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A Note on Best Response Dynamics

  • Hopkins, Ed

We investigate the relationship between the continuous time best response dynamic, its perturbed version and evolutionary dynamics in relation to mixed strategy equilibria. We find that as the level of noise approaches zero, the perturbed best response dynamic has the same quantitative properties as a broad class of evolutionary dynamics. That is, stability properties of equilibria are robust across learning dynamics of quite different origins and motivations.

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File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(97)90636-9
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 29 (1999)
Issue (Month): 1-2 (October)
Pages: 138-150

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Handle: RePEc:eee:gamebe:v:29:y:1999:i:1-2:p:138-150
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  2. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  3. Ed Hopkins & Robert M. Seymour, 1996. "Price Dispersion: An Evolutionary Approach," ESE Discussion Papers 1, Edinburgh School of Economics, University of Edinburgh.
  4. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  5. Ed Hopkins, 1995. "Learning, Matching and Aggregation," Game Theory and Information 9512001, EconWPA.
  6. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, March.
  7. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
  8. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
  9. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
  10. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  11. 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.
  12. Cressman, R., 1997. "Local stability of smooth selection dynamics for normal form games," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 1-19, August.
  13. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  14. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
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