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A Note on Best Response Dynamics

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.econ.ed.ac.uk/papers/id3_esedps.pdf
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Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 3.

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Length: 13
Date of creation: 25 Mar 1997
Date of revision:
Handle: RePEc:edn:esedps:3
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  1. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  2. Ed Hopkins, . "Learning, Matching and Aggregation," ELSE working papers 033, ESRC Centre on Economics Learning and Social Evolution.
  3. Itzhak Gilboa & Akihiko Matsui, 1991. "Social Stability and Equilibrium," Post-Print hal-00753235, HAL.
  4. Ed Hopkins, . "Price Dispersion: An Evolutionary Approach," Department of Economics 1996 : III, Edinburgh School of Economics, University of Edinburgh.
  5. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  6. 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.
  7. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  8. Jeroen M. Swinkels, 1991. "Adjustment Dynamics and Rational Play in Games," Discussion Papers 1001, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Tilman Börgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
  10. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
  11. 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.
  12. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
  13. Cressman, R., 1997. "Local stability of smooth selection dynamics for normal form games," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 1-19, August.
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