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Ordinal Games

  • 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)

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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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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  1. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06.
  2. Basu, K. & Weibull, J.W., 1990. "Strategy Subsets Closed Under Rational Behaviour," Papers 479, Stockholm - International Economic Studies.
  3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  4. 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.
  5. 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.
  6. Josephson, Jens & Matros, Alexander, 2004. "Stochastic imitation in finite games," Games and Economic Behavior, Elsevier, vol. 49(2), pages 244-259, November.
  7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  8. Norde, H.W. & Tijs, S.H., 1996. "Determinateness of Strategic Games with a Potential," Research Memorandum 720, Tilburg University, School of Economics and Management.
  9. EHLERS, Lars, 2001. "Multiple Public Goods and Lexicographic Preferences Replacement Principle," Cahiers de recherche 2001-25, Universite de Montreal, Departement de sciences economiques.
  10. Vitaly Pruzhansky, 2003. "On finding curb sets in extensive games," International Journal of Game Theory, Springer, vol. 32(2), pages 205-210, December.
  11. 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.
  12. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  13. 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.
  14. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
  15. Morris, Stephen Morris & Takashi Ui, 2002. "Best Response Equivalence," Cowles Foundation Discussion Papers 1377, Cowles Foundation for Research in Economics, Yale University.
  16. Voorneveld, M. & Norde, H.W., 1996. "A Characterization of Ordinal Potential Games," Research Memorandum 734, Tilburg University, School of Economics and Management.
  17. 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.
  18. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  19. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-19, September.
  20. 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.
  21. 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.
  22. 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).
  23. Kukushkin, Nikolai S., 1999. "Potential games: a purely ordinal approach," Economics Letters, Elsevier, vol. 64(3), pages 279-283, September.
  24. Voorneveld, Mark, 1997. "Equilibria and approximate equilibria in infinite potential games," Economics Letters, Elsevier, vol. 56(2), pages 163-169, October.
  25. 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.
  26. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  27. 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.
  28. 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.
  29. 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.
  30. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  31. 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.
  32. 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.
  33. 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.
  34. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
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