Dynamic Quadratic Cheap Talk and Signaling Games

Simultaneous (Nash) and sequential (Stackelberg) equilibria of two-player dynamic quadratic cheap talk and signaling game problems are investigated under a perfect Bayesian formulation. For the dynamic scalar cheap talk, a zero-delay communication setup is considered for i.i.d. and Markov sources; it is shown that the final stage equilibrium is always quantized and under further restrictive conditions the equilibria for all time stages are quantized. Contrarily, the Stackelberg equilibria are always fully revealing for both scalar and multi-dimensional sources. In the dynamic 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 both scalar and multi-dimensional sources under Nash equilibria; whereas the Stackelberg equilibria always admit linear policies for scalar sources but such policies may be nonlinear for multi-dimensional sources. A dynamic programming formulation is presented for multi-dimensional sources for optimal linear encoding policies, and conditions under which the Stackelberg equilibria are non-informative are derived.