Elsevier

Games and Economic Behavior

Volume 22, Issue 2, February 1998, Pages 238-259
Games and Economic Behavior

Regular Article
On the Rate of Convergence of Continuous-Time Fictitious Play☆

https://doi.org/10.1006/game.1997.0582Get rights and content

Abstract

This paper shows, first, that continuous-time fictitious play converges (in both payoff and strategy terms) uniformly at ratet − 1in any finite two-person zero-sum game. The proof is, in essence, a simple Lyapunov-function argument. The convergence of discrete-time fictitious play is a straightforward corollary of this result. The paper also shows that continuous-time fictitious play converges in all finite weighted-potential games. In this case, the convergence is not uniform. It is conjectured, however, that any given continuous-time fictitious play of a finite weighted-potential game converges (in both payoff and strategy terms) at ratet − 1.Journal of Economic LiteratureClassification Numbers: C6, C7.

References (20)

  • Brown, G. W. 1949, Some Notes on Computation of Games Solutions, P-78, The Rand...
  • J.-P. Aubin et al.

    Differential Inclusions

    (1984)
  • G.W. Brown

    Iterative Solutions of Games by Fictitious Play

    Activity Analysis of Production and Allocation

    (1951)
  • G.W. Brown

    Notes on the Solution of Linear Systems Involving Inequalities

    Proceedings of a Second Symposium on Large Scale Digital Calculating Machinery

    (1951)
  • G.W. Brown et al.

    Solutions of Games by Differential Equations

  • I. Gilboa et al.

    Social Stability and Equilibrium

    Econometrica

    (1991)
  • Hofbauer, J. 1994, Stability for the Best Response Dynamics, Institut für Mathematik, Universität...
  • S. Karlin

    Mathematical Methods and Theory in Games

    (1959)
  • Krishna, V. Sjöström, T. 1995, On the Convergence of Fictitious Play, Penn State University, Harvard...
There are more references available in the full text version of this article.

Cited by (0)

☆

T. C. Koopmans

*

I would particularly like to thank Ehud Kalai, Vijay Krishna, Dov Monderer, two anonymous referees, and an anonymous associate editor for their help with this paper.

View full text
Copyright © 1998 Academic Press. All rights reserved.