Local Network Effects and Complex Network Structure

This paper presents a model of local network effects in which agents connected in a social network each value the adoption of a product by a heterogeneous subset of other agents in their neighborhood, 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 this network game are in monotone strategies, can be strictly Pareto-ranked based on a scalar neighbor-adoption probability value, and that the greatest such equilibrium is uniquely coalition-proof. Each Bayes-Nash equilibrium has a corresponding fulfilled-expectations equilibrium under which agents form local adoption expectations. Examples illustrate cases in which the social network is an instance of a Poisson random graph, when it is a complete graph, a standard model of network effects, and when it is a generalized random graph. A generating function describing the structure of networks of adopting agents is characterized as a function of the Bayes-Nash equilibrium they play, and empirical implications of this characterization are discussed.