Endogenous networks, social games, and evolution

This paper studies a social game where agents choose their partners as well as their actions. Players interact with direct and indirect neighbors in the endogenous network. We show that the architecture of any nontrivial Nash equilibrium is minimally connected, and equilibrium actions approximate a symmetric equilibrium of the underlying game. We apply the model to analyze stochastic stability in 2 × 2 coordination games. We find that long-run equilibrium selection depends on a trade-off between efficiency and risk dominance due to the presence of scale effects arising from network externalities. Our results suggest a general pattern of equilibrium selection.