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Undiscounted Bandit Games

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  • Godfrey Keller
  • Sven Rady

Abstract

We analyze undiscounted continuous-time games of strategic experimentation with two-armed bandits. The risky arm generates payoffs according to a Lévy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, players use Markov strategies with the common posterior belief about the unknown parameter as the state variable. We show that the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the payoff of the safe arm, the expected current payoff of the risky arm, and the expected full-information payoff, given the current belief. In particular, the equilibrium does not depend on the precise specification of the payoff-generating processes.

Suggested Citation

  • Godfrey Keller & Sven Rady, 2019. "Undiscounted Bandit Games," CRC TR 224 Discussion Paper Series crctr224_2019_130, University of Bonn and University of Mannheim, Germany.
  • Handle: RePEc:bon:boncrc:crctr224_2019_130
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    File URL: https://www.crctr224.de/en/research-output/discussion-papers/discussion-papers#DP130
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    References listed on IDEAS

    as
    1. Pietro Veronesi, 2000. "How Does Information Quality Affect Stock Returns?," Journal of Finance, American Finance Association, vol. 55(2), pages 807-837, April.
    2. Martin Peitz & Sven Rady & Piers Trepper, 2017. "Experimentation in Two-Sided Markets," Journal of the European Economic Association, European Economic Association, vol. 15(1), pages 128-172.
    3. Asaf Cohen & Eilon Solan, 2013. "Bandit Problems with Lévy Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 92-107, February.
    4. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 475-507.
    5. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    6. Alessandro Bonatti, 2011. "Menu Pricing and Learning," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 124-163, August.
    7. Bergemann, Dirk & Valimaki, Juuso, 2002. "Entry and Vertical Differentiation," Journal of Economic Theory, Elsevier, vol. 106(1), pages 91-125, September.
    8. Dutta, Prajit K., 1991. "What do discounted optima converge to?: A theory of discount rate asymptotics in economic models," Journal of Economic Theory, Elsevier, vol. 55(1), pages 64-94, October.
    9. Moscarini, Giuseppe & Squintani, Francesco, 2010. "Competitive experimentation with private information: The survivor's curse," Journal of Economic Theory, Elsevier, vol. 145(2), pages 639-660, March.
    10. Jovanovic, Boyan, 1979. "Job Matching and the Theory of Turnover," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 972-990, October.
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    13. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, vol. 67(2), pages 349-374, March.
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    More about this item

    Keywords

    Strategic Experimentation; Two-Armed Bandit; Strong Long-Run Average Criterion; Markov Perfect Equilibrium; HJB Equation; Viscosity Solution;
    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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