Network effects on coordination in asymmetric games

Abstract

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.

Nash Equilibria in the Response Strategy of Correlated Games

“…While extensive research has been done to study how humans behave when they play games on networks, particularly through simulations 10,32,33 and experiments 32,34,35 , we hope to provide analytical insight into these systems, since for the two-player game the renormalized probabilities of the optimal Nash equilibrium are equivalent to a two-site Ising model in a magnetic field. To this effect, we show how the players can introduce an energy parameter to change the Hamiltonian to effectively obtain the renormalized probabilities.…”

An experimental study of network effects on coordination in asymmetric games

“…These situations are often formalized by asymmetric coordination games, such as the ‘battle of the sexes’. Computational models 9,10 and other theoretical studies 11,12 show that network structure is an important predictor of behavior in iterated asymmetric games. Although these models convincingly show that there are network effects on equilibrium behavior, no empirical studies have been conducted to corroborate these findings.…”

“…In this study we empirically test behavioral predictions from previous computational 9,10 and theoretical studies 11,12 ; specifically, we consider the influence of network structure on equilibrium behavior in iterated asymmetric ‘battle of the sexes’ games. We focus on the computational model described in Broere et al .…”

“…We focus on the computational model described in Broere et al . 9 . In this study nodes play iterated 2 × 2 games with their neighbors.…”

“…It is therefore crucial to test the predictions and assumptions made by these models. In this paper we empirically test predictions made by computational and theoretical studies in an experimental study with human subjects 9–12 .…”