Limits of Global Games
Abstract:
Games with strategic complementarities often exhibit multiple equilibria. In a global game, players privately observe a noisy signal of the underlying payoff matrix. As the noise diminishes, a unique equilibrium is selected in almost all binary-action games with strategic complementarities - a property known as "limit uniqueness.'' This paper describes the limits of that approach in two-player games, as we move beyond two actions. Unlike binary-action games, limit uniqueness is not an intrinsic feature of all games with strategic complementarities. When the noise is symmetric, we demonstrate that limit uniqueness holds if and only if the payoffs exhibit a generalized ordinal potential property. Moreover, we provide an example illustrating how this condition can be easily violated.