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Strongly Symmetric Equilibria in Bandit Games

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Listed:
  • Hörner, Johannes
  • Klein, Nicolas
  • Rady, Sven

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

  • Hörner, Johannes & Klein, Nicolas & Rady, Sven, 2014. "Strongly Symmetric Equilibria in Bandit Games," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 469, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    • Handle: RePEc:trf:wpaper:469
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    References listed on IDEAS

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    1. Murto, Pauli & Välimäki, Juuso, 2013. "Delay and information aggregation in stopping games with private information," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2404-2435.
    2. Johannes Hörner & Larry Samuelson, 2013. "Incentives for experimenting agents," RAND Journal of Economics, RAND Corporation, vol. 44(4), pages 632-663, December.
    3. 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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    5. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    6. , & ,, 2010. "Strategic experimentation with Poisson bandits," Theoretical Economics, Econometric Society, vol. 5(2), May.
    7. 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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    12. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    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. Heidhues, Paul & Rady, Sven & Strack, Philipp, 2015. "Strategic experimentation with private payoffs," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 531-551.
    2. Johannes Hoelzemann & Nicolas Klein, 2021. "Bandits in the lab," Quantitative Economics, Econometric Society, vol. 12(3), pages 1021-1051, July.
    3. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    4. 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.
    5. Boyarchenko, Svetlana, 2021. "Inefficiency of sponsored research," Journal of Mathematical Economics, Elsevier, vol. 95(C).

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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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