Repeated Games with Asymptotically Finite Horizon and Imperfect Public Monitoring

We consider a two-player infinitely repeated game with asymptotically finite horizons: discount factors converge to zero over time. The stage-game has a continuum of actions and a unique and interior Nash equilibrium. It is known that when players perfectly observe each oth- ers actions, cooperation can be achieved and equilibrium payoffs will be strictly higher than the stage-game equilibrium payoff. I show that introducing an arbitrarily small amount of smooth noise in the monitoring makes cooperation impossible and players play the static Nash equilibrium of the stage-game forever.