## 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 who have no knowledge of the data-generating process and 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. Like contracts, tests have to be computable to be implemented. Considering only computable tests, we show that there is a test that passes true experts with a high probability yet is not manipulable by any computable strategy. In particular, the constructed test is both prequential and future-independent. Alternatively, any computable test is manipulable by a strategy that is computable relative to the halting problem. Our conclusion overturns earlier results that prequential or future-independent tests are manipulable, and shows that computability considerations have significant effects in these problems.

Original language | English (US) |
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Pages (from-to) | 263-280 |

Number of pages | 18 |

Journal | Theoretical Economics |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - May 2013 |

## Keywords

- Calibration tests
- Computability
- Expert testing
- Zero-sum games

## ASJC Scopus subject areas

- Economics, Econometrics and Finance(all)