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