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Ordinal Games

Author

Listed:
  • JACQUES DURIEU

    (CREUSET, University of Saint-Etienne, 42023 Saint-Etienne, France)

  • HANS HALLER

    (Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0316, USA)

  • NICOLAS QUEROU

    (Queen's University Management School, Queen's University, Belfast, Northern Ireland, UK)

  • PHILIPPE SOLAL

    (CREUSET, University of Saint-Etienne, 42023 Saint-Etienne, France)

Abstract

We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we extend Voorneveld's concept of best-response potential from cardinal to ordinal games and derive the analogue of his characterization result: An ordinal game is a best-response potential game if and only if it does not have a best-response cycle. Further, Milgrom and Shannon's concept of quasi-supermodularity is extended from cardinal games to ordinal games. We find that under certain topological assumptions, the ordinal Nash equilibria of a quasi-supermodular game form a nonempty complete lattice. Finally, we extend several set-valued solution concepts from cardinal to ordinal games in our sense.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:02:n:s0219198908001868
    DOI: 10.1142/S0219198908001868
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    5. 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.
    6. Jamal Ouenniche & Aristotelis Boukouras & Mohammad Rajabi, 2016. "An Ordinal Game Theory Approach to the Analysis and Selection of Partners in Public–Private Partnership Projects," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 314-343, April.
    7. Kokkala, Juho & Poropudas, Jirka & Virtanen, Kai, 2015. "Rationalizable Strategies in Games With Incomplete Preferences," MPRA Paper 68331, University Library of Munich, Germany.
    8. Juho Kokkala & Kimmo Berg & Kai Virtanen & Jirka Poropudas, 2019. "Rationalizable strategies in games with incomplete preferences," Theory and Decision, Springer, vol. 86(2), pages 185-204, March.

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    More about this item

    Keywords

    Ordinal games; potential games; quasi-supermodularity; rationalizable sets; sets closed under behavior relations; C72;
    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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