Evolutionary game dynamics in a growing structured population

Abstract

We discuss a model for evolutionary game dynamics in a growing,\nnetwork-structured population. In our model, new players can either make\nconnections to random preexisting players or preferentially attach to those\nthat have been successful in the past. The latter depends on the dynamics of\nstrategies in the game, which we implement following the so-called Fermi rule\nsuch that the limits of weak and strong strategy selection can be explored. Our\nframework allows to address general evolutionary games. With only two\nparameters describing the preferential attachment and the intensity of\nselection, we describe a wide range of network structures and evolutionary\nscenarios. Our results show that even for moderate payoff preferential\nattachment, over represented hubs arise. Interestingly, we find that while the\nnetworks are growing, high levels of cooperation are attained, but the same\nnetwork structure does not promote cooperation as a static network. Therefore,\nthe mechanism of payoff preferential attachment is different to those usually\ninvoked to explain the promotion of cooperation in static, already-grown\nnetworks.\n