Evolutionarily stable payoff matrix in hawk–dove games

Király, Balázs and Varga, Tamás and Szabó, György and Garay, József (2024) Evolutionarily stable payoff matrix in hawk–dove games. BMC ECOLOGY AND EVOLUTION, 24 (1). ISSN 2730-7182

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Abstract

Background Classical matrix game models aim to fnd the endpoint of behavioural evolution for a set of fxed possible interaction outcomes. Here, we introduce an evolutionary model in which not only the players’ strategies but also the payof matrix evolves according to natural selection. Results We start out from the hawk–dove matrix game and, in a way that is consistent with the monomorphic model setup of Maynard Smith and Price, introduce an evolving phenotypic trait that quantifes fghting ability and determines the probability of winning and the cost of losing escalated hawk–hawk fghts. We defne evolutionarily stable phenotypes as consisting of an evolutionarily stable strategy and an evolutionarily stable trait, which in turn describes a corresponding evolutionarily stable payof matrix. Conclusions We fnd that the maximal possible cost of escalating fghts remains constant during evolution assuming a separation in the time scales of fast behavioural and slow trait selection, despite the fact that the fnal evolutionarily stable phenotype maximizes the payof of hawk–hawk fghts. Our results mirror the dual nature of Darwinian evolution whereby the criteria of evolutionary success, as well as the successful phenotypes themselves, are a product of natural selection.

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