Robust Information Design with Heterogeneous Beliefs in Bayesian Congestion Games

TL;DR

This paper investigates how to design signaling in Bayesian congestion games with heterogeneous beliefs, ensuring obedience and robustness across belief variations, and analyzes the tradeoffs involved.

Contribution

It introduces a robust information design framework for Bayesian congestion games with belief heterogeneity, characterizing robustness radii and obedience regions.

Findings

Robust obedience regions can be nonempty under certain regimes.

The optimal cost is monotone in the robustness requirement.

Local sensitivity is governed by active obedience constraints.

Abstract

In many engineered systems, agents make decisions under incomplete information, creating opportunities for a planner to influence decentralized behavior through signaling. We study how such signaling can be designed in parallel-network, affine latency congestion games when users may not interpret recommendations using the same beliefs assumed by the planner. To do so, we consider Bayesian congestion games with private recommendations and formulate a robust information design problem in which obedience must hold uniformly over a neighborhood of a nominal prior. This addresses the previously uncharacterized issue of whether obedience itself remains reliable under belief heterogeneity, rather than only under the single prior used at the design stage. We characterize policy-level robustness radii, identify regimes in which the robust obedience region remains nonempty, and analyze the resulting robustness--performance tradeoff through a robust value function whose optimal cost is monotone in the robustness requirement and whose local sensitivity is governed by the active obedience constraints.