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.

翻译：本文分析了编码器与解码器存在线性灵敏度失配的斯塔克尔贝格高斯信号博弈问题。与标准加性偏差模型不同，灵敏度失配意味着编码器更倾向于解码器跟踪状态的线性变换而非简单平移。我们推导了无噪声（廉价交谈）和有噪声信号通道的均衡结构。在无噪声情形中，均衡具有谱特征表征：编码器仅沿失配矩阵负特征值对应的特征空间传输信息。在有噪声情形中，我们推导了信息传输的分析阈值，表明若灵敏度失配或传输成本超过信道相关阈值，通信将完全崩溃。