Repeated minimum-effort coordination games

We consider the repeated minimum-effort coordination game where each player follows an adaptive strategy in each period and his choice is made via the logit probability distribution. We find that there exists a stable probability distribution of the minimum effort levels (called the equilibrium of the game), and the expected value of the minimum effort levels at the equilibrium has the same comparative-statics properties as in the experimental outcomes of Van Huyck et al. (Am Econ Rev 80(1):234–248 1990): it decreases with the effort cost and the number of players. We also find that the expected value at the equilibrium responds differently to the noise parameter, contingent on the effort-cost structure. This provides us with an implication about how we could increase the coordination among the players.