Chapter 13 - Evolutionary games: Natural selection of strategies

Abstract

In this chapter, we model and analyze the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. We derive and solve an equation that is a natural generalization of the Taylor-Jonker replicator equation that describes dynamics of pure strategy frequencies. We then investigate the evolution of not only frequencies of pure strategies but also total distribution of mixed strategies. We show that the process of natural selection of strategies for all games obeys the dynamical principle of minimal information gain (see Chapter 8). We also show a principal difference between mixed-strategy hawk-dove (HD) game and all other 2×2 matrix games (prisoner's dilemma, harmony and stag hunt games). Mathematically, for HD game the limit distribution of strategies is nonsingular, and the information gain tends to a finite value, in contrast to all other games. Biologically the process of natural selection in the HD game follows non-Darwinian “selection of everybody,” while for all other games we observe Darwinian “selection of the fittest.”