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Payoff-dependent balancedness and cores

Author

Listed:
  • Jean-Marc Bonnisseau

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Vincent Iehlé

    (CODE - UAB - Universitat Autònoma de Barcelona = Autonomous University of Barcelona = Universidad Autónoma de Barcelona)

Abstract

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings.We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parameterized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parameterized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non-convexities. Applications to extant results taken from game theory and economic theory are given.

Suggested Citation

  • Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00176203, HAL.
    • Handle: RePEc:hal:cesptp:hal-00176203
    DOI: 10.1016/j.geb.2007.01.002
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    Citations

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    Cited by:

    1. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    2. Yan-An Hwang & Yu-Hsien Liao, 2022. "The Replicated Core under Multi-Choice Non-Transferable- Utility Situations: Converse Reduction Axiomatic Enlargements," Mathematics, MDPI, vol. 10(5), pages 1-8, March.
    3. Predtetchinski, A., 2004. "The fuzzy core and the (Π, β)- balanced core," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 203-210, June.
    5. Sonja Brangewitz & Jan-Philip Gamp, 2014. "Competitive outcomes and the inner core of NTU market games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 529-554, November.
    6. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 203-210, June.
    7. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    8. V. Filipe Martins-da-Rocha & Nicholas C. Yannelis, 2011. "Nonemptiness of the alpha-core," Economics Discussion Paper Series 1105, Economics, The University of Manchester.
    9. Vincent Iehlé, 2004. "Transfer rate rules and core selections in NTU games," Economics Bulletin, AccessEcon, vol. 3(42), pages 1-10.
    10. Liu, Jiuqiang & Liu, Xiaodong, 2013. "A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 150-156.
    11. repec:dau:papers:123456789/84 is not listed on IDEAS
    12. Yan-An Hwang & Yu-Hsien Liao, 2020. "A Solution Concept and Its Axiomatic Results under Non-Transferable-Utility and Multi-Choice Situations," Mathematics, MDPI, vol. 8(9), pages 1-10, September.
    13. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
    14. Ken Urai & Hiromi Murakami & Weiye Chen, 2023. "Generalization of the social coalitional equilibrium structure," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 1-25, April.
    15. Vincent Iehlé, 2004. "Stable pricing in monopoly and equilibrium-core of cost games," Cahiers de la Maison des Sciences Economiques b05023, Université Panthéon-Sorbonne (Paris 1).

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    More about this item

    Keywords

    Balancedness; Cooperative game; Core; Parameterized game;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • 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
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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