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We consider communications through a Gaussian noise channel between anencoder and a decoder which have subjective probabilistic models on the sourcedistribution. Although they consider the same cost function, the inducedexpected costs are misaligned due to their prior mismatch, which requires agame theoretic approach. We consider two approaches: a Nash setup, with noprior commitment, and a Stackelberg solution concept, where the encoder iscommitted to a given announced policy apriori. We show that the Stackelbergequilibrium cost of the encoder is upper semi continuous, under the Wassersteinmetric, as encoder's prior approaches the decoder's prior, and it is also lowersemi continuous with Gaussian priors. For the Stackelberg setup, the optimalityof affine policies for Gaussian signaling no longer holds under prior mismatch,and thus team-theoretic optimality of linear/affine policies are not robust toperturbations. We provide conditions under which there exist informative Nashand Stackelberg equilibria with affine policies. Finally, we show existence offully informative Nash and Stackelberg equilibria for the cheap talk problemunder an absolute continuity condition.

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