Robust Information Design with Heterogeneous Beliefs in Bayesian Congestion Games

In a new arXiv paper, researchers Yuwei Hu and Bryce L. Ferguson tackle a fundamental problem in coordinating AI agents: what happens when the agents don't share the same 'beliefs' as the system designer? They study this in the context of Bayesian congestion games—a model for scenarios like traffic routing or network load balancing—where a central planner sends signals to influence decentralized decisions. The core issue is 'obedience': will an agent follow a recommendation if its internal model of costs and probabilities differs from the planner's assumed prior? Their work is the first to formally address whether obedience holds under this belief heterogeneity, rather than just under a single, idealized prior.

The authors formulate a 'robust information design' problem where obedience must be guaranteed uniformly across a whole neighborhood of possible agent beliefs around a nominal prior. They mathematically characterize 'policy-level robustness radii'—essentially, how much belief divergence the system can tolerate before agents start disobeying. They identify conditions under which a 'robust obedience region' remains non-empty and analyze the inherent trade-off: demanding more robustness to belief differences can reduce the overall performance (or 'value') of the coordinated system. The analysis shows the optimal cost is monotone in the robustness requirement, and its local sensitivity is governed by which obedience constraints are most critical.