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Brown's Original Fictitious Play

  • Ulrich Berger

    (Vienna Univrsity of Economics)

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.

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File URL: http://econwpa.repec.org/eps/game/papers/0503/0503008.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0503008.

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Length: 12 pages
Date of creation: 21 Mar 2005
Date of revision:
Handle: RePEc:wpa:wuwpga:0503008
Note: Type of Document - pdf; pages: 12
Contact details of provider: Web page: http://econwpa.repec.org

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  1. 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.
  2. 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.
  3. Shlomit Hon-Snir & Dov Monderer & Aner Sela, 1996. "A Learning Approach to Auctions," Game Theory and Information 9610004, EconWPA, revised 07 Oct 1996.
  4. 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.
  5. Monderer, Dov & Sela, Aner, 1997. "Fictitious play and- no-cycling conditions," Sonderforschungsbereich 504 Publications 97-12, Sonderforschungsbereich 504, Universit├Ąt Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  6. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  7. 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.
  8. 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.
  9. Vijay Krishna & T. Sjostrom, 2010. "On the Convergence of Fictitious Play," Levine's Working Paper Archive 417, David K. Levine.
  10. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, EconWPA.
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