Strategic Gaussian Signaling under Linear Sensitivity Mismatch

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.

Figures (3)

• Figure 1: System model. The encoder observes the source $\boldsymbol{m}$, transmits $\boldsymbol{x}$ over a noisy channel, and the decoder produces an estimate $\boldsymbol{u}$ of $\boldsymbol{m}$.
• Figure 2: Phase diagram for the scalar signaling game. The solid boundary separates the region where communication is beneficial for the encoder (informative) from the region where the optimal strategy is silence (non-informative). The color intensity represents the optimal power $P^*$.
• Figure 3: Illustration of equilibrium behavior for 2D cheap talk with $A=\mathrm{diag}(0.8, 0.2)$. (a) Independent Source: The problem decouples; Component 1 is revealed, while Component 2 is suppressed ($u_2=0$). (b) Correlated Source: The encoder still doesn't reveal $m_2$, but the decoder infers partial information about $m_2$ via its correlation with the revealed $m_1$, illustrating the interaction between mismatch geometry and source statistics.