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We study infinitely repeated games in settings of imperfect monitoring. Wefirst prove a family of theorems that show that when the signals observed bythe players satisfy a condition known as $(\epsilon, \gamma)$-differentialprivacy, that the folk theorem has little bite: for values of $\epsilon$ and$\gamma$ sufficiently small, for a fixed discount factor, any equilibrium ofthe repeated game involve players playing approximate equilibria of the stagegame in every period. Next, we argue that in large games ($n$ player games inwhich unilateral deviations by single players have only a small impact on theutility of other players), many monitoring settings naturally lead to signalsthat satisfy $(\epsilon,\gamma)$-differential privacy, for $\epsilon$ and$\gamma$ tending to zero as the number of players $n$ grows large. We concludethat in such settings, the set of equilibria of the repeated game collapse tothe set of equilibria of the stage game.

An Anti-Folk Theorem for Large Repeated Games with Imperfect Monitoring