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The relative interior of the base polyhedron and the core

Author

Listed:
  • Jingang Zhao

    (Department of Economics, Iowa State University, 260 Heady Hall, Ames, IA 50011-1070, USA)

Abstract

This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalition's payoff is greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also imply results on the sensitivity of the base polyhedron and the core.

Suggested Citation

  • Jingang Zhao, 2001. "The relative interior of the base polyhedron and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 635-648.
    • Handle: RePEc:spr:joecth:v:18:y:2001:i:3:p:635-648
    Note: Received: June 25, 1999; revised version: May 8, 2000
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    Citations

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    Cited by:

    1. Aymeric Lardon, 2019. "On the coalitional stability of monopoly power in differentiated Bertrand and Cournot oligopolies," Post-Print halshs-02355341, HAL.
    2. Aymeric Lardon, 2017. "On the Coalitional Stability of Monopoly Power in Differentiated Bertrand and Cournot Oligopolies," GREDEG Working Papers 2017-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    3. Takeda, Kohei & Hosoe, Toyoki & Watanabe, Takayuki & Matsubayashi, Nobuo, 2018. "Stability analysis of horizontal mergers in a market with asymmetric substitutability," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 73-84.
    4. Stéphane Gonzalez & Aymeric Lardon, 2018. "Optimal deterrence of cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 207-227, March.
    5. Zhao, Jingang, 2008. "The Maximal Payoff and Coalition Formation in Coalitional Games," Coalition Theory Network Working Papers 6298, Fondazione Eni Enrico Mattei (FEEM).
    6. Camelia Bejan & Juan Camilo Gómez, 2018. "Equal treatment without large numbers," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1239-1259, November.
    7. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
    8. 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.
    9. Jingang Zhao, 2009. "Estimating Merging Costs by Merger Preconditions," Theory and Decision, Springer, vol. 66(4), pages 373-399, April.
    10. Camelia Bejan & Juan Camilo Gómez, 2017. "Employment lotteries, endogenous firm formation and the aspiration core," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 215-226, October.
    11. Aymeric Lardon, 2019. "On the coalitional stability of monopoly power in differentiated Bertrand and Cournot oligopolies," Theory and Decision, Springer, vol. 87(4), pages 421-449, November.
    12. Takayuki Watanabe & Nobuo Matsubayashi, 2013. "Note on Stable Mergers in a Market with Asymmetric Substitutability," Economics Bulletin, AccessEcon, vol. 33(3), pages 2024-2033.

    More about this item

    Keywords

    Base polyhedron; Core; Minimum no-blocking payoff; Nucleolus; Sensitivity analysis.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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