Network Formation in Symmetric 2x2 Games

A population of players is considered in which each agent can select her neighbors in
order to play a symmetric 2£2 game with each of them. The result of the simultaneous
neighborhood choice of each agent is a network on the population from. We analyze all
types of 2 £ 2 games and show how the payo® structure in the 2 £ 2 games a®ects the
resulting equilibrium networks. Depending on the size of the communication costs the
resulting equilibrium networks may be characterized by bipartite graphs if the coordina-
tion 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 strategy distribution which is realized in the
equilibrium networks.