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Fictitious play and no-cycling conditions

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  • Monderer, Dov
  • Sela, Aner

Abstract

We investigate the paths of pure strategy profiles induced by the fictitious play process. We present rules that such paths must follow. Using these rules we prove that every non-degenerate 2x3 game has the continuous fictitious play property, that is, every continuous fictitious play process, independent of initial actions and beliefs, approaches equilibrium in such games.

Suggested Citation

  • Monderer, Dov & Sela, Aner, 1997. "Fictitious play and no-cycling conditions," Papers 97-12, Sonderforschungsbreich 504.
    • Handle: RePEc:mnh:spaper:2899
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    References listed on IDEAS

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    1. 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.
    2. Sjostrom, T. & Krishna, V., 1995. "On the Convergence of Ficticious Play," Papers 04-95-07, Pennsylvania State - Department of Economics.
    3. 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.
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    Cited by:

    1. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
    2. Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    3. J. Durieu & P. Solal & O. Tercieux, 2011. "Adaptive learning and p-best response sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 735-747, November.
    4. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.
    5. Ulrich Berger, 2003. "Fictitious play in 2xn games," Game Theory and Information 0303009, University Library of Munich, Germany.
    6. 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.
    7. Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    8. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    9. Ulrich Berger, 2004. "Some Notes on Learning in Games with Strategic Complementarities," Game Theory and Information 0409001, University Library of Munich, Germany.
    10. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    11. Alfredo Garcia & Stephen D. Patek & Kaushik Sinha, 2007. "A Decentralized Approach to Discrete Optimization via Simulation: Application to Network Flow," Operations Research, INFORMS, vol. 55(4), pages 717-732, August.

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