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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 L\'{e}vy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, plus a free background signal, 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," Papers 1909.13323, arXiv.org, revised Aug 2020.
  • Handle: RePEc:arx:papers:1909.13323
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    References listed on IDEAS

    as
    1. 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.
    2. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 475-507.
    3. Alessandro Bonatti, 2011. "Menu Pricing and Learning," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 124-163, August.
    4. 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.
    5. 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.
    6. 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.
    7. Martin Peitz & Sven Rady & Piers Trepper, 2015. "Experimentation in Two-Sided Markets," CESifo Working Paper Series 5346, CESifo.
    8. Keller, Godfrey & Rady, Sven, 2003. "Price Dispersion and Learning in a Dynamic Differentiated-Goods Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 138-165, Spring.
    9. Dutta, P.K., 1991. "What Do Discounted Optima Converge To? A Theory of Discount Rate Asymptotics in Economic Models," RCER Working Papers 264, University of Rochester - Center for Economic Research (RCER).
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    More about this item

    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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