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Brown's Original Fictitious Play

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  • Ulrich Berger

    (Vienna Univrsity of Economics)

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.

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File URL: http://128.118.178.162/eps/game/papers/0503/0503008.pdf
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Bibliographic Info

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
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Web page: http://128.118.178.162

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Keywords: Fictitious Play; Learning Process; Ordinal Potential Games;

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  1. 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.
  2. Monderer, Dov & Shlomit Hon-Snir & Aner Sela, 1996. "A Learning Approach to Auctions," Discussion Paper Serie B 388, University of Bonn, Germany.
  3. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
  4. Vijay Krishna & Tomas Sjostrom, 1995. "On the Convergence of Fictitious Play," Harvard Institute of Economic Research Working Papers 1717, Harvard - Institute of Economic Research.
  5. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  6. 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.
  7. 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.
  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. 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.
  10. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, EconWPA.
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Cited by:
  1. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
  2. In, Younghwan, 2014. "Fictitious play property of the Nash demand game," Economics Letters, Elsevier, vol. 122(3), pages 408-412.
  3. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.

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