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Learning Purified Mixed Equilibria

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  • Ellison, Glenn
  • Fudenberg, Drew

Abstract

better understand when mixed equilibria might arise within populations of interact acting agents, we examine a model of smoothed fictitious play that is designed to capture Harsanyi's "Purification", view of mixed equilibria in a setting with a large population of agents. Our analysis concerns the local stability of equilibria when the degree of heterogeneity in the population is small. In 2 x 2 games our model is easy to analyze and yields the same conclusions as have previous models. Our primary focus is on 3 x 3 games where we provide a general characterization of which equilibria are locally stable, and discuss its implications in several particular cases. Among our conclusions are that learning can sometimes provide a justification for mixed equilibria outside of 2 x 2 games, that whether an equilibrium is stable or unstable is often dependent on the distribution of payoff heterogeneity in the population, that the totally mixed equilibria of zero sum games are generically stable, and that under a "balanced perturbation" condition the equilibria of symmetric games are generically unstable.
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Suggested Citation

  • Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
  • Handle: RePEc:eee:jetheo:v:90:y:2000:i:1:p:84-115
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    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
    3. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    4. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    5. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    6. Aoyagi, Masaki, 1996. "Evolution of Beliefs and the Nash Equilibrium of Normal Form Games," Journal of Economic Theory, Elsevier, vol. 70(2), pages 444-469, August.
    7. Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November.
    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.
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