Bayesian persuasion with cheap talk

We study a sender-receiver game with a two-dimensional state of the world and state dependent sender preferences. The sender can commit to a signal as in the Bayesian persuasion framework for only one of the dimensions. We show how the ability to engage in cheap talk changes the optimal signal and makes the sender better off. The results have implications for some real world applications. For instance, they can help explain why schools prefer not to adopt grading policies that fully reveal student ability.