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Consistency and cautious fictitious play

  • Fudenberg, Drew
  • Levine, David K.

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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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 19 (1995)
Issue (Month): 5-7 ()
Pages: 1065-1089

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Handle: RePEc:eee:dyncon:v:19:y:1995:i:5-7:p:1065-1089
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  1. 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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  3. 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.
  4. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  6. 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.
  7. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  9. Stephen J. DeCanio, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, Oxford University Press, vol. 93(1), pages 47-57.
  10. Lawrence E. Blume, 1994. "How Noise Matters," Game Theory and Information 9407002, EconWPA, revised 27 Jul 1994.
  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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