  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.
