  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.
