Repeated Games with Many Players; Takuo Sugaya (Stanford Graduate School of Business)

Abstract

Motivated by the problem of sustaining cooperation in large communities with limited information, we analyze sequences of repeated games with imperfect public monitoring where the population size N, discount factor c, and signal information K (which can measure either the cardinality of the signal space or the mutual information between signals and actions) vary together. We show that if (1 - ꞩ) N/K  —› ∞ then payoffs cannot exceed those consistent with approximately myopic play. If instead (1 - ꞩ) N log (N) /K —› 0 then a folk theorem holds under random auditing, where each player's action is monitored with the same probability in every period. Thus, up to log (N) slack, the prospects for cooperation are determined by the ratio of the discount rate r ≈ 1 - ꞩ and the per-capita information K/N, and there is no benefit of monitoring different players' actions "jointly." If attention is restricted to strongly symmetric equilibria, cooperation is possible only under much more severe parameter restrictions.

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