Games on Endogenous Networks

Abstract: We study network games in which players choose both the partners with whom they associate and an action level (e.g., effort) that creates spillovers for those partners. We introduce a framework and two solution concepts, extending standard approaches for analyzing each choice in isolation: Nash equilibrium in actions and pairwise stability in links. Our main results show that, under suitable order conditions on incentives, stable networks take simple forms. The first condition concerns whether links create positive or negative payoff spillovers. The second concerns whether actions are strategic complements to links, or strategic substitutes. Together, these conditions yield a taxonomy of the relationship between network structure and economic primitives organized around two network architectures: ordered overlapping cliques and nested split graphs. We apply our model to understand the consequences of competition for status, to microfound matching models that assume clique formation, and to interpret empirical findings that highlight unintended consequences of group design.