Repeated games with probabilistic horizon

Repeated games with probabilistic horizon are those games where players have a common probability structure over the length of the game's repetition, T. In particular, for each t, players assign a probability pt to the event that “the game ends in period t”, such that ∑t≥1pt=1, i.e., the game ends in a finite number of periods. In this framework, we analyze the pure strategy equilibrium outcomes of the repetition of both finite and differentiable Generalized Prisoners' Dilemma stage games. We show that it is possible to reach cooperation under some conditions on the distribution of the discrete random variable T even if the expected length of the game is finite.