Strategic Experimentation with Uncertainty about Sender’s Credibility

This study introduces the uncertainty about Sender’s credibility into the Bayesian persuasion framework, investigating how Receiver’s capability of finding information on Sender’s credibility affects players’ behavior and welfare. We consider a one-sender/one-receiver model in which Receiver (she) needs to choose between multiple actions. Her payoff depends on her choice and an unobservable underlying state. Sender (he), who has conflicting interests with her, can influence her belief about the state by designing an experiment generating state-dependent signals.

Sender announces the signal structure of the experiment before running the experiment. However, Sender commits to the announced signal structure when designing the experiment only if he is credible, but may use different signal structure if he is not credible. Receiver only knows the announced signal structure but not the true signal structure and Sender’s credibility. She can draw a message from the information on Sender’s credibility that she finds. The probability that she draws the correct message about Sender’s type depends on her capability.

We find that there is a unique critical level of Receiver’s capability such that both Receiver’s welfare and the informativeness of Sender’s experiment reach their maximums if and only if Receiver’s ability is at this level, and Receiver benefits from Sender’s experimentation only if her ability does not exceed this critical level. Moreover, although Sender always benefits from his experimentation, when Receiver’s capability is at this critical level, Sender’s expected payoff is minimized if he is credible but maximized if he is no credible.