Memory retrieval and harshness of conflict in the hawk–dove game

Abstract

We study the long-run dynamics of a repeated non-symmetric hawk–dove type interaction between agents of two different populations. Agents choose a strategy based on their previous experience with the other population by sampling from a collective memory of past interactions. We assume that the sample size differs between populations and define a measure of harshness of conflict in the hawk–dove interaction. We then show how the properties of the long-run equilibrium depend on the harshness of conflict and the relative length of the sample. In symmetric interactions, if conflict is harsh, the population which samples relatively more past interactions is able to appropriate a higher payoff in the long-run, while the population with a relatively smaller sample does so if conflict is mild. These results hold subject to constraints on the sample size which we discuss in detail. We further extend our results to non-symmetric hawk–dove games.