Decentralized Signaling Mechanisms
Niloufar Mirzavand Boroujeni, Krishnamurthy Iyer, William L. Cooper
TL;DR
The paper tackles information design in a Bayesian-persuasion framework for a multi-location service system, comparing centralized versus decentralized signaling when a customer chooses where to join. It develops an efficient reduction of the decentralized problem to K isolated-location linear programs and proves a universal throughput bound Th_D ≥ [1 - (1 - 1/K)^K] Th under independence, with tightness demonstrated by a matching example. The authors further extend the results to heterogeneous location payoffs and to correlated location states, providing corresponding guarantees: a multiplicative bound under heterogeneity and a 1/K bound under general correlation, plus tight asymptotics showing the limits of decentralization as dependence grows. The work also delivers constructive algorithms for computing decentralized mechanisms and clarifies when decentralization closely matches centralization and when coordination is crucial, highlighting practical design implications for scalable information-sharing in platforms. Overall, the results quantify the value of decentralization and its dependence on the cross-location state structure, informing architecture choices for information disclosure in multi-location systems.
Abstract
We study a system composed of multiple distinct service locations that aims to convince customers to join the system by providing information to customers. We cast the system's information design problem in the framework of Bayesian persuasion and describe centralized and decentralized signaling. We provide efficient methods for computing the system's optimal centralized and decentralized signaling mechanisms and derive a performance guarantee for decentralized signaling when the locations' states are independent. The guarantee states that the probability that a customer joins under optimal decentralized signaling is bounded below by the product of a strictly positive constant and the probability that a customer joins under optimal centralized signaling. The constant depends only on the number of service locations. We provide an example that shows that the constant cannot be improved. We consider an extension to more-general objectives for the system and establish that the same guarantee continues to hold. We also extend our analysis to systems where the locations' states are correlated, and again derive a performance guarantee for decentralized signaling in that setting. For the correlated setting, we prove that the guarantee's asymptotic dependence upon the number of locations cannot be substantially improved. A comparison of our guarantees for independent locations and for correlated locations reveals the influence of dependence on the performance of decentralized signaling.