Decentralized Signaling Mechanisms

2025-04-19

AI Summary

This paper studies Bayesian persuasion for information design in multi-server systems, aiming to guide customer joining decisions via signaling mechanisms. We consider two settings: server states are either independent or correlated. First, we establish the first tight lower bound on the performance of decentralized (distributed) signaling mechanisms, proving that their utility loss decays controllably with the number of servers—and that this bound is asymptotically unimprovable. Second, we propose an efficient algorithm to compute the optimal decentralized signal and prove that the induced customer joining probability is at least a constant factor (depending only on the number of servers) of that under the optimal centralized mechanism—guaranteeing performance robustly across both independence and correlation settings, with asymptotic tightness. Our approach integrates tools from Bayesian persuasion, convex optimization, probabilistic analysis, and distributed information structure design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized 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.

Problem

• Study decentralized signaling in multi-location service systems
• Compare performance of centralized vs decentralized signaling mechanisms
• Analyze impact of location state dependence on signaling effectiveness

Innovation

• Bayesian persuasion for decentralized signaling mechanisms
• Performance guarantees for independent location states
• Extension to correlated location states analysis