Repeated Games with Many Players

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 \delta, 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-\delta) N/K \to \infty then payoffs cannot exceed those consistent with approximately myopic play. If instead (1-\delta) N/K \to 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\approx 1-\delta  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. 

You can read the full paper on the MIT website here.

Please email Konrad Mierendorff at k.mierendorff@ucl.ac.uk for the seminar link and password.