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Consistency and Cautious Fictitious Play

  • Drew Fudenberg
  • David K. Levine

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://www.dklevine.com/papers/c1-2v8.pdf
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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 470.

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Date of creation: 29 Oct 1996
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Handle: RePEc:cla:levarc:470
Contact details of provider: Web page: http://www.dklevine.com/

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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. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
  3. Dov Monderer & Dov Samet & Aner Sela, 2010. "Belief Affirming in Learning Processes," Levine's Working Paper Archive 420, David K. Levine.
  4. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  5. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  6. D. Blackwell & L. Dubins, 2010. "Merging of Opinions with Increasing Information," Levine's Working Paper Archive 565, David K. Levine.
  7. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
  8. 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.
  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  11. DeCanio, Stephen J, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 47-57, February.
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