Repeated Cheap-Talk Games of Common Interest between a Decision-Maker and an Expert of Unknown Statistical Bias

Abstract

Two agents are engaged in a joint activity that yields a common perperiod payoff at two rounds of play. The expert announces the probability that the current state of the world is low, instead of high, at each stage. Having received the report of the expert, the decision-maker takes action at every period according to his posterior beliefs. At the end of each round of play, the true current state is verifiable. The distinctive assumption of the paper is that the decision-maker makes a subjective appraisal of the expert’s reliability: he considers the expert’s true forecasts as the outcomes of an experiment of unknown statistical bias. The paper shows that the expert will have instrumental reputational concerns, related to the future estimate of the systematic error associated to his predictions. In contrast with previous work, reputational concerns are shown to enhance the credibility of the initial messages, and to increase both the agents’ expected payoff at the first round of play in equilibrium. The equilibrium messages will be noisy, but noisiness will be less costly than it would be in single-stage games.