Repeated games with many players

Motivated by the problem of sustaining cooperation in large groups with limited information, we analyze the relationship between group size, monitoring precision, and discounting in repeated games with independent, player-level noise. The viability of cooperation under independent noise is linked to the per-capita channel capacity of the stage game monitoring structure. We show that cooperation is impossible if the per-capita channel capacity is much smaller than the discount rate. A folk theorem under a novel identification condition provides a near converse. If attention is restricted to co-linear equilibria (a generalization of strongly symmetric equilibria), cooperation is possible only under much more severe parameter restrictions.