Coordination and growth: the Stag Hunt game on evolutionary networks

Recently, the study of evolutionary games on networks has attracted great interest, focused mainly on the problem of the emergence of cooperation. A well studied framework for this problem is the Prisoner's Dilemma game on fixed, evolving or growing networks. In this paper we present a complete picture of the behavior of another important social dilemma, the Stag Hunt game, under an evolutionary preferential attachment model, in which the network grows according to the dynamical states of the elements of the system. We observe the emergence of a scale-free and hierarchical organization of the strategies according to connectivity classes as a by-product of the diffusion of cooperation in the network. Depending on the parametrization of the game dynamics, we find a smooth transition from cooperation to defection and a polymorphic state with simultaneous presence of cooperator and defector hubs, which is very unusual in coordination games.