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Strongly rational sets for normal-form games

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  • GRANDJEAN, Gilles

    ()
    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • MAULEON, Ana

    ()
    (FNRS and Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • VANNETELBOSCH, Vincent

    ()
    (FNRS and Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009066.

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Date of creation: 01 Nov 2009
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Handle: RePEc:cor:louvco:2009066

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Keywords: set-valued solution concept; coalitional best-response; strong curb set; learning;

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  1. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  2. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  3. Ambrus, Attila, 2009. "Theories of Coalitional Rationality," Scholarly Articles 3204917, Harvard University Department of Economics.
  4. Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," Working Paper Series in Economics and Finance 590, Stockholm School of Economics.
  5. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  6. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 2000. "The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability," Economic Theory, Springer, vol. 15(3), pages 677-687.
  7. Ambrus, Attila, 2009. "Theories of coalitional rationality," Journal of Economic Theory, Elsevier, vol. 144(2), pages 676-695, March.
  8. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  9. 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.
  10. Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
  11. Mark Voorneveld & Willemien Kets & Henk Norde, 2005. "An axiomatization of minimal curb sets," International Journal of Game Theory, Springer, vol. 33(4), pages 479-490, November.
  12. 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.
  13. Voorneveld, Mark, 2005. "Persistent retracts and preparation," Games and Economic Behavior, Elsevier, vol. 51(1), pages 228-232, April.
  14. Basu, K. & Weibull, J., 1990. "Strategy Subsets Closed Under Rational Behavior," Papers 62, Princeton, Woodrow Wilson School - Discussion Paper.
  15. Ambrus, Attila, 2006. "Coalitional Rationalizability," Scholarly Articles 3200266, Harvard University Department of Economics.
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