For the pairwise interactions, the evolution of individual behavior should involve two major factors: one is what you will do in an interaction with a given opponent, and another is what type of opponents you prefer to interact with. In this study, we developed a two-phenotype iterated bimatrix replicator dynamics model based on individuals' own volition, where, different from the classic iterated game model, we assume that (i) for all interaction pairs, the maximum expected interaction time is same and it is limited even if two individuals in an interaction pair would like to keep their interaction; and (ii) all individuals are able to unilaterally break off the interactions with their opponents according to their own volition. Therefore, we define that, at any time t, an interaction pair will be disbanded with a given probability and the new interaction pairs will be randomly formed. The main results show that: (i) the existence of locally asymmetrically stable interior equilibrium is possible; and (ii) the evolutionary stability of the system is similar to the classic asymmetric evolutionary game. These results may provide a new insight for revealing the evolutionary significance of asymmetric game dynamics.
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