IDEAS home Printed from https://ideas.repec.org/p/hhs/osloec/2010_001.html
   My bibliography  Save this paper

Epistemically Stable Strategy Sets

Author

Listed:
  • Geir B. , Asheim

    (Dept. of Economics, University of Oslo)

  • Voorneveld, Max

    (Department of Economics, Stockholm School of Economics)

  • W. Weibull, Jörgen

    (Department of Economics, Stockholm School of Economics)

Abstract

This paper provides a definition of epistemic stability of sets of strategy profiles,and uses it to characterize variants of curb sets in finite games, including the set of rationalizable strategies and minimal curb sets.

Suggested Citation

  • Geir B. , Asheim & Voorneveld, Max & W. Weibull, Jörgen, 2009. "Epistemically Stable Strategy Sets," Memorandum 01/2010, Oslo University, Department of Economics.
  • Handle: RePEc:hhs:osloec:2010_001
    as

    Download full text from publisher

    File URL: https://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2010/Memo-01-2010.pdf
    Download Restriction: no
    ---><---

    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. Hu, Tai-Wei, 2007. "On p-rationalizability and approximate common certainty of rationality," Journal of Economic Theory, Elsevier, vol. 136(1), pages 379-391, September.
    3. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    4. Sanchirico, Chris William, 1996. "A Probabilistic Model of Learning in Games," Econometrica, Econometric Society, vol. 64(6), pages 1375-1393, November.
    5. Jean-François Mertens, 1989. "Stable Equilibria---A Reformulation," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 575-625, November.
    6. MERTENS, Jean-François, 1989. "Stable equilibria - a reformulation. Part I. Definition and basic properties," LIDAM Reprints CORE 866, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    8. Geir B. Asheim, 2006. "The Consistent Preferences Approach to Deductive Reasoning in Games," Theory and Decision Library C, Springer, number 978-0-387-26237-6, March.
    9. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    10. Ehud Kalai & Dov Samet, 1982. "Persistent Equilibria in Strategic Games," Discussion Papers 515, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    12. Hurkens, Sjaak, 1996. "Multi-sided Pre-play Communication by Burning Money," Journal of Economic Theory, Elsevier, vol. 69(1), pages 186-197, April.
    13. Blume, Andreas, 1998. "Communication, Risk, and Efficiency in Games," Games and Economic Behavior, Elsevier, vol. 22(2), pages 171-202, February.
    14. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    15. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
    16. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    17. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
    18. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    19. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
    20. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    21. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    22. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    23. 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.
    24. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    25. Zambrano, Eduardo, 2008. "Epistemic conditions for rationalizability," Games and Economic Behavior, Elsevier, vol. 63(1), pages 395-405, May.
    26. van Damme, E.E.C., 1983. "Refinements of the Nash Equilibrium Concept," Other publications TiSEM 116b3ec4-be4d-48c2-ad1b-8, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. John Duggan & Michel Le Breton, 2014. "Choice-theoretic Solutions for Strategic Form Games," RCER Working Papers 580, University of Rochester - Center for Economic Research (RCER).
    2. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.

    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. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    2. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Weibull, Jorgen W., 1998. "Evolution, rationality and equilibrium in games," European Economic Review, Elsevier, vol. 42(3-5), pages 641-649, May.
    4. Battigalli, Pierpaolo & Dufwenberg, Martin, 2009. "Dynamic psychological games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 1-35, January.
    5. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics.
    6. 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.
    7. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    8. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    9. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    10. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    11. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    12. Balkenborg, Dieter & Jansen, Mathijs & Vermeulen, Dries, 2001. "Invariance properties of persistent equilibria and related solution concepts," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 111-130, January.
    13. Gilles Grandjean & Ana Mauleon & Vincent Vannetelbosch, 2017. "Strongly rational sets for normal-form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 35-46, April.
    14. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    15. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    16. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    17. Peyton Young, H., 1998. "Individual learning and social rationality1," European Economic Review, Elsevier, vol. 42(3-5), pages 651-663, May.
    18. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
    19. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.
    20. Barelli, Paulo & Galanis, Spyros, 2013. "Admissibility and event-rationality," Games and Economic Behavior, Elsevier, vol. 77(1), pages 21-40.

    More about this item

    Keywords

    Epistemic game theory; epistemic stability; rationalizability; closedness under rational behavior; mutual p-belief;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:osloec:2010_001. 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: Mari Strønstad Øverås (email available below). General contact details of provider: https://edirc.repec.org/data/souiono.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.