Keeping your story straight: truthtelling and liespotting

Johannes Hörner (), Xiaosheng Mu () and Nicolas Vieille ()
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Johannes Hörner: Toulouse School of Economics
Xiaosheng Mu: Department of Economics, Princeton University
Nicolas Vieille: HEC Paris

Theoretical Economics, Forthcoming

Abstract: An agent privately observes a Markov chain online and reports it to a designer. To what patterns in the reported data should the designer pay attention? We show that, in general, keeping track of the empirical frequency of transition counts in the agent’s reports is insufficient, despite the true state being Markovian. Nonetheless, we derive conditions under which any deviation that can be distinguished from truth-telling by checking the frequency of strings of an arbitrary (finite) size can be detected by “checking pairs.” Further, we find that some undetectable deviations cannot be profitable, independent of the agent’s preferences. Hence, we provide weaker sufficient conditions that ensure that the agent finds honesty to be the best strategy. We explore the implications of these results for the literature on (i) linking incentives, (ii) dynamic implementation, and (iii) repeated games and agency models.

Keywords: Detectability; testing; Markov chains; implementation; repeated games (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2026-07-15
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