Strategic Interaction and Networks

Abstract

This paper brings a general network analysis to a wide class of games, including strategic innovation, public goods, investment, and social interactions. The major interest, and challenge, is seeing how network structure shapes outcomes. We have a striking result. Equilib- rium conditions depend on a single number: the lowest eigenvalue of a network matrix. When the graph is sufficiently tight (as measured by this eigenvalue), there is a unique equilibrium. When it is loose, stable equilibria always involve extreme play where some agents take no actions at all. We combine tools from potential games, optimization, and spectral graph theory to solve for all Nash and stable equilibria. This paper is the first to uncover the importance of the lowest eigenvalue to social and economic outcomes, and we relate this measure to different network link patterns.