Rate-Distortion Theory for Strategic Semantic Communication

This paper analyzes the fundamental limit of the strategic semantic communication problem in which a transmitter obtains a limited number of indirect observations of an intrinsic semantic information source and can then influence the receiver's decoding by sending a limited number of messages over an imperfect channel. The transmitter and the receiver can have different distortion measures and can make rational decisions 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 solution concepts including the optimal Stackelberg equilibrium, robust Stackelberg equilibrium, as well as Nash equilibrium are studied and compared. The optimal encoding and decoding strategy profiles under various equilibrium solutions are derived. We prove that committing to an encoding strategy cannot always bring benefit to the encoder. We provide a feasible condition under which committing to an encoding strategy can always reduce the distortion of semantic communication. We consider an example with a dictionary-based semantic information source to verify our observation.