Learning in games with strategic complementarities revisited
Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result.
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- Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
- Hon-Snir, Shlomit & Monderer, Dov & Sela, Aner, 1998.
"A Learning Approach to Auctions,"
Journal of Economic Theory,
Elsevier, vol. 82(1), pages 65-88, September.
- Dov Monderer & Dov Samet & Aner Sela, 2010.
"Belief Affirming in Learning Processes,"
Levine's Working Paper Archive
420, David K. Levine.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
- Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
- Fudenberg, Drew & Levine, David, 1995.
"Consistency and Cautious Fictitious Play,"
3198694, Harvard University Department of Economics.
- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
- Leslie, David S. & Collins, E.J., 2006. "Generalised weakened fictitious play," Games and Economic Behavior, Elsevier, vol. 56(2), pages 285-298, August.
- Paul Milgrom & John Roberts, 2010. "Adaptive and Sophisticated Learning in Repeated Normal-Form Games," Levine's Working Paper Archive 418, David K. Levine.
- Vives, X., 1988.
"Nash Equilibrium With Strategic Complementarities,"
UFAE and IAE Working Papers
107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
- Drew Fudenberg & David K. Levine, 1998.
"The Theory of Learning in Games,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262061945, December.
- Ulrich Berger, 2005.
"Brown's Original Fictitious Play,"
Game Theory and Information
- Fudenberg, D. & Kreps, D.M., 1992.
"Learning Mixed Equilibria,"
92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
- 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.
- 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.
- 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.
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