Stag Hunt with Unknown Outside Options

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We study the well known Stag Hunt game where two players simultaneously decide whether to cooperate or not. Each player's type is his outside option in the case where he decides not to cooperate. The types are private information and independently drawn from a continuous distribution. We provide a class of type distributions (including the uniform distribution) and prove that if with su ciently small probability players bene t from their outside options more than from their cooperation, then (i) in a oneshot interaction with probability 1 cooperation is not achieved, (ii) but if the players may meet twice, with probability close to 1 cooperation can be achieved and already in the rst period, and (iii) the above is true even if the probability of meeting twice is arbitrarily small.

 Joint work with Yair Tauman and Chang Zhao.

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