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

Dynamic Signaling Games with Quadratic Criteria under Nash and Stackelberg Equilibria