The emergence of cooperation through leadership

We characterize stochastically stable states in noisy asynchronous repeated games. Players repeatedly play a 2 × 2 coordination game with random pairwise matching. The games are noisy because the players may make mistakes when choosing their actions and are asynchronous because only one player can move in each period. We show that if there is a sufficiently patient player, the efficient state can be the unique stochastically stable outcome even if it is risk-dominated. We argue that heterogeneity among the players in terms of their discount factors is important for our results because it enables the most patient player to take the leadership effectively. JEL classification: C72, C73.