Network formation in symmetric 2 × 2 games

Abstract A population of players is considered in which each agent can select her neighbours in order to play a symmetric ×2 2 game with each of them. The result of the simultaneous neighbourhood choice of each agent is a network on the population form. We analyse all types of ×2 2 games and show how the payoff structure affects the resulting equilibrium networks. Depending on the size of the connection costs, these networks may be characterised by bipartite graphs if the game is of the Hawk/Dove type, while networks show a tendency to build complete or disconnected graphs if agents play a pure coordination game. Furthermore, for each ×2 2 game, we determine the equilibrium action distribution realised in the equilibrium networks