Local Network Effects and Network Structure

This paper presents a model of local network effects in which agents connected in a social network each value adoption by a heterogeneous subset of others, and have incomplete information about the structure and strength of adoption complementarities between all other agents. I show that the symmetric Bayes-Nash equilibria of a general adoption game are in monotone strategies, can be strictly Pareto-ranked, and that the greatest equilibrium is uniquely coalition-proof. Each Bayes-Nash equilibrium has a corresponding fulfilled-expectations equilibrium under which agents form local-adoption expectations. Examples analyze three special cases including a standard model with completely connected agents, and characterize the distributions of equilibrium networks of adopters when the social network is an instance of a generalized random graph.