IDEAS home Printed from https://ideas.repec.org/p/unm/umamet/2009059.html
   My bibliography  Save this paper

Strongly rational sets for normal-form games

Author

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

    (Externe publicaties SBE)

  • Vannetelbosch, V.

    (Externe publicaties SBE)

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.
(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
    as

    Download full text from publisher

    File URL: https://cris.maastrichtuniversity.nl/ws/files/941106/guid-0aaec778-2856-4cee-ba6d-5975ebb819f5-ASSET1.0.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.26481/umamet.2009059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    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, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    2. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    3. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    4. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    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. Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," SSE/EFI Working Paper Series in Economics and Finance 590, Stockholm School of Economics.
    7. Luo, Xiao & Yang, Chih-Chun, 2009. "Bayesian coalitional rationalizability," Journal of Economic Theory, Elsevier, vol. 144(1), pages 248-263, January.
    8. Geir B. Asheim & Mark Voorneveld & Jörgen Weibull, 2009. "Epistemically stable strategy sets," Working Papers hal-00440098, HAL.
    9. Weibull, Jorgen W., 1998. "Evolution, rationality and equilibrium in games," European Economic Review, Elsevier, vol. 42(3-5), pages 641-649, May.
    10. Olivier Tercieux & Mark Voorneveld, 2010. "The cutting power of preparation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 85-101, February.
    11. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    12. Ambrus, Attila, 2009. "Theories of Coalitional Rationality," Scholarly Articles 3204917, Harvard University Department of Economics.
    13. Balkenborg, Dieter & Hofbauer, Josef & Kuzmics, Christoph, 2016. "Refined best reply correspondence and dynamics," Center for Mathematical Economics Working Papers 451, Center for Mathematical Economics, Bielefeld University.
    14. Balkenborg, Dieter G. & Hofbauer, Josef & Kuzmics, Christoph, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
    15. Tercieux, O.R.C. & Voorneveld, M., 2005. "The Cutting Power of Preparation," Other publications TiSEM 75173341-627f-4eb2-91f1-0, Tilburg University, School of Economics and Management.
    16. Ambrus, Attila, 2009. "Theories of coalitional rationality," Journal of Economic Theory, Elsevier, vol. 144(2), pages 676-695, March.
    17. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    18. Ambrus, Attila, 2006. "Coalitional Rationalizability," Scholarly Articles 3200266, Harvard University Department of Economics.
    19. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    20. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:unm:umamet:2009059. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Andrea Willems or Leonne Portz (email available below). General contact details of provider: https://edirc.repec.org/data/meteonl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.