Efficiency Gains in Repeated Games at Random Moments in Time

This paper studies repeated games where the time of repetitions of the stage game is not known or controlled by the players. Many economic situations of interest where players repeatedly interact share this feature, players do not know exactly when is the next time they will be called to play again. We call this feature random monitoring. We show that perfect random monitoring is always superior to perfect deterministic monitoring when players discount function is convex in time domain. Surprisingly when the monitoring is imperfect but public the result does not extend in the same absolute sense. The positive effect in the players discounting is not sufficient to compensate for a larger probability of punishment for all frequencies of play. However, we establish conditions under which random monitoring allows efficiency gains on the value of the best strongly symmetric equilibrium payoffs, when compared with the classic deterministic approach.