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Many inspections are manipulable

Author

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    (Information Science and Technology, California Institute of Technology)

Abstract
A self-proclaimed expert uses past observations of a stochastic process to make probabilistic predictions about the process. An inspector applies a test function to the infinite sequence of predictions provided by the expert and the observed realization of the process in order to check the expert's reliability. If the test function is Borel and the inspection is such that a true expert always passes it, then it is also manipulable by an ignorant expert. The proof uses Martin's theorem about the determinacy of Blackwell games. Under the axiom of choice, there exist non-Borel test functions that are not manipulable.

Suggested Citation

  • ,, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    • Handle: RePEc:the:publsh:398
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    Citations

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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. Yossi Feinberg & Nicolas Lambert, 2015. "Mostly calibrated," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 153-163, February.
    3. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
    6. Arieli, Itai & Levy, Yehuda John, 2015. "Determinacy of games with Stochastic Eventual Perfect Monitoring," Games and Economic Behavior, Elsevier, vol. 91(C), pages 166-185.
    7. János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eilon Solan & Koos Vrieze, 2010. "Perfect-Information Games with Lower-Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 742-755, November.
    8. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Kavaler, Itay & Smorodinsky, Rann, 2019. "On comparison of experts," Games and Economic Behavior, Elsevier, vol. 118(C), pages 94-109.
    10. Mark Whitmeyer & Kun Zhang, 2023. "Redeeming Falsifiability?," Papers 2303.15723, arXiv.org.
    11. Al-Najjar, Nabil I. & Sandroni, Alvaro & Smorodinsky, Rann & Weinstein, Jonathan, 2010. "Testing theories with learnable and predictive representations," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2203-2217, November.
    12. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
    13. David Lagziel & Ehud Lehrer, 2021. "Transferable deposits as a screening mechanism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 483-504, March.
    14. David Lagziel & Ehud Lehrer, 2015. "On the Failures of Bonus Plans," Papers 1505.04587, arXiv.org.
    15. Wojciech Olszewski & Alvaro Sandroni, 2009. "Strategic Manipulation of Empirical Tests," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 57-70, February.
    16. , & ,, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
    17. Kuehn, S., 2010. "A new Keynesian model with endogenous technology trend," Research Memorandum 040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    More about this item

    Keywords

    Forecasting; calibration; zero-sum games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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