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Strongly rational sets for normal-form games

Author

Listed:
  • Grandjean, J G.
  • Mauleon, A.

    (Externe publicaties SBE)

  • Vannetelbosch, V.

    (Externe publicaties SBE)

Abstract

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 contains all actions she may rationally select in every coalition she might belong to, for any 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 provide a dynamic learning process leading the players to play strategies from a minimal strong curb set only.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Grandjean, J G. & Mauleon, A. & Vannetelbosch, V., 2009. "Strongly rational sets for normal-form games," Research Memorandum 059, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2009059
    DOI: 10.26481/umamet.2009059
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    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. 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.
    3. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    4. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    5. Mark Voorneveld & Willemien Kets & Henk Norde, 2006. "An Axiomatization of Minimal Curb Sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 153-153, April.
    6. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 2000. "The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 677-687.
    7. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 1999. "Refinements of rationalizability for normal-form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 53-68.
    8. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    9. Attila Ambrus, 2006. "Coalitional Rationalizability," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(3), pages 903-929.
    10. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    12. Ambrus, Attila, 2009. "Theories of Coalitional Rationality," Scholarly Articles 3204917, Harvard University Department of Economics.
    13. Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," SSE/EFI Working Paper Series in Economics and Finance 590, Stockholm School of Economics.
    14. Voorneveld, Mark, 2005. "Persistent retracts and preparation," Games and Economic Behavior, Elsevier, vol. 51(1), pages 228-232, April.
    15. Ambrus, Attila, 2009. "Theories of coalitional rationality," Journal of Economic Theory, Elsevier, vol. 144(2), pages 676-695, March.
    16. Ambrus, Attila, 2006. "Coalitional Rationalizability," Scholarly Articles 3200266, Harvard University Department of Economics.
    17. Luo, Xiao & Yang, Chih-Chun, 2009. "Bayesian coalitional rationalizability," Journal of Economic Theory, Elsevier, vol. 144(1), pages 248-263, January.
    18. 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.
    19. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
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    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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