Using chemical reaction network theory to show stability of distributional dynamics in game theory

This article shows how to apply results of chemical reaction network theory (CRNT) prove uniqueness and stability a positive equilibrium for pairs/groups distributional dynamics that arise in game theoretic models. Evolutionary assumes individuals accrue their fitness through interactions with other individuals. When there are two or more different strategies the population, this pairs (groups) formed instantaneously randomly so corresponding distribution is described by Hardy–Weinberg (binomial) distribution. If times phenotype dependent Hardy-Weinberg does not apply. Even if it becomes impossible calculate analytically we show CRNT general tool very useful only existence equilibrium, but also its stability. In article, pair formation model arises player games (e.g., Hawk-Dove, Prisoner's Dilemma game), group arises, e.g., Public Goods Game, single population patchy environments. We generalizing Battle Sexes methodology always