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Evolutionary games on networks traditionally involve the same game at eachinteraction. Here we depart from this assumption by considering mixed games,where the game played at each interaction is drawn uniformly at random from aset of two different games. While in well-mixed populations the random mixtureof the two games is always equivalent to the average single game, in structuredpopulations this is not always the case. We show that the outcome is in factstrongly dependent on the distance of separation of the two games in theparameter space. Effectively, this distance introduces payoff heterogeneity,and the average game is returned only if the heterogeneity is small. For higherlevels of heterogeneity the distance to the average game grows, which ofteninvolves the promotion of cooperation. The presented results support precedingresearch that highlights the favorable role of heterogeneity regardless of itsorigin, and they also emphasize the importance of the population structure inamplifying facilitators of cooperation.

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity