Continuous Fictitious Play via Projective Geometry

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Continuous Fictitious Play via Projective Geometry

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Ulrich Berger (Vienna University of Economics)

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Ulrich Berger

Abstract

Using insights from the theory of projective geometry one can prove convergence of continuous fictitious play in a certain class of games. As a corollary, we obtain a kind of equilibrium selection result, whereby continuous fictitious play converges to a particular equilibrium contained in a continuum of equivalent equilibria for symmetric 4x4 zero-sum games.

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Paper provided by EconWPA in its series Game Theory and Information with number 0303004.

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Length: 15 pages
Date of creation: 20 Mar 2003
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Handle: RePEc:wpa:wuwpga:0303004

Note: Type of Document - pdf file; pages: 15; figures: included
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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

This paper has been announced in the following NEP Reports:

NEP-ALL-2003-03-25 (All new papers)
NEP-GTH-2003-03-25 (Game Theory)

References listed on IDEAS
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.:

Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer, vol. 30(4), pages 527-538. [Downloadable!] (restricted)
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.
Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)

Full references

Cited by:
(explanations, 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.)

Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, EconWPA. [Downloadable!]
Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, EconWPA. [Downloadable!]
Ulrich Berger, 2003. "Fictitious play in 2xn games," Game Theory and Information 0303009, EconWPA. [Downloadable!]

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