This paper considers dynamic (multi-stage) signaling games involving an encoder and a decoder who have subjective models on the cost functions. We consider both Nash (simultaneous-move) and Stackelberg (leader–follower) equilibria of dynamic signaling games under quadratic criteria. For the multi-stage scalar cheap talk, we show that the final stage equilibrium is always quantized and under further conditions the equilibria for all time stages must be quantized. In contrast, the Stackelberg equilibria are always fully revealing. In the multi-stage signaling game where the transmission of a Gauss–Markov source over a memoryless Gaussian channel is considered, affine policies constitute an invariant subspace under best response maps for Nash equilibria; whereas the Stackelberg equilibria always admit linear policies for scalar sources but such policies may be non-linear for multi-dimensional sources. We obtain an explicit recursion for optimal linear encoding policies for multi-dimensional sources, and derive conditions under which Stackelberg equilibria are informative.

本文考虑了动态（多阶段）信号博弈，其中涉及具有成本函数主观模型的编码器和解码器。我们同时考虑了二次条件下的动态信号博弈的纳什（同时移动）和斯塔克尔伯格（领导者与跟随者）均衡。对于多阶段标量廉价讨论，我们表明最终阶段的均衡总是被量化，并且在进一步的条件下，所有时间阶段的均衡都必须被量化。相比之下，斯塔克尔伯格平衡总是充分地展现出来。在多级信号博弈中，考虑了高斯-马尔可夫源在无记忆高斯信道上的传输，仿射策略构成了纳什均衡最佳响应图下的不变子空间。而Stackelberg均衡总是允许标量源采用线性策略，但对于多维源则此类策略可能是非线性的。我们获得了针对多维源的最佳线性编码策略的显式递归，并推导了Stackelberg均衡可提供信息的条件。