Impact of Private Observation in the Bayesian Persuasion Game

Abstract

In the Bayesian persuasion setting, the sender aims at persuading the decision maker, so called the decoder, to choose a certain action among a set of possible actions. This paper considers two Bayesian persuasion games: one that involves the observation of a private signal by the decoder in addition to the signal transmitted by the encoder, and another version where no private signal is accessible by the decoder. Our goal is to examine the impact of this private signal on the encoder’s optimal utility. In order to do so, we investigate an example involving a binary state, a binary private signal and a binary receiver’s actions set. We identify the optimal splitting of the decoder’s beliefs satisfying the information constraint imposed by the restricted communication channel, and we compute the encoder’s optimal utility value, with and without private signal. Varying the parameters such as the prior belief, the precision of the private signal and the channel capacity, we aim at determining which of the two settings is more favorable to the encoder.