This paper studies a wide class of games, representing many different economic environments. In all games, best replies are linear. We use a graph to capture strategic interactions between different players: a player?s payoff is impacted directly by another player if and only if they are linked. Because linked players interact with other linked players, the equilibrium outcomes depend on the entire network structure. We provide a general analysis of Nash and stable equilibria for any network pattern. We construct an algorithm to find all Nash equilibria and show that all equilibrium play is characterized by players? centrality in the network. We derive conditions on the graph structure for unique, corner, and stable equilibria. In strategic substitutes games, equilibria are stable only when the graph connecting active agents is sufficiently absorptive. Except for small payoff impacts, stable equilibria always involve extreme play: some agents take no actions at all. Thus restricting attention to interior equilibria may be misleading. We also tackle comparative statics for strategic substitutes and find aggregate play always decreases as links are added to a network. To derive our results, we use a new combination of optimization, potential games, and spectral graph theory.

http://econ.duke.edu/~rek8/strategicinteractionandnetworksfinalapril2009.pdf