A Unified Approach to Strategic Network Formation and Classical Matching Theory
15 Pages Posted: 5 Jun 2023
Date Written: May 18, 2023
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
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