Strategic Gaussian Signaling under Linear Sensitivity Mismatch

TL;DR

This paper studies Gaussian signaling games with linear sensitivity mismatch, deriving equilibrium structures and thresholds for informative communication in noiseless and noisy channels.

Contribution

It introduces a novel analysis of Stackelberg Gaussian signaling with sensitivity mismatch, providing spectral characterizations and thresholds for communication viability.

Findings

Equilibrium in noiseless case characterized by eigenspaces of the mismatch matrix.

Communication collapses when sensitivity mismatch or cost exceeds certain thresholds.

Analytical thresholds for informative signaling in noisy channels derived.

Abstract

We analyze Stackelberg Gaussian signaling games where the encoder and decoder have a linear sensitivity mismatch. Unlike the standard additive-bias model, a sensitivity mismatch means the encoder prefers the decoder to track a linear transformation of the state rather than a shifted one. We derive the equilibrium structure for both noiseless (cheap-talk) and noisy signaling channels. In the noiseless case, the equilibrium admits a spectral characterization: the encoder transmits information only along eigenspaces associated with the negative eigenvalues of a mismatch matrix. In the noisy regime, we derive analytical thresholds for informative signaling, showing that communication collapses if the sensitivity mismatch or transmission cost exceeds a channel-dependent threshold.