  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.
