Some Notes on Learning in Games with Strategic Complementarities
AbstractFictitious play is the classical myopic learning process, and games with strategic complementarities are an important class of games including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond dominance solvable games, global convergence has only been established for games with strategic complementarities and diminishing marginal returns (Krishna, 1992, HBSWorking Paper 92-073). This result is known to depend critically on the assumption of a tie-breaking rule. We show that restricting the analysis to nondegenerate games allows us to drop this assumption. More importantly, an ordinal version of strategic complementarities turns out to suffice. As a byproduct, we also obtain global convergence in generalized ordinal potential games with diminishing marginal returns.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. 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.
Bibliographic InfoPaper provided by EconWPA in its series Game Theory and Information with number 0409001.
Length: 14 pages
Date of creation: 01 Sep 2004
Date of revision:
Note: Type of Document - pdf; pages: 14
Contact details of provider:
Web page: http://126.96.36.199
Fictitious Play; Learning Process; Strategic Complementarities; Supermodular Games;
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:
- NEP-ALL-2004-09-05 (All new papers)
- NEP-EVO-2004-09-05 (Evolutionary Economics)
- NEP-MIC-2004-09-05 (Microeconomics)
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.:
- Vives, Xavier, 1990.
"Nash equilibrium with strategic complementarities,"
Journal of Mathematical Economics,
Elsevier, vol. 19(3), pages 305-321.
- Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
- Gilboa, Itzhak & Matsui, Akihiko, 1991.
"Social Stability and Equilibrium,"
Econometric Society, vol. 59(3), pages 859-67, May.
- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- 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.
- 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.
- Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
- 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.
- Christopher Harris, 1994. "On theRate of Convergence of Continuous-Time Fictitious Play," Papers 0052, Boston University - Industry Studies Programme.
- 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.
- 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.
- Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.