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Ordinality in non cooperative games

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  • Jean-François Mertens

Abstract

We first analyse what a conceptual definition of ordinality for non cooperative games should be. The resulting concept is highly abstract and apparently unmanageable. Nevertheless we obtain in a second part a very simple and fully operational characterization. In the last part, this is used to check the ordinality of a number of concepts that have been proposed in the literature. Copyright Springer-Verlag 2004

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  • Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 387-430, June.
    • Handle: RePEc:spr:jogath:v:32:y:2004:i:3:p:387-430
    DOI: 10.1007/s001820400166
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    Cited by:

    1. Vermeulen, Dries & Jansen, Mathijs, 1998. "The reduced form of a game," European Journal of Operational Research, Elsevier, vol. 106(1), pages 204-211, April.
    2. Joseph Abdou & Nikolaos Pnevmatikos & Marco Scarsini, 2014. "Uniformity and games decomposition," Documents de travail du Centre d'Economie de la Sorbonne 14084r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Mar 2017.
    3. Eric van Damme & Xu Lang, 2022. "Two-Person Bargaining when the Disagreement Point is Private Information," Papers 2211.06830, arXiv.org, revised Jan 2024.
    4. Fabrizio Germano, 2006. "On some geometry and equivalence classes of normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 561-581, November.
    5. Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
    6. GERMANO, Fabrizio, 1998. "On Nash equivalence classes of generic normal form games," LIDAM Discussion Papers CORE 1998033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Balkenborg, Dieter & Jansen, Mathijs & Vermeulen, Dries, 2001. "Invariance properties of persistent equilibria and related solution concepts," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 111-130, January.
    8. De Sinopoli, Francesco & Pimienta, Carlos, 2009. "Undominated (and) perfect equilibria in Poisson games," Games and Economic Behavior, Elsevier, vol. 66(2), pages 775-784, July.
    9. Dries Vermeulen & Mathijs Jansen & Andrés Perea y Monsuwé, 2000. "Player splitting in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 433-450.
    10. John Hillas & Elon Kohlberg, 1996. "Foundations of Strategic Equilibrium," Game Theory and Information 9606002, University Library of Munich, Germany, revised 18 Sep 1996.
    11. Srihari Govindan & Robert Wilson, 2008. "Metastable Equilibria," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 787-820, November.
    12. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2016. "Behavioral perfect equilibrium in Bayesian games," Games and Economic Behavior, Elsevier, vol. 98(C), pages 78-109.
    13. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics.
    14. Bich, Philippe, 2019. "Strategic uncertainty and equilibrium selection in discontinuous games," Journal of Economic Theory, Elsevier, vol. 183(C), pages 786-822.
    15. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    16. Vermeulen, A. J. & Jansen, M. J. M., 1997. "Extending Invariant Solutions," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 135-147, October.
    17. Lucas Pahl, 2022. "Polytope-form games and Index/Degree Theories for Extensive-form games," Papers 2201.02098, arXiv.org, revised Jul 2023.
    18. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    19. Vermeulen, A. J. & Jansen, M. J. M., 2000. "Ordinality of solutions of noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 13-34, February.
    20. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    21. Vermeulen, A. J. & Jansen, M. J. M., 1997. "On the invariance of solutions of finite games," Mathematical Social Sciences, Elsevier, vol. 33(3), pages 251-267, June.
    22. John Hillas & Mathijs Jansen & Jos Potters & Dries Vermeulen, 2001. "On the Relation Among Some Definitions of Strategic Stability," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 611-635, August.
    23. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2013. "Perfect equilibrium in games with compact action spaces," Games and Economic Behavior, Elsevier, vol. 82(C), pages 490-502.
    24. GRIGIS DE STEFANO, Federico, 2014. "Strategic stability of equilibria: the missing paragraph," LIDAM Discussion Papers CORE 2014015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    25. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.

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