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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- Eddie Dekel & Yossi Feinberg, 2006.
"Non-Bayesian Testing of a Stochastic Prediction,"
1418, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Wojciech Olszewski & Alvaro Sandroni, 2006.
"Strategic Manipulation of Empirical Tests,"
1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-1347, September.
- 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.
- 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.
- Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
- Lehrer, Ehud, 2003.
"A wide range no-regret theorem,"
Games and Economic Behavior,
Elsevier, vol. 42(1), pages 101-115, January.
- Lance Fortnow & Rakesh V. Vohra, 2009. "The Complexity of Forecast Testing," Econometrica, Econometric Society, vol. 77(1), pages 93-105, 01.
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