Contracts and Uncertainty

A decision maker wants to know if an expert has relevant information about a stochastic process. The expert either perfectly knows the probability of all future events or knows nothing about these probabilities. The expert announces the probability distribution of all future events before any data is observed. An empirical test is finite if, in some finite time, the announced probability measure is either rejected or not rejected. A test is good if it can determine the expert type based on the data. In this paper, I show that a good finite test does not exist.