Strategic Successive Refinement Coding for Bayesian Persuasion with Two Decoders

TL;DR

This paper analyzes a multi-user Bayesian persuasion game involving an encoder and two decoders with different information levels, focusing on optimal coding strategies under strategic distortion minimization.

Contribution

It introduces a novel successive refinement coding framework that accounts for strategic incentives of multiple decoders with arbitrary distortion functions.

Findings

Characterizes the optimal encoder distortion using auxiliary random variables.

Provides a strategic source coding solution for multi-decoder Bayesian persuasion.

Integrates incentive constraints into the successive refinement coding model.

Abstract

We study the multi-user Bayesian persuasion game between one encoder and two decoders, where the first decoder is better informed than the second decoder. We consider two perfect links, one to the first decoder only, and the other to both decoders. We consider that the encoder and both decoders are endowed with distinct and arbitrary distortion functions. We investigate the strategic source coding problem in which the encoder commits to an encoding while the decoders select the sequences of symbols that minimize their respective distortion functions. We characterize the optimal encoder distortion value by considering successive refinement coding with respect to a specific probability distribution which involves two auxiliary random variables, and captures the incentives constraints of both decoders.