This paper studies the repeated prisoner’s dilemma with private monitoring for arbitrary number of players. It is shown that a mixture of a grim trigger strategy and permanent defection can achieve an almost efficient outcome for some range of discount factors if private monitoring is almost perfect and the number of players is large. This result also holds when the number of players is two for any prisoner’s dilemma as long as monitoring is almost perfect and symmetric. A detailed characterization of this sequential equilibrium is provided.