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Ordinal Games

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Abstract
We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we ex- tend Voorneveld's concept of best-response potential from cardinal to ordi- nal games and derive the analogue of his characterization result: An ordi- nal 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 compactness and semicontinuity 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, 2007. "Ordinal Games," CER-ETH Economics working paper series 07/74, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    • Handle: RePEc:eth:wpswif:07-74
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    File URL: https://www.ethz.ch/content/dam/ethz/special-interest/mtec/cer-eth/cer-eth-dam/documents/working-papers/wp_07_74.pdf
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    • Jacques Durieu & Hans Haller & Nicolas Quérou & Philippe Solal, 2007. "Ordinal Games," Post-Print ujm-00194794, HAL.

    References listed on IDEAS

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    Cited by:

    1. Balistreri, Edward J. & Hillberry, Russell H. & Rutherford, Thomas F., 2011. "Structural estimation and solution of international trade models with heterogeneous firms," Journal of International Economics, Elsevier, vol. 83(2), pages 95-108, March.
    2. 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.
    3. Thomas Demuynck, 2009. "Absolute and Relative Time-Consistent Revealed Preferences," Theory and Decision, Springer, vol. 66(3), pages 283-299, March.
    4. Balistreri, Edward J. & Hillberry, Russell H. & Rutherford, Thomas F., 2010. "Trade and welfare: Does industrial organization matter?," Economics Letters, Elsevier, vol. 109(2), pages 85-87, November.
    5. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.
    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 Correspondences;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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