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Expressible inspections

  • Hu, Tai Wei

    ()

    (Kellogg School of Management, Northwestern University)

  • Shmaya, Eran

    ()

    (Kellogg School of Management, Northwestern University)

Registered author(s):

    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.

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    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20130263/8769/259
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    Article provided by Econometric Society in its journal Theoretical Economics.

    Volume (Year): 8 (2013)
    Issue (Month): 2 (May)
    Pages:

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    Handle: RePEc:the:publsh:992
    Contact details of provider: Web page: http://econtheory.org

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    1. Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
    2. Lance Fortnow & Rakesh V. Vohra, 2009. "The Complexity of Forecast Testing," Econometrica, Econometric Society, vol. 77(1), pages 93-105, 01.
    3. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer, vol. 32(1), pages 151-159, December.
    4. Alvaro Sandroni & Wojciech Olszewski, 2008. "Strategic Manipulation of Empirical Tests," PIER Working Paper Archive 08-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    5. 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.
    6. 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.
    7. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    8. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-47, September.
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