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Consistency and Cautious Fictitious Play

  • Fudenberg, Drew
  • Levine, David

We study a variation of fictitious play, in which the probability of each action is an exponential function of that action's utility against the historical frequency of opponents' play. Regardless of the opponents' strategies, the utility received by an agent using this rule is nearly the best that could be achieved against the historical frequency. Such rules are approximately optimal in i.i.d. environments, and guarantee nearly the minmax regardless of opponents' behavior. Fictitious play shares these properties provided it switches 'infrequently' between actions. We also study the long-run outcomes when all players use consistent and cautious rules.

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File URL: http://dash.harvard.edu/bitstream/handle/1/3198694/fudenberg_consistency.pdf
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Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3198694.

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Date of creation: 1995
Date of revision:
Publication status: Published in Journal of Economic Dynamics and Control
Handle: RePEc:hrv:faseco:3198694
Contact details of provider: Postal: Littauer Center, Cambridge, MA 02138
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Web page: http://www.economics.harvard.edu/

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  1. Anderlini, Luca & Sabourian, Hamid, 1995. "Cooperation and Effective Computability," Econometrica, Econometric Society, vol. 63(6), pages 1337-69, November.
  2. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
  3. Dov Monderer & Dov Samet & Aner Sela, 1994. "Belief Affirming in Learning Processes," Game Theory and Information 9408002, EconWPA, revised 11 Aug 1994.
  4. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  6. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
  7. Lawrence E. Blume, 1994. "How Noise Matters," Game Theory and Information 9407002, EconWPA, revised 27 Jul 1994.
  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  9. DeCanio, Stephen J, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 47-57, February.
  10. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  11. D. Blackwell & L. Dubins, 2010. "Merging of Opinions with Increasing Information," Levine's Working Paper Archive 565, David K. Levine.
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