Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium

This paper revisits the minimum-effort coordination game with a continuum of Paretoranked Nash equilibria. Noise is introduced via a logit probabilistic choice function. The resulting logit equilibrium distribution of decisions is unique and maximizes a stochastic potential function. In the limit as the noise vanishes, the distribution converges to an outcome that is analogous to the risk-dominant outcome for 2×2 games. In accordance with experimental evidence, logit equilibrium efforts decrease with increases in effort costs and the number of players, even though these parameters do not affect the Nash equilibria. JEL Classifications: C72, C92