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The Equilibrium-Value Convergence for the Multiple-Partners Game

Author

Listed:
  • Chenghong Luo
  • David Pérez-Castrillo
  • Chaoran Sun
Abstract
We study the multiple-partners game (Sotomayor, 1992), the simplest many-to- many generalization of the assignment game. 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. Furthermore, 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. In the proof of our theorem, we use properties of the “multiple-partners game with types,” where several agents are of each type. We show, in particular, that every competitive equilibrium outcome of a “large” game with types satisfies equal treatment of equals and equal treatment of partnerships.

Suggested Citation

  • Chenghong Luo & David Pérez-Castrillo & Chaoran Sun, 2023. "The Equilibrium-Value Convergence for the Multiple-Partners Game," Working Papers 1400, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1400
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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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