A Unified Approach to Strategic Network Formation and Classical Matching Theory
20 Pages Posted: 5 Jun 2023 Last revised: 10 Jul 2023
Date Written: May 18, 2023
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
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