  We propose a strategic formulation for the joint source-channel coding
problem in which the encoder and the decoder are endowed with distinct
distortion functions. We provide the solutions in four different scenarios.
First, we assume that the encoder and the decoder cooperate in order to achieve
a certain pair of distortion values. Second, we suppose that the encoder
commits to a strategy whereas the decoder implements a best response, as in the
persuasion game where the encoder is the Stackelberg leader. Third, we consider
that the decoder commits to a strategy, as in the mismatched rate-distortion
problem or as in the mechanism design framework. Fourth, we investigate the
cheap talk game in which the encoding and the decoding strategies form a Nash
equilibrium.
