A Unified Approach to Strategic Network Formation and Classical Matching Theory

Abstract

Despite addressing similar underlying questions, the literatures on network formation and matching have evolved more or less independently. This paper offers a common framework, studying a general model of network formation without externalities---equivalently, a one-sided many-to-many matching model. I give conditions for the existence and uniqueness of stable graphs, I prove a rural hospital theorem, and I highlight a link-by-link conflict of interest across different stable graphs. Special cases contain and extend classic results for the roommate problem and two-sided matching markets. An iterated deletion algorithm adapted from Gutin et al. (2022) furnishes a crucial tool, reducing network formation games to a normal form with helpful properties.

Keywords: Network formation, matching, iterated deletion

JEL Classification: D85