Quadratic Signaling With Prior Mismatch at an Encoder and Decoder: Equilibria, Continuity, and Robustness Properties

We consider communications through a Gaussian noise channel between an encoder and decoder which have subjective probabilistic models on the source distribution. Although they same cost function, induced expected costs are misaligned due to their prior mismatch, requires game-theoretic approach. two approaches: Nash setup, with no commitment, Stackelberg solution concept, where is committed given announced policy a priori . show that equilibrium of upper semicontinuous, under Wasserstein metric, as encoder’s approaches decoder’s prior, it also lower semicontinuous priors. For optimality affine policies for signaling longer holds thus, team-theoretic linear/affine not robust perturbations. provide conditions there exist informative equilibria policies. Finally, we existence fully cheap talk problem absolute continuity condition.