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The equilibrium-value convergence for the multiple-partners game

Author

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  • Luo, Chenghong
  • Pérez-Castrillo, David
  • Sun, Chaoran

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.

Suggested Citation

  • Luo, Chenghong & Pérez-Castrillo, David & Sun, Chaoran, 2024. "The equilibrium-value convergence for the multiple-partners game," Journal of Economic Theory, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:jetheo:v:220:y:2024:i:c:s0022053124000760
    DOI: 10.1016/j.jet.2024.105870
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    Keywords

    Assignment game; Shapley value; Replica; Semivalues;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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