Strategic Interaction and Networks

Geography and social links shape economic interactions. In industries, schools, and markets, the entire network determines outcomes. This paper analyzes a large class of games and obtains a striking result. Equilibria depend on a single network measure: the lowest eigenvalue. This paper is the first to uncover the importance of the lowest eigenvalue to economic and social outcomes. It captures how much the network amplifies agents' actions. The paper combines new tools—potential games, optimization, and spectral graph theory—to solve for all Nash and stable equilibria and applies the results to R&D, crime, and the econometrics of peer effects.