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A proof of Calibration via Blackwell's Approachability Theorem

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  • Dean P Foster

Abstract

Over the past few years many proofs of calibration have been presented (Foster and Vohra (1991, 1997), Hart (1995), Fudenberg and Levine (1995), Hart and Mas-Colell (1996)). Does the literature really need one more? Probably not, but this algorithim for being calibrated is particularly simple and doesn't require a matrix inversion. Further the proof follows directly from Blackwell's approachability theorem. For these reasons it might be useful in the class room.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Dean P Foster, 1997. "A proof of Calibration via Blackwell's Approachability Theorem," Levine's Working Paper Archive 591, David K. Levine.
    • Handle: RePEc:cla:levarc:591
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    File URL: http://www.dklevine.com/archive/calibration_via_blackwell.pdf
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
    2. 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..
    3. D. Blackwell, 2010. "An Analog of the Minmax Theorem for Vector Payoffs," Levine's Working Paper Archive 466, David K. Levine.
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    Cited by:

    1. Foster, Dean & Hart, Sergiu, 2023. ""Calibeating": beating forecasters at their own game," Theoretical Economics, Econometric Society, vol. 18(4), November.
    2. DeMarzo, Peter M. & Kremer, Ilan & Mansour, Yishay, 2016. "Robust option pricing: Hannan and Blackwell meet Black and Scholes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 410-434.
    3. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
    5. Flesch, János & Laraki, Rida & Perchet, Vianney, 2018. "Approachability of convex sets in generalized quitting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 411-431.
    6. Dean P. Foster & Sergiu Hart, 2021. "Forecast Hedging and Calibration," Journal of Political Economy, University of Chicago Press, vol. 129(12), pages 3447-3490.
    7. Shie Mannor & Gilles Stoltz, 2009. "A Geometric Proof of Calibration," Working Papers hal-00442042, HAL.
    8. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Venkat Anantharam, 2022. "Weakening the grip of the model," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 385-387, April.
    10. Foster, Dean P. & Hart, Sergiu, 2018. "Smooth calibration, leaky forecasts, finite recall, and Nash dynamics," Games and Economic Behavior, Elsevier, vol. 109(C), pages 271-293.
    11. Ehud Lehrer & Eilon Solan, 2016. "A General Internal Regret-Free Strategy," Dynamic Games and Applications, Springer, vol. 6(1), pages 112-138, March.
    12. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
    13. Vianney Perchet, 2015. "Exponential Weight Approachability, Applications to Calibration and Regret Minimization," Dynamic Games and Applications, Springer, vol. 5(1), pages 136-153, March.
    14. Mannor, Shie & Shimkin, Nahum, 2008. "Regret minimization in repeated matrix games with variable stage duration," Games and Economic Behavior, Elsevier, vol. 63(1), pages 227-258, May.
    15. Varun Gupta & Christopher Jung & Georgy Noarov & Mallesh M. Pai & Aaron Roth, 2021. "Online Multivalid Learning: Means, Moments, and Prediction Intervals," Papers 2101.01739, arXiv.org.
    16. Shie Mannor & Gilles Stoltz, 2010. "A Geometric Proof of Calibration," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 721-727, November.

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