Strategic Gaussian Signaling under Linear Sensitivity Mismatch
Provides theoretical insights for strategic communication under model mismatch, relevant to information theory and game theory.
The paper analyzes Stackelberg Gaussian signaling games with linear sensitivity mismatch between encoder and decoder, deriving equilibrium structures and showing that communication collapses when mismatch or cost exceeds a threshold.
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.