April 2017
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.