Successive Refinement Source Coding for Bayesian Persuasion

In this paper, we study the multi-user Bayesian Persuasion Game between one informed and biased encoder and two decoders communicating together through a perfect channel. We consider a degraded broadcast channel where one decoder is better informed than the other. Assuming that all players have misaligned objectives, we investigate the information theoretic limit of repeating several independent copies of the same problem. We use successive refinement for source coding to characterize the sets of target distributions, and we show that the encoder's long run optimal distortion converges to, and is bounded by its single-letter optimal distortion.