Evolutionary games: natural selection of strategies

In this paper, I model and study the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. I derive and solve an equation that is a natural generalization of the Taylor-Jonker replicator equation that describes dynamics of pure strategy frequencies. I then investigate the evolution of not only frequencies of pure strategies but also of total distribution of mixed strategies. I show that the process of natural selection of strategies for all games obeys the dynamical Principle of minimum of information gain. It is also shown a principle difference between mixed-strategies Hawk-Dove (HD) game and all other games (Prisoner’s Dilemma, Harmony and Stag-Hunt games). Mathematically, the limit distribution of strategies is non-singular and the information gain tends to a finite value for HD-game, in contrast with all other games. Biologically, the process of natural selection in HD-game follows non-Darwinian “selection of everybody” but for all other games we observe Darwinian “selection of the fittest”. Introduction. Problem formulation Mathematical game theory was initially developed for economic and social problems to make predictions about how different behavioral strategies can affect individuals’ behavior