A Unified Approach to Strategic Network Formation and Classical Matching Theory

Abstract

The literatures on network formation and matching have for the most part evolved independently from one another, despite addressing similar underlying questions. This paper offers a common framework. I study a general model of network formation without externalities — equivalently, a one-sided many-to-many matching model — giving conditions for the existence and uniqueness of stable graphs and proving a strong version of the rural hospital theorem. 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) provides a crucial tool, reducing a network formation game to a normal form with helpful properties.

Keywords: Network formation, matching, iterated deletion

JEL Classification: D85