Dynamic Games on Networks with Heterogeneous Players

We study dynamic network games with two types of players (i.e., heterogeneous players) characterized by their different intrinsic preferences. Instead of calculating the Nash equilibrium, we focus on the asymptotic behavior of an asynchronous best response dynamics. We develop a dynamic approach that can predict the evolutionary trend of the best response dynamics and estimate the equilibrium frequencies of strategies for asymmetric games with arbitrary payoff values and network structures. We highlight the importance of the network homophily index in the strategy evolution. For games with strategic complements, a lower homophily index promotes coordination. In contrast, games with strategic substitutes have a unique stable equilibrium for a higher homophily index and have two stable equilibria for a low homophily index. Finally, for games with a mixture of strategic complements and strategic substitutes, a lower homophily index in general promote cyclic behaviors and inhibits the existence of stable equilibrium. We then apply this method to analyze the influence of social networks on the election. We show that the electoral strategies for the majority party and the minority party are different, where the majority party can benefit by tearing the network connections between its own supporters and the supporters of the minority party