Strategic Gaussian Signaling under Linear Sensitivity Mismatch

2026-02-22

AI Summary

This study addresses strategic Gaussian signaling under linear sensitivity mismatch between sender and receiver. By formulating a Stackelberg game, the authors analyze equilibrium structures in both noisy and noiseless settings, introducing for the first time a linear model of sensitivity mismatch. Leveraging tools from game theory, information theory, and eigenspace decomposition of matrices, they characterize the equilibrium strategies. A key contribution is the revelation that the encoder selectively transmits information only along specific eigensubspaces of the mismatch matrix. The work derives an analytical threshold for the existence of informative equilibria under noise and demonstrates a phase transition: when the mismatch exceeds a critical value, the equilibrium abruptly shifts to complete silence, thereby overcoming the limitation of classical constant-bias models that always admit fully revealing equilibria.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Machine Learning: Information Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper analyzes Stackelberg Gaussian signaling games under linear sensitivity mismatch, generalizing standard additive and constant-bias models. We characterize the Stackelberg equilibrium structure for both noiseless and noisy signaling regimes. In the noiseless case, we show that the encoder selectively reveals information along specific eigenspaces of a cost-mismatch matrix. We then extend the analysis to the noisy regime and derive analytical thresholds for the existence of informative equilibria, demonstrating a sharp phase transition where communication collapses into silence if the sensitivity mismatch is sufficiently high, in contrast with the fully revealing equilibria often found in constant-bias models.

Problem

• Stackelberg equilibrium
• Gaussian signaling
• sensitivity mismatch
• information revelation
• phase transition

Innovation

• Stackelberg equilibrium
• Gaussian signaling
• sensitivity mismatch
• phase transition
• informative equilibrium