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Nonempty Core-Type Solutions Over Balanced Coalitions In Tu-Games

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  • JUAN C. CESCO

    (IMASL, CONICET-UNSL, Av. Ejército de los Andes 950, San Luis, 5700 San Luis, Argentina)

Abstract

In this paper we introduce two related core-type solutions for games with transferable utility (TU-games) the$\mathcal{B}$-core and the$\mathcal{M}$-core. The elements of the solutions are pairs$(x, \mathcal{B}), $wherex, as usual, is a vector representing a distribution of utility and$\mathcal{B}$is a balanced family of coalitions, in the case of the$\mathcal{B}$-core, and a minimal balanced one, in the case of the$\mathcal{M}$-core, describing a plausible organization of the players to achieve the vectorx. Both solutions extend the notion of classical core but, unlike it, they are always nonempty for any TU-game. For the$\mathcal{M}$-core, which also exhibits a certain kind of "minimality" property, we provide a nice axiomatic characterization in terms of the four axioms nonemptiness (NE), individual rationality (IR), superadditivity (SUPA) and a weak reduced game property (WRGP) (with appropriate modifications to adapt them to the new framework) used to characterize the classical core. However, an additional axiom, the axiom of equal opportunity is required. It roughly states that if$(x, \mathcal{B})$belongs to the$\mathcal{M}$-core then, any other admissible element of the form$(x, \mathcal{B}^{\prime})$should belong to the solution too.

Suggested Citation

  • Juan C. Cesco, 2012. "Nonempty Core-Type Solutions Over Balanced Coalitions In Tu-Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 1-16.
    • Handle: RePEc:wsi:igtrxx:v:14:y:2012:i:03:n:s0219198912500181
    DOI: 10.1142/S0219198912500181
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    References listed on IDEAS

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    1. Jingang Zhao, 2008. "The Maximal Payoff and Coalition Formation in Coalitional Games," Working Papers 2008.27, Fondazione Eni Enrico Mattei.
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    Cited by:

    1. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    2. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    3. Jingang Zhao, 2018. "A Reexamination of the Coase Theorem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 3(1), pages 111-132, December.

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      More about this item

      Keywords

      Solution concept; core extension; axiomatic characterization; 91A12;
      All these keywords.

      JEL classification:

      • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
      • C0 - Mathematical and Quantitative Methods - - General
      • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
      • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
      • D5 - Microeconomics - - General Equilibrium and Disequilibrium
      • D7 - Microeconomics - - Analysis of Collective Decision-Making
      • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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