Local Network Effects and Network Structure

Abstract

This paper presents a model of local network effects in which agents 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. It shows that the symmetric Bayes-Nash equilibria of a general adoption game are in monotone strategies, can be strictly Pareto-ranked, and the greatest such equilibrium is uniquely coalition-proof. Each Bayes-Nash equilibrium has a corresponding fulfilled-expectations equilibrium under which agents form adoption expectations locally. Examples analyze social networks that are instances of a generalized random graph, and that are complete graphs (a standard model of network effects). The structure of the network of adopting agents is characterized as a function of the equilibrium played, and empirical implications of this characterization are discussed.