Games on Endogenous Networks

TL;DR

This paper develops a framework for analyzing network games where players choose both their connections and actions, revealing how incentive conditions shape stable network structures and their economic implications.

Contribution

It introduces a novel model combining link formation and action choices with solution concepts, providing a taxonomy of stable networks based on incentive conditions.

Findings

Stable networks are simple under certain incentive conditions.

Network structure depends on whether links create positive or negative spillovers.

The model explains phenomena like status competition and group formation effects.

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.