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Expressible inspections

Author

Listed:
  • Hu, Tai Wei

    (Kellogg School of Management, Northwestern University)

  • Shmaya, Eran

    (Kellogg School of Management, Northwestern University)

Abstract

A decision maker needs predictions about the realization of a repeated experiment in each period. An expert provides a theory that, conditional on each finite history of outcomes, supplies a probabilistic prediction about the next outcome. However, there may be false experts without any knowledge of the data-generating process who deliver theories strategically. Hence, empirical tests for predictions are necessary. A test is manipulable if a false expert can pass the test with a high probability. For tests, as contracts, to be implementable, they have to be computable. Considering only computable tests, we show that there is a test that is not manipulable by any computable strategies and that accepts true experts with high probabilities. In particular, the constructed test is both future independent (Olszewski and Sandroni, 2008) and sequential (Shmaya, 2008). On the other hand, any computable test is manipulable by a strategy that is computable relative to the halting problem. Our conclusion overturns earlier results that future independent tests are manipulable, and shows that computability considerations have significant effects in these problems.

Suggested Citation

  • Hu, Tai Wei & Shmaya, Eran, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
  • Handle: RePEc:the:publsh:992
    as

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    References listed on IDEAS

    as
    1. 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.
    2. Wojciech Olszewski & Alvaro Sandroni, 2009. "Strategic Manipulation of Empirical Tests," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 57-70, February.
    3. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 151-159, December.
    4. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 893-906.
    5. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
    7. Lance Fortnow & Rakesh V. Vohra, 2009. "The Complexity of Forecast Testing," Econometrica, Econometric Society, vol. 77(1), pages 93-105, January.
    8. 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.
    9. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    10. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-1347, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. “Expressible Inspections,” T-W. Hu & E. Shmaya (2012)
      by afinetheorem in A Fine Theorem on 2012-05-09 10:59:35

    Citations

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    Cited by:

    1. Bavly, Gilad & Peretz, Ron, 2015. "How to gamble against all odds," Games and Economic Behavior, Elsevier, vol. 94(C), pages 157-168.
    2. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Hu, Tai-Wei, 2014. "Unpredictability of complex (pure) strategies," Games and Economic Behavior, Elsevier, vol. 88(C), pages 1-15.

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    More about this item

    Keywords

    Computability; expert testing; calibration tests; zero-sum games;
    All these keywords.

    JEL classification:

    • D00 - Microeconomics - - General - - - General

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