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Belief Affirming in Learning Processes

Author

Listed:
  • Dov Monderer
  • Dov Samet
  • Aner Sela

Abstract

A learning process is belief affirming if for each player, the difference between her expected payoff in the next period, and the average of her past payoffs converges to zero. We show that every smooth discrete fictitious play and every continuous fictitious play is belief affirming. We also provide conditions under which general averaging processes are belief affirming.

Suggested Citation

  • Dov Monderer & Dov Samet & Aner Sela, 1994. "Belief Affirming in Learning Processes," Game Theory and Information 9408002, University Library of Munich, Germany, revised 11 Aug 1994.
    • Handle: RePEc:wpa:wuwpga:9408002
    Note: 14 p. AmS TeX. (for a PostScript file call samet@vm.tau.ac il).
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    Citations

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    Cited by:

    1. Kalai, Ehud & Lehrer, Ehud & Smorodinsky, Rann, 1999. "Calibrated Forecasting and Merging," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 151-169, October.
    2. Vijay Krishna & Tomas Sjostrom, 1995. "On the Convergence of Fictitious Play," Harvard Institute of Economic Research Working Papers 1717, Harvard - Institute of Economic Research.
    3. José Pedro Gaivão & Telmo Peixe, 2019. "Periodic attractor in the discrete time best-response dynamics of the rock-paper-scissors game," Working Papers REM 2019/0108, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    4. Sela, Aner, 2000. "Fictitious Play in 2 x 3 Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 152-162, April.
    5. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
    6. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
    7. Viossat, Yannick & Zapechelnyuk, Andriy, 2013. "No-regret dynamics and fictitious play," Journal of Economic Theory, Elsevier, vol. 148(2), pages 825-842.
    8. Phillip Johnson & David K. Levine & Wolfgang Pesendorfer, 1998. "Evolution and Information in a Prisoner's Dilemma Game," Working Papers 9805, Centro de Investigacion Economica, ITAM.
    9. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    10. Jos'e Pedro Gaiv~ao & Telmo Peixe, 2019. "Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game," Papers 1912.06831, arXiv.org.
    11. Driesen, B.W.I., 2009. "Continuous fictitious play in zero-sum games," Research Memorandum 049, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    13. Drew Fudenberg & David K Levine, 2016. "Whither Game Theory?," Levine's Working Paper Archive 786969000000001307, David K. Levine.
    14. Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    15. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    16. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    17. José Pedro Gaivão & Telmo Peixe, 2021. "Periodic Attractor in the Discrete Time Best-Response Dynamics of the Rock-Paper-Scissors Game," Dynamic Games and Applications, Springer, vol. 11(3), pages 491-511, September.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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