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Heterogeneous beliefs and local information in stochastic fictitious play

Author

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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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    Cited by:

    1. Block, Juan I. & Fudenberg, Drew & Levine, David K., 2019. "Learning dynamics with social comparisons and limited memory," Theoretical Economics, Econometric Society, vol. 14(1), January.
    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. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    4. Kai A. Konrad & Florian Morath, 2020. "Escalation in conflict games: on beliefs and selection," Experimental Economics, Springer;Economic Science Association, vol. 23(3), pages 750-787, September.
    5. , & ,, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    6. Naoki Funai, 2019. "Convergence results on stochastic adaptive learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 907-934, November.
    7. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    8. Takako Fujiwara-Greve & Carsten Krabbe Nielsen, 2021. "Algorithms may not learn to play a unique Nash equilibrium," Journal of Computational Social Science, Springer, vol. 4(2), pages 839-850, November.
    9. Lahkar, Ratul & Seymour, Robert M., 2014. "The dynamics of generalized reinforcement learning," Journal of Economic Theory, Elsevier, vol. 151(C), pages 584-595.
    10. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    11. Dridi, Slimane & Lehmann, Laurent, 2014. "On learning dynamics underlying the evolution of learning rules," Theoretical Population Biology, Elsevier, vol. 91(C), pages 20-36.
    12. 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.
    13. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. 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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