Local Conventions in Game Play in an Evolving Dual Social Network Framework

People usually perform economic interactions within the social setting of a small group, while they obtain relevant information from a broader source. We capture this feature with a dynamic interaction model based on two separate social networks. Individuals play a coordination game in an interaction network, while updating their strategies using information from a separate influence network through which information is disseminated. In each time period, the interaction and influence networks co-evolve, and the individuals’ strategies are updated through a modified naive learning process. We show that both network structures and players’ strategies always reach a steady state, in which players form fully connected groups and converge to local conventions. We also analyze the influence exerted by a minority group of strongly opinionated players on these outcomes.