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A General Internal Regret-Free Strategy

Author

Listed:
  • Ehud Lehrer

    () (Tel Aviv University
    INSEAD)

  • Eilon Solan

    () (Tel Aviv University)

Abstract

Abstract We study sequential decision problems where the decision maker does not observe the states of nature, but rather receives a noisy signal, whose distribution depends on the current state and on the action that she plays. We do not assume that the decision maker considers the worst-case scenario, but rather has a response correspondence, which maps distributions over signals to subjective best responses. We extend the concept of internal regret-free strategy to this setup and provide an algorithm that generates such a strategy.

Suggested Citation

  • Ehud Lehrer & Eilon Solan, 2016. "A General Internal Regret-Free Strategy," Dynamic Games and Applications, Springer, vol. 6(1), pages 112-138, March.
  • Handle: RePEc:spr:dyngam:v:6:y:2016:i:1:d:10.1007_s13235-015-0143-5
    DOI: 10.1007/s13235-015-0143-5
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    References listed on IDEAS

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    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
    2. Foster, Dean P., 1999. "A Proof of Calibration via Blackwell's Approachability Theorem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 73-78, October.
    3. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
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    5. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    6. Gábor Lugosi & Shie Mannor & Gilles Stoltz, 2008. "Strategies for Prediction Under Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 513-528, August.
    7. Ehud Lehrer & Eilon Solan, 2007. "Learning to play partially-specified equilibrium," Levine's Working Paper Archive 122247000000001436, David K. Levine.
    8. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
    9. Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
    10. Rustichini, Aldo, 1999. "Minimizing Regret: The General Case," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 224-243, October.
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