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Strongly Rational Sets for Normal-Form Games

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  • Grandjean Gilles
  • Mauleon Ana
  • Vannetelbosch Vincent

    (METEOR)

Abstract

Curb sets [Basu and Weibull, Econ. Letters 36 (1991), 141-146] are product sets of pure strategies containing all individual best-responses against beliefs restricted to the recommendations to the remaining players. The concept of minimal curb sets is a set-theoretic coarsening of the notion of strict Nash equilibrium. We introduce the concept of minimal strong curb sets which is a set-theoretic coarsening of the notion of strong Nash equilibrium. Strong curb sets are product sets of pure strategies such that each player.s set of recommended strategies must contain all coalitional best-responses of each coalition to whatever belief each coalition member may have that is consistent with the recommendations to the other players. Minimal strong curb sets are shown to exist and are compared with other well known solution concepts. We also provide a dynamic learning process leading the players to playing strategies from a minimal strong curb set.

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Bibliographic Info

Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 059.

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Date of creation: 2009
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Handle: RePEc:dgr:umamet:2009059

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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm

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Keywords: mathematical economics;

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  1. P. Jean-Jacques Herings & Vincent J. Vannetelbosch, 1998. "The Equivalence of the Dekel-Fudenberg Iterative Procedure and Weakly Perfect Rationalizability," Cowles Foundation Discussion Papers 1173, Cowles Foundation for Research in Economics, Yale University.
  2. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 1999. "Refinements of rationalizability for normal-form games," International Journal of Game Theory, Springer, vol. 28(1), pages 53-68.
  3. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
  4. Kets, W. & Voorneveld, M., 2005. "Learning to be Prepared," Discussion Paper 2005-117, Tilburg University, Center for Economic Research.
  5. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent J., 2004. "Rationalizability for social environments," Games and Economic Behavior, Elsevier, vol. 49(1), pages 135-156, October.
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  7. Mark Voorneveld & Willemien Kets & Henk Norde, 2006. "An Axiomatization of Minimal Curb Sets," International Journal of Game Theory, Springer, vol. 34(1), pages 153-153, April.
  8. Ambrus, Attila, 2009. "Theories of Coalitional Rationality," Scholarly Articles 3204917, Harvard University Department of Economics.
  9. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
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  12. Ehud Kalai & Dov Samet, 1982. "Persistent Equilibria in Strategic Games," Discussion Papers 515, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215.
  14. Ambrus, Attila, 2009. "Theories of coalitional rationality," Journal of Economic Theory, Elsevier, vol. 144(2), pages 676-695, March.
  15. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
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  17. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
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