IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v135y2007i1p572-578.html
   My bibliography  Save this article

Brown's original fictitious play

Author

Listed:
  • Berger, Ulrich

Abstract

What modern game theorists describe as 'fictitious play' is not the learning process George W. Brown defined in his 1951 paper. His original version differs in a subtle detail, namely the order of belief updating. In this note we revive Brown's original fictitious play process and demonstrate that this seemingly innocent detail allows for an extremely simple and intuitive proof of convergence in an interesting and large class of games: nondegenerate ordinal potential games.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    • Handle: RePEc:eee:jetheo:v:135:y:2007:i:1:p:572-578
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(06)00029-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    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. Monderer, Dov & Sela, Aner, 1997. "Fictitious play and no-cycling conditions," Papers 97-12, Sonderforschungsbreich 504.
    3. Hon-Snir, Shlomit & Monderer, Dov & Sela, Aner, 1998. "A Learning Approach to Auctions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 65-88, September.
    4. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    5. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
    6. 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.
    7. Sela, Aner, 2000. "Fictitious Play in 2 x 3 Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 152-162, April.
    8. Monderer, Dov & Sela, Aner, 1996. "A2 x 2Game without the Fictitious Play Property," Games and Economic Behavior, Elsevier, vol. 14(1), pages 144-148, May.
    9. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    10. Hahn, Sunku, 1999. "The convergence of fictitious play in 3 x 3 games with strategic complementarities," Economics Letters, Elsevier, vol. 64(1), pages 57-60, July.
    11. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    12. Vijay Krishna & Tomas Sjostrom, 1995. "On the Convergence of Fictitious Play," Harvard Institute of Economic Research Working Papers 1717, Harvard - Institute of Economic Research.
    13. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
    14. Foster, Dean P. & Young, H. Peyton, 1998. "On the Nonconvergence of Fictitious Play in Coordination Games," Games and Economic Behavior, Elsevier, vol. 25(1), pages 79-96, October.
    15. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
    16. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    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. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
    2. Jiaxi Liu & Shuyi Lin & Linwei Xin & Yidong Zhang, 2023. "AI vs. Human Buyers: A Study of Alibaba’s Inventory Replenishment System," Interfaces, INFORMS, vol. 53(5), pages 372-387, September.
    3. Vinil T Chackochan & Vittorio Sanguineti, 2019. "Incomplete information about the partner affects the development of collaborative strategies in joint action," PLOS Computational Biology, Public Library of Science, vol. 15(12), pages 1-23, December.
    4. In, Younghwan, 2014. "Fictitious play property of the Nash demand game," Economics Letters, Elsevier, vol. 122(3), pages 408-412.
    5. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
    6. Dimitris Batzilis & Sonia Jaffe & Steven Levitt & John A. List & Jeffrey Picel, 2019. "Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games," Games, MDPI, vol. 10(2), pages 1-34, April.
    7. Zhao, Huan, 2011. "Four Market Studies for the Beef and Electric Power Industries," ISU General Staff Papers 201101010800001360, Iowa State University, Department of Economics.
    8. Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
    9. Stefan Rass & Sandra König & Stefan Schauer, 2017. "Defending Against Advanced Persistent Threats Using Game-Theory," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-43, January.

    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. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    2. Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
    3. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
    4. van Strien, Sebastian & Sparrow, Colin, 2011. "Fictitious play in 3x3 games: Chaos and dithering behaviour," Games and Economic Behavior, Elsevier, vol. 73(1), pages 262-286, September.
    5. Sparrow, Colin & van Strien, Sebastian & Harris, Christopher, 2008. "Fictitious play in 3x3 games: The transition between periodic and chaotic behaviour," Games and Economic Behavior, Elsevier, vol. 63(1), pages 259-291, May.
    6. Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    7. Ulrich Berger, 2004. "Some Notes on Learning in Games with Strategic Complementarities," Game Theory and Information 0409001, University Library of Munich, Germany.
    8. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    9. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    10. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
    11. Pangallo, Marco & Sanders, James B.T. & Galla, Tobias & Farmer, J. Doyne, 2022. "Towards a taxonomy of learning dynamics in 2 × 2 games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 1-21.
    12. Ulrich Berger, 2003. "Fictitious play in 2xn games," Game Theory and Information 0303009, University Library of Munich, Germany.
    13. Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, University Library of Munich, Germany.
    14. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    15. Sobel, Joel, 2000. "Economists' Models of Learning," Journal of Economic Theory, Elsevier, vol. 94(2), pages 241-261, October.
    16. Ding, Zhanwen & Wang, Qiao & Cai, Chaoying & Jiang, Shumin, 2014. "Fictitious play with incomplete learning," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 1-8.
    17. Ramsza, Michal & Seymour, Robert M., 2010. "Fictitious play in an evolutionary environment," Games and Economic Behavior, Elsevier, vol. 68(1), pages 303-324, January.
    18. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
    19. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    20. Ellison, Glenn, 1997. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Games and Economic Behavior, Elsevier, vol. 19(2), pages 180-210, May.

    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:eee:jetheo:v:135:y:2007:i:1:p:572-578. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.