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Approachability with delayed information

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  • Lagziel, David
  • Lehrer, Ehud

Abstract

We consider a sequential decision problem where the decision maker is informed of the actual payoff with delay. We introduce a new condition, which generalizes the condition given by Blackwell and ensures that the decision maker can approach a fixed closed and convex set under delay. We show how the convergence rate to the approachable set is sensitive to changes in the information lag and apply our approachability strategy to games with one-sided incomplete information and to regret-free strategies.

Suggested Citation

  • Lagziel, David & Lehrer, Ehud, 2015. "Approachability with delayed information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 425-444.
    • Handle: RePEc:eee:jetheo:v:157:y:2015:i:c:p:425-444
    DOI: 10.1016/j.jet.2015.01.010
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    References listed on IDEAS

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    1. Fudenberg, Drew & Ishii, Yuhta & Kominers, Scott Duke, 2014. "Delayed-response strategies in repeated games with observation lags," Journal of Economic Theory, Elsevier, vol. 150(C), pages 487-514.
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    6. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
    8. Vianney Perchet, 2011. "Approachability of Convex Sets in Games with Partial Monitoring," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 665-677, June.
    9. Rustichini, Aldo, 1999. "Minimizing Regret: The General Case," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 224-243, October.
    10. Alvaro Sandroni & Rann Smorodinsky & Rakesh V. Vohra, 2003. "Calibration with Many Checking Rules," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 141-153, February.
    11. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
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    Cited by:

    1. Carmona, G. & Sabourian, H., 2021. "Approachability with Discounting," Cambridge Working Papers in Economics 2124, Faculty of Economics, University of Cambridge.
    2. Gordon, Sidartha & Marlats, Chantal & Ménager, Lucie, 2021. "Observation delays in teams and effort cycles," Games and Economic Behavior, Elsevier, vol. 130(C), pages 276-298.
    3. Du, Ye & Lehrer, Ehud, 2020. "Constrained no-regret learning," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 16-24.

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    More about this item

    Keywords

    Approachability; Delayed information; Imperfect and asymmetric information;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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