Strategic Communication with Cost-Dependent Decoders via the Gray-Wyner Network

TL;DR

This paper analyzes a strategic communication game involving an encoder and two decoders over a Gray-Wyner network, focusing on optimal compression schemes that align with the agents' rational, yet conflicting, objectives.

Contribution

It introduces a framework for strategic communication with cost-dependent decoders in a Gray-Wyner network, characterizing minimal long-term costs under incentive constraints.

Findings

Characterization of optimal compression schemes for strategic decoders.

Analysis of incentive compatibility in decentralized communication.

Derivation of minimal long-run cost functions.

Abstract

In decentralized decision-making problems, communicating agents choose their actions based on locally available information and knowledge about decision rules or strategies of other agents. In this work, we consider a strategic communication game between an informed encoder and two decoders communicating via a Gray-Wyner network. All three agents are assumed to be rational and endowed with distinct objectives captured by non-aligned cost functions. The encoder selects and announces beforehand the compression scheme to be implemented. Then, it transmits three signals: a public signal, and a private signal to each decoder inducing a Bayesian game among the decoders. Our goal is to characterize the encoder's minimal long-run cost function subject to the optimal compression scheme that satisfies both decoders incentives constraints.