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Axiomatic Foundations of a Unifying Core

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  • Stéphane Gonzalez

    (UJM - Université Jean Monnet - Saint-Étienne, GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Aymeric Lardon

    (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur)

Abstract

We provide an axiomatic characterization of the core of games in effectiveness form. We point out that the core, whenever it applies to appropriate classes of these games, coincides with a wide variety of prominent stability concepts in social choice and game theory, such as the Condorcet winner, the Nash equilibrium, pairwise stability, and stable matchings, among others. Our characterization of the core invokes the axioms of restricted non-emptiness, coalitional unanimity, and Maskin invariance together with a principle of independence of irrelevant states, and uses in its proof a holdover property echoing the conventional ancestor property. Taking special cases of this general characterization of the core, we derive new characterizations of the previously mentioned stability concepts.

Suggested Citation

  • Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers halshs-01872098, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01872098
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01872098
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    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
    3. Sean Horan & Martin J. Osborne & M. Remzi Sanver, 2019. "Positively Responsive Collective Choice Rules And Majority Rule: A Generalization Of May'S Theorem To Many Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(4), pages 1489-1504, November.
    4. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
    5. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    6. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    7. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    8. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    9. Peleg, Bezalel & Potters, Jos A M & Tijs, Stef H, 1996. "Minimality of Consistent Solutions for Strategic Games, in Particular for Potential Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 81-93, January.
    10. van Heumen, R.W.J. & Peleg, B. & Tijs, S.H. & Borm, P.E.M., 1994. "Axiomatic characterizations of solutions for Bayesian games," Other publications TiSEM b16fc7d9-aee7-4f36-95f2-3, Tilburg University, School of Economics and Management.
    11. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2011. "Aggregation of multiple prior opinions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2563-2582.
    12. Norde, Henk & Potters, Jos & Reijnierse, Hans & Vermeulen, Dries, 1996. "Equilibrium Selection and Consistency," Games and Economic Behavior, Elsevier, vol. 12(2), pages 219-225, February.
    13. Klaus, Bettina, 2017. "Consistency and its converse for roommate markets," Games and Economic Behavior, Elsevier, vol. 104(C), pages 43-58.
    14. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    15. Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1996. "On Consistent Solutions for Strategic Games," Other publications TiSEM 07b489e5-dff2-45d0-bd65-1, Tilburg University, School of Economics and Management.
    16. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    17. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    18. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
    19. repec:dau:papers:123456789/13220 is not listed on IDEAS
    20. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
    21. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    22. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    23. Mehmet Karakaya & Bettina Klaus, 2017. "Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 435-455, May.
    24. Hervé Crès & Itzhak Gilboa & Nicolas Vieille, 2011. "Aggregation of multiple prior opinions," Post-Print hal-00656618, HAL.
    25. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    26. William Thomson, 2018. "On the terminology of economic design: a critical assessment and some proposals," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 67-99, June.
    27. Indrajit Ray, 2000. "Consistency, dummy and independence of irrelevant strategies for strategic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 217-222.
    28. Nizamogullari, Duygu & Özkal-Sanver, İpek, 2014. "Characterization of the core in full domain marriage problems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 34-42.
    29. Peleg, Bezalel & Sudholter, Peter, 1997. "An Axiomatization of Nash Equilibria in Economic Situations," Games and Economic Behavior, Elsevier, vol. 18(2), pages 277-285, February.
    30. Sen, Amartya, 1993. "Internal Consistency of Choice," Econometrica, Econometric Society, vol. 61(3), pages 495-521, May.
    31. Voorneveld, Mark & van den Nouweland, Anne, 1998. "A new axiomatization of the core of games with transferable utility," Economics Letters, Elsevier, vol. 60(2), pages 151-155, August.
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    More about this item

    Keywords

    Effectiveness function; core; axiomatization; holdover property; consistency;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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