Adaptive agents on evolving networks

We propose a model of strategic network formation in repeated games where players adopt actions and connections simultaneously using a simple reinforcement learning scheme. We demonstrate that under certain plausible assumptions the dynamics of such systems can be described by so called replicator equations that characterize the co-evolution of agent strategies and network topology. Within this framework, the network structures emerging as a result of the game-dynamical interactions are described by the stable rest points of the replicator dynamics. In particular, we show using both simulations and analytical methods that for certain N-agent games the stable equilibria consist of star motifs as the main building blocks of the network.