Evolutionary games: natural selection of strategies

TL;DR

This paper models the natural selection process among all mixed strategies in two-player, two-strategy games, generalizing the replicator equation and revealing that strategy evolution follows a principle of minimal information gain.

Contribution

It introduces a generalized replicator equation for mixed strategies and demonstrates that strategy evolution adheres to a minimum information gain principle.

Findings

Derived a generalized replicator equation for mixed strategies

Showed strategy evolution follows a minimum information gain principle

Analyzed the dynamics of pure and mixed strategy distributions

Abstract

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.