The evolution of cooperation in mixed games

Cooperation has been studied in the context of game evolutionary theory by assuming that individuals play always the same game. Here we consider a mixture of two games G1G1 and G2G2. In each interaction of two individuals, they can play the games G1G1 or G2G2 with probabilities w   and 1-w1-w, respectively. We define the evolutionary model and study the cooperation evolution in a well-mixed population and in a cycle. We show that in the well-mixed population the evolution is equivalent to the evolution given by the average game. In a cycle, we show that the intensity of selection plays an important role in the promotion or inhibition of cooperation, depending on the games that are mixed.