The equilibrium-value convergence for the multiple-partners game

• 成果类型: Article
• 署名作者: Luo, Chenghong; Perez-Castrillo, David; Sun, Chaoran
• 署名单位: Shanghai University of International Business & Economics; Autonomous University of Barcelona; Shanghai University of International Business & Economics
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2024.105870
• 发表日期: 2024
• 关键词: Assignment game; Shapley value; Replica; Semivalues

摘要

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.