Decentralized learning from failure

We study decentralized learning in organizations. Decentralization is captured through Crawford and Haller's [Learning how to cooperate: optimal play in repeated coordination games, Econometrica 58 (1990) 571-595] attainability constraints on strategies. We analyze a repeated game with imperfectly observable actions. A fixed subset of action profiles are successes and all others are failures. The location of successes is unknown. The game is played until either there is a success or the time horizon is reached. We partially characterize optimal attainable strategies in the infinite horizon game by showing that after any fixed time, agents will occasionally randomize while at the same time mixing probabilities cannot be uniformly bounded away from zero.