Network effects on coordination in asymmetric games

Network structure can have an important effect on the behavior of players in an iterated 2 × 2 game. We study the effect of network structure on global and local behavior in asymmetric coordination games using best response dynamics. We find that global behavior is highly dependent on network topology. Random (Erdös-Rényi) networks mostly converge to homogeneous behavior, but the higher the clustering in the network the more heterogeneous the behavior becomes. Behavior within the communities of the network is almost exclusively homogeneous. The findings suggest that clustering of networks facilitates self-organization of uniform behavior within clusters, but heterogeneous behavior between clusters. At the local level we find that some nodes are more important in determining the equilibrium behavior than other nodes. Degree centrality is for most networks the main predictor for the behavior and nodes with an even degree have an advantage over nodes with an uneven degree in dictating the behavior. We conclude that the behavior is difficult to predict for (Erdös-Rényi) networks and that the network imposes the behavior as a function of clustering and degree heterogeneity in other networks.