DP17084 Community Formation in Networks
We study a strategic model of community formation on networks. Starting from a seed community member, the process of community formation is sequential, with infinitely-patient and forward-looking agents making strategic offers to their neighbours. Each agent makes an irreversible binary choice, and each time she accepts an offer, she joins the community. For arbitrary payoffs, there is essentially a unique subgame perfect equilibrium, which maximizes the payoff of the seed. Next, we assume that the payoffs are a function of the community and neighbourhood sizes. This allows us to pin down the different types of communities that emerge in the equilibrium. Such equilibrium communities are a direct function of the monotonicity -positive or negative- of payoffs in community and neighbourhood sizes. Finally, we examine the impact of a key-player policy on the formation of communities and how denser networks affect the welfare of the equilibrium communities. Our results are informative for several economic situations in which the formation of communities is salient.