Strategy and sub-strategy dynamics in an evolutionary game
Hinke M. Osinga, and James A.R. Marshall
It has long been known in the field of population genetics that the equilibria attained by selection on a trait are not independent of the genetic bases of that trait. Whether one chooses to model selection acting on a single locus or multiple loci does matter. In evolutionary game theory, analysis of a simple and general game involving distinct roles for the two players has shown how correlated asymmetries can arise, in which one action is favoured in one role, but a different action in the other. The results of analysis of this game at the level of the entire strategy, or at the level of independent sub-strategies for the different roles, are in agreement, however. This is curious given the aforementioned population genetical results on the importance of the genetic bases of traits. Here we present a novel dynamical systems analysis of our game with roles, and show that while the stable equilibria in this game are unchanged according to whether one models selection on entire strategies, or independent selection for `genes' for different components of the strategies, equilibrium selection, however, may differ under the two modelling approaches. Our results are an evolutionary game theory counterpart to existing results from the population genetics literature.
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