Gradual cooperation in the existence of outside options

The paper shows that efficient cooperation processes exhibit gradualism when each player does not know the likelihood that the other player exercises a stochastically available outside option. Two players, asymmetrically informed on this likelihood, play an infinitely repeated prisoner's dilemma game. Each player is either the high type with the high probability to obtain the outside option or the low type. As time proceeds with neither player exercising the outside option, each player puts more probability on the belief that his partner is the low type, enabling the players to raise cooperation levels in the efficient pooling equilibrium.