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Ordinal Games

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Author Info

  • 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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 10 (2008)
Issue (Month): 02 ()
Pages: 177-194

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Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:02:p:177-194

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Related research

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

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References

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  1. SCHMEIDLER, David, . "Competitive equilibria in markets with a continuum of traders and incomplete preferences," CORE Discussion Papers RP -62, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  3. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
  4. Basu, K. & Weibull, J.W., 1990. "Strategy Subsets Closed Under Rational Behaviour," Papers 479, Stockholm - International Economic Studies.
  5. Borglin, Anders & Keiding, Hans, 1976. "Existence of equilibrium actions and of equilibrium : A note on the `new' existence theorems," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 313-316, December.
  6. Vitaly Pruzhansky, 2003. "On Finding Curb Sets in Extensive Games," Tinbergen Institute Discussion Papers 03-098/1, Tinbergen Institute.
  7. Josephson, Jens & Matros, Alexander, 2000. "Stochastic Imitation in Finite Games," Working Paper Series in Economics and Finance 363, Stockholm School of Economics, revised 26 Nov 2002.
  8. Toranzo, Margarita Estevez & Beloso, Carlos Herves, 1995. "On the existence of continuous preference orderings without utility representations," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 305-309.
  9. MERTENS, Jean-François, . "Ordinality in non cooperative games," CORE Discussion Papers RP -1738, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Voorneveld, Mark & Norde, Henk, 1997. "A Characterization of Ordinal Potential Games," Games and Economic Behavior, Elsevier, vol. 19(2), pages 235-242, May.
  11. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  12. Wayne Shafer & Hugo Sonnenschein, 1974. "Some Theorems on the Existence of Competitive Equilibrium," Discussion Papers 103, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Voorneveld, Mark, 1997. "Equilibria and approximate equilibria in infinite potential games," Economics Letters, Elsevier, vol. 56(2), pages 163-169, October.
  14. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
  15. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
  16. Norde, H.W. & Tijs, S.H., 1998. "Determinateness of strategic games with a potential," Open Access publications from Tilburg University urn:nbn:nl:ui:12-78038, Tilburg University.
  17. Ehlers, L., 2001. "Multiple Public Goods and Lexicographic Preferences Replacement Principle," Cahiers de recherche 2001-25, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  18. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
  19. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  20. Perea,Andres & Peters,Hans & Schulteis,Tim & Vermeulen,Dries, 2005. "Stochastic dominance equilibria in two-person noncooperative games," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  21. Henk Norde & Fioravante Patrone, 2001. "A potential approach for ordinal games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 9(1), pages 69-75, June.
  22. Morris, Stephen Morris & Takashi Ui, 2002. "Best Response Equivalence," Cowles Foundation Discussion Papers 1377, Cowles Foundation for Research in Economics, Yale University.
  23. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
  24. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  25. Shafer, Wayne J., 1976. "Equilibrium in economies without ordered preferences or free disposal," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 135-137, July.
  26. 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.
  27. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
  28. Candeal, Juan C. & Herves, Carlos & Indurain, Esteban, 1998. "Some results on representation and extension of preferences," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 75-81, January.
  29. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  30. Vitaly Pruzhansky, 2003. "On finding curb sets in extensive games," International Journal of Game Theory, Springer, vol. 32(2), pages 205-210, December.
  31. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
  32. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  33. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
  34. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September.
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Citations

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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. Edward J. Balistreri & Russell H. Hillberry & Thomas F. Rutherford, 2009. "Trade and Welfare: Does Industrial Organization Matter?," CER-ETH Economics working paper series 09/119, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  3. T. Demuynck, 2007. "Absolute and Relative Time-Consistent Revealed Preferences," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 07/485, Ghent University, Faculty of Economics and Business Administration.

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