  We investigate the problem of strategic point-to-point communication with
side information at the decoder, in which the encoder and the decoder have
mismatched distortion functions. The decoding process is not supervised, it
returns the output sequence that minimizes the decoder's distortion function.
The encoding process is designed beforehand and takes into account the
decoder's distortion mismatch. When the communication channel is perfect and no
side information is available at the decoder, this problem is referred to as
the Bayesian persuasion game of Kamenica-Gentzkow in the Economics literature.
We formulate the strategic communication scenario as a joint source-channel
coding problem with side information at the decoder. The informational content
of the source influences the design of the encoding since it impacts
differently the two distinct distortion functions. The side information
complexifies the analysis since the encoder is uncertain about the decoder's
belief on the source statistics. We characterize the single-letter optimal
solution by controlling the posterior beliefs induced by the Wyner-Ziv's source
encoding scheme. This confirms the benefit of sending encoded data bits even if
the decoding process is not supervised.
