pareto-Optimal Nash Equilibria are Competitive in a Repeated Economy

Mordecai Kurz and Sergiu Hart


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Abstract
Consider a finite exchange economy first as a static, 1 period, economy and then as a repeated economy over T periods when the utility of each agent is the mean utility over T. A family of strategic games is defined via a set of six general properties the most distinct of which is the ability of agents to move commodities forward in time. Now consider Pareto optimal allocations in the T period economy which are also Nash equilibria in this family of strategic games. We prove that as T becomes large this set converges to the set of competitive utility allocations in the one period economy. The key idea is that a repetition of the economy when agents can move commodities forward in time acts as a convexification of the set of individually feasible outcomes for player i holding all other strategies fixed.

Journal of Economic Literature Classification Numbers: 021, 022.