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Ordinal Games

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Author Info

  • Jacques Durieu

    ()
    (University of Saint Etienne, France)

  • Hans Haller

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

  • Nicolas Querou

    (Department of Economics, Queen's University, Belfast, Northern Ireland, UK.)

  • Philippe Solal

    ()
    (University of Saint Etienne, France)

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.

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Bibliographic Info

Paper provided by CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich in its series CER-ETH Economics working paper series with number 07/74.

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Length: 50 pages
Date of creation: Oct 2007
Date of revision:
Handle: RePEc:eth:wpswif:07-74

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Related research

Keywords: Ordinal Games; Potential Games; Quasi-Supermodularity; Rationalizable Sets; Sets Closed under Behavior Correspondences;

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References

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  1. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
  2. Voorneveld, Mark, 1997. "Equilibria and approximate equilibria in infinite potential games," Economics Letters, Elsevier, vol. 56(2), pages 163-169, October.
  3. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  4. Andres Perea & Hans Peters & Tim Schulteis & Dries Vermeulen, 2006. "Stochastic dominance equilibria in two-person noncooperative games," International Journal of Game Theory, Springer, vol. 34(4), pages 457-473, November.
  5. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  6. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06.
  7. Josephson, Jens & Matros, Alexander, 2004. "Stochastic imitation in finite games," Games and Economic Behavior, Elsevier, vol. 49(2), pages 244-259, November.
  8. 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.
  9. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  10. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  11. 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.
  12. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  13. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  14. Henk Norde & Stef Tijs, 1998. "Determinateness of strategic games with a potential," Computational Statistics, Springer, vol. 48(3), pages 377-385, December.
  15. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-85, October.
  16. EHLERS, Lars, 2001. "Multiple Public Goods and Lexicographic Preferences Replacement Principle," Cahiers de recherche 2001-25, Universite de Montreal, Departement de sciences economiques.
  17. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
  18. 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.
  19. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September.
  20. 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.
  21. 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.
  22. Vitaly Pruzhansky, 2003. "On Finding Curb Sets in Extensive Games," Tinbergen Institute Discussion Papers 03-098/1, Tinbergen Institute.
  23. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Some theorems on the existence of competitive equilibrium," Journal of Economic Theory, Elsevier, vol. 11(1), pages 83-93, August.
  24. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
  25. 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.
  26. Voorneveld, M. & Norde, H.W., 1997. "A characterisation of ordinal potential games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74020, Tilburg University.
  27. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
  28. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  29. 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.
  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. 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.
  32. 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.
  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. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
  35. 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.
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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. 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.
  3. 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.

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