Coordination Failures under Incomplete Information and Global Games

Carlsson and van Damme (1991, 93) presented a notion of a global game, which is an incomplete information game where the actual payoff structure is affected by a realization of a common shock and where each player gets noisy private information of the shock. For n -person symmetric games with two possible actions characterized by strategic complementarity, they showed that equilibrium play in a global game with vanishing noise is uniquely determined. The concept of global games is important not only as a theory of the most refined notion of equilibrium but also as a theory of coordination failures under private information. From this viewpoint, this paper makes the theory of global games more general and more applicable to such problems. The implications of the theory of global games are investigated in two specific models: a speculative attack model and a network externality model. It is shown that both the monetary authority in the speculative attack model and the central planner in the network externality model will prefer the equilibrium in a global game with small noise to the worst equilibrium in the corresponding complete information game. Therefore, they will welcome the existence of small noise, if they apply mini-max principle to multiple equilibrium problems.