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Strong Nash Implementation of the Weak Core in Simple Strong Cooperative Games

Author

Listed:
  • Mohamed Bouchta

    (INSEA - Institut National de Statistique et d’Economie Appliquée [Rabat])

  • Ahmed Doghmi

    (INSEA - Institut National de Statistique et d’Economie Appliquée [Rabat])

  • Abderrahmane Ziad

    (UNICAEN - Université de Caen Normandie - NU - Normandie Université, CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, UFAS1 - Université Ferhat-Abbas Sétif 1 [Sétif])

Abstract

In this paper, we consider simple cooperative games with winning coalitions that satisfy three natural assumptions: monotonicity, non-emptiness, and inverse consistency. We investigate the implementability of the weak core in two cases: when there are at least two agents under strong Nash equilibria, and when there are exactly two agents under Nash equilibria. To achieve this, we use a strong version of Maskin monotonicity, introduced by Yi [2012], which we call Y-monotonicity. We demonstrate that, when combined with unanimity, this property is sufficient for implementation in both cases. Based on this result, we extend the findings of Shinotsuka and Takamiya [2003] on the implementability of the weak core in our setting, moving from Nash equilibrium to strong Nash equilibrium for at least three agents, while also addressing the case with two agents. Finally, we relate our results to the existing literature on the existence of the weak core.

Suggested Citation

  • Mohamed Bouchta & Ahmed Doghmi & Abderrahmane Ziad, 2025. "Strong Nash Implementation of the Weak Core in Simple Strong Cooperative Games," Post-Print hal-05107314, HAL.
    • Handle: RePEc:hal:journl:hal-05107314
    DOI: 10.3917/redp.351.0039
    as

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