Abundance of strategies for trimatrix games in finite populations

Abstract

In this study, we aim to capture the consequences of stochastic evolutionary dynamics of trimatrix games in finite populations from the viewpoint of strategy abundances characterized by the stationary distribution of strategy frequencies. We then apply the obtained general result to some specific games that are important to consider the three-person social relationships. We investigate which set of strategies is most likely to be observed in evolutionary dynamics. Furthermore, we compare between the results of this study and those of previous studies relying on the concepts of ‘subgame perfection’ and ‘fixation probability.’ As a result, we find that sets of strategies, which are not supported by either of those previous studies, can be most frequently observed in our dynamics. Besides, the implication of the present result for the establishment of cooperative relationships is also discussed.