Asymmetric private information amplifies the difficulty for players to cooperate and achieve efficiency in strategic games. We give a new cooperative solution for two-player *Bayesian* strategic games, which takes into account both elements of cooperation and competition.

Under a revealed payoff assumption, we give a simple incentive-compatible, efficient mechanism that implements this solution. We argue that this solution gives the unique 'fair' value using the axiomatic approach.

Based on joint works with Adam Tauman Kalai and Ehud Kalai