Theoretical analyses of stochastic evolutionary game systems

Abstract

Evolutionary game theory is a powerful tool for studying the frequency-dependent selection, where the success of one strategy depends on the frequency of all strategies. The classic theoretical approach is the replicator equation, where the strategy evolution is deterministic for infinitely large populations. However for the stochastic evolutionary systems of finite populations, one of the most difficult obstacles lies in making qualitative or quantitative analytical deductions about evolutionary outcomes. In this paper, we present a brief yet important report about quantitative analytical methods for finite-size evolutionary game systems, from the two perspectives of how to calculate fixation probabilities and stationary frequencies. Importantly, we not only review some crucial developments about theoretical approaches which were achieved in this field but also put forward two remarkable prospects for further research.