SMU SOE Seminar Series (April 9, 2026): Limits of Global Games

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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 two-player, binary-action games with strategic complementarities - a property known as ``limit uniqueness.'' This paper describes the limits of that approach as we move beyond two actions. Unlike binary-action games, limit uniqueness is not an intrinsic feature of all games with strategic complementarities. 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.