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Heterogeneous beliefs and local information in stochastic fictitious play

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  • Takahashi, Satoru
  • Fudenberg, Drew

Abstract

Stochastic fictitious play (SFP) assumes that agents do not try to influence the future play of their current opponents, an assumption that is justified by appeal to a setting with a large population of players who are randomly matched to play the game. However, the dynamics of SFP have only been analyzed in models where all agents in a player role have the same beliefs. We analyze the dynamics of SFP in settings where there is a population of agents who observe only outcomes in their own matches and thus have heterogeneous beliefs. We provide conditions that ensure that the system converges to a state with homogeneous beliefs, and that its asymptotic behavior is the same as with a single representative agent in each player role.

Suggested Citation

  • Takahashi, Satoru & Fudenberg, Drew, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Scholarly Articles 27755310, Harvard University Department of Economics.
  • Handle: RePEc:hrv:faseco:27755310
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    References listed on IDEAS

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    Cited by:

    1. Lahkar, Ratul & Seymour, Robert M., 2014. "The dynamics of generalized reinforcement learning," Journal of Economic Theory, Elsevier, vol. 151(C), pages 584-595.
    2. Armenter Roc, 2016. "Sustainable monetary policy and inflation expectations," The B.E. Journal of Macroeconomics, De Gruyter, vol. 16(2), pages 301-334, June.
    3. Ignacio Esponda & Demian Pouzo, 2014. "Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models," Papers 1411.1152, arXiv.org, revised May 2016.
    4. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    5. repec:eee:thpobi:v:91:y:2014:i:c:p:20-36 is not listed on IDEAS
    6. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    7. Ellison, Glenn & Fudenberg, Drew & Imhof, Lorens A., 2016. "Fast convergence in evolutionary models: A Lyapunov approach," Journal of Economic Theory, Elsevier, vol. 161(C), pages 1-36.
    8. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    9. Lahkar, Ratul & Seymour, Robert M., 2013. "Reinforcement learning in population games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 10-38.

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