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Fictitious play in 2xn games

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Author Info
Ulrich Berger (Vienna University of Economics)
Abstract

It is known that every continuous time fictitious play process approaches equilibrium in every nondegenerate 2x2 and 2x3 game, and it has been conjectured that convergence to equilibrium holds generally for 2xn games. We give a simple geometric proof of this.

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File URL: http://129.3.20.41/eps/game/papers/0303/0303009.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0303009.

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Length: 11 pages
Date of creation: 25 Mar 2003
Date of revision:
Handle: RePEc:wpa:wuwpga:0303009

Note: Type of Document - pdf-file; pages: 11; figures: included
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Web page: http://129.3.20.41

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Related research
Keywords: Fictitious Play Learning Process 2xn Games

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, EconWPA. [Downloadable!]
  4. Metrick, Andrew & Polak, Ben, 1994. "Fictitious Play in 2 x 2 Games: A Geometric Proof of Convergence," Economic Theory, Springer, vol. 4(6), pages 923-33, October.
  5. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  8. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
  9. Diana Richards, 1997. "The geometry of inductive reasoning in games," Economic Theory, Springer, vol. 10(1), pages 185-193. [Downloadable!] (restricted)
  10. Monderer, Dov & Sela, Aner, 1997. "Fictitious play and- no-cycling conditions," Sonderforschungsbereich 504 Publications 97-12, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
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