Evolutionary path from a prisoner's dilemma to a harmony game via hawk-dove games

In most evolutionary matrix game models, the payoffs are assumed to be constant. Here, we develop a toy model of hunting in pairs in which interaction outcomes are determined not only by the behavioural strategy choice of the players but also a second, evolvable physical trait of them. We analyse the evolutionary dynamics of this model in a limiting case of the classical monomorphic framework introduced by Maynard Smith and Price characterised by rare mutations in physical trait, moderately frequent mutations in behaviour, and very fast selection in both. We show that this process can transform the evolutionarily stable strategy and, as a result, even the nature of the game played in the population: We present an illustrative numerical example in which the concurrent evolution of the behavioural and trait components of the phenotype turns a social dilemma into a harmony game via an intermediate phase of coexistence.