Evolution via imitation among like-minded individuals

TL;DR

This paper introduces a model of evolutionary game dynamics among like-minded individuals in heterogeneous populations, showing how slight differences in payoff matrices can lead to divergent stable strategies.

Contribution

It develops a multipopulation replicator dynamics model that captures imitation within subpopulations with similar preferences, revealing unique stability properties.

Findings

No internal equilibrium exists in the model.

Small payoff differences can cause opposite strategies to be stably adopted.

Dynamics differ significantly from bimatrix game models.

Abstract

In social situations with which evolutionary game is concerned, individuals are considered to be heterogeneous in various aspects. In particular, they may differently perceive the same outcome of the game owing to heterogeneity in idiosyncratic preferences, fighting abilities, and positions in a social network. In such a population, an individual may imitate successful and similar others, where similarity refers to that in the idiosyncratic fitness function. I propose an evolutionary game model with two subpopulations on the basis of multipopulation replicator dynamics to describe such a situation. In the proposed model, pairs of players are involved in a two-person game as a well-mixed population, and imitation occurs within subpopulations in each of which players have the same payoff matrix. It is shown that the model does not allow any internal equilibrium such that the dynamics differs from that of other related models such as the bimatrix game. In particular, even a slight difference in the payoff matrix in the two subpopulations can make the opposite strategies to be stably selected in the two subpopulations in the snowdrift and coordination games.