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Learning Purified Mixed Equilibria

  • Glenn Ellison
  • Drew Fudenberg

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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Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 1817.

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Date of creation: 1998
Date of revision:
Handle: RePEc:fth:harver:1817
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  1. Drew Fudenberg & David K. Levine, 1996. "Consistency and Cautious Fictitious Play," Levine's Working Paper Archive 470, David K. Levine.
  2. 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.
  3. 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.
  4. 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.
  5. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  6. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
  8. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
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