Abundance of strategies for trimatrix games in finite populations

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 charac-terized 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 so-cial 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 ei-ther 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.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this study, we investigate the consequences of stochastic evolutionary dynamics of trimatrix games in finite populations. We analyze the stationary distribution of strategy frequencies and apply the findings to specific games relevant to three-person social relationships. We compare our results with previous studies and find that strategies not supported by those studies are frequently observed in our dynamics. The implication for cooperative relationships is also discussed.