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