Evolutionary dynamics of multiple games

Evolutionary game theory has been successful in describing phenomena from bacterial population dynamics to the evolution of social behavior. Interactions between individuals are usually captured by a single game. In reality, however, individuals take part in many interactions. Here, we include multiple games and analyze their individual and combined evolutionary dynamics. A typical assumption is that the evolutionary dynamics of individual behavior can be understood by constructing one big comprehensive interactions structure, a single big game. But if any one of the multiple games has more than two strategies, then the combined dynamics cannot be understood by looking only at individual games. Devising a method to study multiple games - where each game could have an arbitrary number of players and strategies - we provide a concise replicator equation, and analyze its resulting dynamics. Moreover, in the case of finite populations, we formulate and calculate a basic and useful property of stochasticity, fixation probability. Our results reveal that even when interactions become incredibly complex, their properties can be captured by relatively simple concepts of evolutionary game(s) theory.