Robust Information Design with Heterogeneous Beliefs in Bayesian Congestion Games
For system planners designing signaling in congestion games, this work addresses the previously uncharacterized issue of whether obedience remains reliable under belief heterogeneity.
The paper studies robust information design in Bayesian congestion games where agents may have heterogeneous beliefs. It characterizes robustness radii and tradeoffs between robustness and performance, showing that optimal cost is monotone in robustness requirements.
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.