This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Two More Classes of Games with the Fictitious Play Property

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Ulrich Berger (Vienna University of Economics)

Additional information is available for the following registered author(s):

Abstract

Fictitious play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for some important classes of games, including weighted potential games, supermodular games with diminishing returns, and 3x3 supermodular games. Extending these results, we establish convergence for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3xm and 4x4 quasi-supermodular games.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://129.3.20.41/eps/game/papers/0408/0408003.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 0408003.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 17 pages
Date of creation: 31 Aug 2004
Date of revision:
Handle: RePEc:wpa:wuwpga:0408003

Note: Type of Document - pdf; pages: 17
Contact details of provider:
Web page: http://129.3.20.41

For technical questions regarding this item, or to correct its listing, contact: (EconWPA).

Related research
Keywords: Fictitious Play; Learning Process; Ordinal Potential Games; Quasi-Supermodular Games;

Other versions of this item:

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

This paper has been announced in the following NEP Reports:

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.:
  1. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June. [Downloadable!] (restricted)
  2. 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)
  3. Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer, vol. 30(4), pages 527-538. [Downloadable!] (restricted)
  4. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February. [Downloadable!] (restricted)
  5. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July. [Downloadable!] (restricted)
  6. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, EconWPA. [Downloadable!]
  7. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July. [Downloadable!] (restricted)
    Other versions:
  8. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
  9. 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!]
  10. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May. [Downloadable!] (restricted)
  11. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October. [Downloadable!] (restricted)
  12. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
    Other versions:
  13. 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)
  14. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April. [Downloadable!] (restricted)
  15. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
    Other versions:
  16. Vijay Krishna & Tomas Sjostrom, 1995. "On the Convergence of Fictitious Play," Game Theory and Information 9503003, EconWPA. [Downloadable!]
    Other versions:
  17. 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.
  18. 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. [Downloadable!] (restricted)
  19. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  20. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November. [Downloadable!] (restricted)
  21. Garcia, Alfredo & Reaume, Daniel & Smith, Robert L., 2000. "Fictitious play for finding system optimal routings in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 147-156, February. [Downloadable!] (restricted)
  22. 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)
  23. Harris, Christopher, 1998. "On the Rate of Convergence of Continuous-Time Fictitious Play," Games and Economic Behavior, Elsevier, vol. 22(2), pages 238-259, February. [Downloadable!] (restricted)
  24. Satoru Takahashi & Tetsuo Yamamori, 2002. "The pure Nash equilibrium property and the quasi-acyclic condition," Economics Bulletin, Economics Bulletin, vol. 3(22), pages 1-6. [Downloadable!]
  25. 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)
  26. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October. [Downloadable!] (restricted)
    Other versions:
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.)

  1. Ulrich Berger, 2005. "Brown's Original Fictitious Play," Game Theory and Information 0503008, EconWPA. [Downloadable!]
    Other versions:
Statistics
Access and download statistics

Did you know? The yearly budget of IDEAS is exactly $0: it relies entirely on volunteer work.

This page was last updated on 2009-11-5.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.