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Learning in games with strategic complementarities revisited

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  • Berger, Ulrich

Abstract

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 This result remained unpublished, and it relies on a specific tie-breaking rule.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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 143 (2008)
Issue (Month): 1 (November)
Pages: 292-301

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Handle: RePEc:eee:jetheo:v:143:y:2008:i:1:p:292-301

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Fictitious play Learning process Strategic complementarities Ordinal complementarities;

References

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  1. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, January.
  2. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
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  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, January.
  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.
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  16. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  17. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  18. Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
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Citations

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Cited by:
  1. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
  2. Schlag, Karl H. & Vida, Péter, 2013. "Commitments, Intentions, Truth and Nash Equilibria," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 438, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  3. van Strien, Sebastian & Sparrow, Colin, 2011. "Fictitious play in 3x3 games: Chaos and dithering behaviour," Games and Economic Behavior, Elsevier, vol. 73(1), pages 262-286, September.
  4. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.

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