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Strongly Symmetric Equilibria in Bandit Games

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Abstract

This paper studies strongly symmetric equilibria (SSE) in continuous-time games of strategic experimentation with Poisson bandits. SSE payoffs can be studied via two functional equations similar to the HJB equation used for Markov equilibria. This is valuable for three reasons. First, these equations retain the tractability of Markov equilibrium, while allowing for punishments and rewards: the best and worst equilibrium payoff are explicitly solved for. Second, they capture behavior of the discrete-time game: as the period length goes to zero in the discretized game, the SSE payoff set converges to their solution. Third, they encompass a large payoff set: there is no perfect Bayesian equilibrium in the discrete-time game with frequent interactions with higher asymptotic efficiency.

Suggested Citation

  • Johannes Horner & Nicolas Klein & Sven Rady, 2014. "Strongly Symmetric Equilibria in Bandit Games," Cowles Foundation Discussion Papers 1956, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1956
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d19/d1956.pdf
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    References listed on IDEAS

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    1. Drew Fudenberg & David K. Levine & Satoru Takahashi, 2008. "Perfect public equilibrium when players are patient," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 16, pages 345-367, World Scientific Publishing Co. Pte. Ltd..
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    3. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
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    5. , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    6. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
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    12. Abrea Dilip & Pearce David & Stacchetti Ennio, 1993. "Renegotiation and Symmetry in Repeated Games," Journal of Economic Theory, Elsevier, vol. 60(2), pages 217-240, August.
    13. Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, July.
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    Cited by:

    1. Svetlana Boyarchenko, 2020. "Super- and submodularity of stopping games with random observations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 983-1022, November.
    2. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    3. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    4. Boyarchenko, Svetlana, 2021. "Inefficiency of sponsored research," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    5. Johannes Hoelzemann & Nicolas Klein, 2021. "Bandits in the lab," Quantitative Economics, Econometric Society, vol. 12(3), pages 1021-1051, July.

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    More about this item

    Keywords

    Two-armed bandit; Bayesian learning; Strategic experimentation; Strongly symmetric equilibrium;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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