  This paper analyzes the fundamental limit of the strategic semantic
communication problem in which a transmitter obtains a limited number of
indirect observation of an intrinsic semantic information source and can then
influence the receiver's decoding by sending a limited number of messages to an
imperfect channel. The transmitter and the receiver can have different
distortion measures and can make rational decision about their encoding and
decoding strategies, respectively. The decoder can also have some side
information (e.g., background knowledge and/or information obtained from
previous communications) about the semantic source to assist its interpretation
of the semantic information. We focus particularly on the case that the
transmitter can commit to an encoding strategy and study the impact of the
strategic decision making on the rate distortion of semantic communication.
Three equilibrium solutions including the strong Stackelberg equilibrium, weak
Stackelberg equilibrium, as well as Nash equilibrium have been studied and
compared. The optimal encoding and decoding strategy profiles under various
equilibrium solutions have been derived. We prove that committing to an
encoding strategy cannot always bring benefit to the encoder. We therefore
propose a feasible condition under which committing to an encoding strategy can
always reduce the distortion performance of semantic communication.
