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Learning in Perturbed Asymmetric Games

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  • Josef Hofbauer
  • Ed Hopkins

    ()

Abstract

We investigate the stability of mixed strategy equilibria in 2 person (bimatrix) games under perturbed best response dynamics. A mixed equilibrium is asymptotically stable under all such dynamics if and only if the game is linearly equivalent to a zero sum game. In this case, the mixed equilibrium is also globally asymptotically stable. Global convergence to the set of perturbed equilibria is shown also for (rescaled) partnership games (also know as games of identical interest). Some applications of these result to stochastic learning models are given.

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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 53.

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Length: 16
Date of creation: Apr 2004
Date of revision:
Handle: RePEc:edn:esedps:53

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Keywords: Games; Learning; Best Response Dynamics; Stochastic Fictitious Play; Mixed Strategy Equilibria; Zero Sum Games;

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  1. Echenique, Federico & Edlin, Aaron, 2002. "Mixed Equilibria in Games of Strategic Complements Are Unstable," Department of Economics, Working Paper Series qt1gr638d8, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
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  13. 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.
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  17. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  18. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," NajEcon Working Paper Reviews 625018000000000226, www.najecon.org.
  19. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
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