Stochastic evolutionary dynamics of minimum-effort coordination games

The minimum-effort coordination game, having potentially important implications in both evolutionary biology and sociology, draws recently more attention for the fact that human behavior in this social dilemma is often inconsistent with the predictions of classic game theory. In the framework of classic game theory, any common effort level is a strict and trembling hand perfect Nash equilibrium, so that no desideratum is provided for selecting among them. Behavior experiments, however, show that the effort levels employed by subjects are inversely related to the effort costs. Here, we combine coalescence theory and evolutionary game theory to investigate this game in finite populations. Both analytic results and individual-based simulations show that effort costs play a key role in the evolution of contribution levels, which is in good agreement with those observed experimentally. Besides well-mixed populations, set structured populations, where the population structure itself is a consequence of the evolutionary process, have also been taken into consideration. Therein we find that large number of sets and moderate migration rate greatly promote effort levels, especially for high effort costs. Our results may provide theoretical explanations for coordination behaviors observed in real life from an evolutionary perspective.