The equilibrium-value convergence for the multiple-partners game

Chenghong Luo, David Perez-Castrillo and Chaoran Sun

Journal of Economic Theory, 2024, vol. 220, issue C

Abstract: We study the assignment game (Shapley and Shubik, 1972) and its generalization of the multiple-partners game (Sotomayor, 1992), the simplest many-to-many extension. Our main result is that the Shapley value of a replicated multiple-partners game converges to a competitive equilibrium payoff when the number of replicas tends to infinity. The result also holds for a large subclass of semivalues since we prove that they converge to the same value as the replica becomes large. Furthermore, in supermodular and monotonic assignment games, the asymptotic Shapley value coincides with the mean stable imputation. The proof of our theorem relies on Hall's theorem.

Keywords: Assignment game; Shapley value; Replica; Semivalues (search for similar items in EconPapers)
JEL-codes: C71 C78 D78 (search for similar items in EconPapers)
Date: 2024
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Working Paper: The Equilibrium-Value Convergence for the Multiple-Partners Game (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:220:y:2024:i:c:s0022053124000760

DOI: 10.1016/j.jet.2024.105870

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