Probabilistic cheap talk

We consider a model in which there is uncertainty over when a one-shot game will be played. We show how a mechanism designer can implement desirable outcomes in certain economic games by manipulating only the probability that the game is played in a given round while leaving all other aspects of the game unchanged. We also show that if there is no discounting, this uncertainty imparts a sequential structure that is almost mathematically equivalent to a repeated version of the game with discounting. In particular, a folk theorem applies to such games. Thus, games of probabilistic cheap provide a third interpretation of the repeated game framework with the additional feature that expected payoff is invariant to the probability of the game ending.