The Semantic Communication Game

This paper proposes a communication framework where meanings of transmitted codewords over a noisy channel are explicitly taken into account. Furthermore, such communication takes place in the presence of an external entity, i.e., an agent, that can influence the receiver. The agent may be adversarial or helpful, and its true nature is unknown to the communicating parties. Actions taken by the agent are governed by its nature to aim to improve/deteriorate the communication performance. We characterize the optimal transmission policies to minimize the end-to-end average semantic error, that we define as the expected error between meanings of intended and recovered messages, under the uncertainty of agent's true intentions. To do so, we first formulate the communication problem as a Bayesian game, and investigate the conditions under which a Bayesian Nash equilibrium exists. Next, we consider a dynamic communication scenario in which parties take actions sequentially, forming beliefs about the other party. By formulating this setting as a sequential game, we investigate the structure of the belief system and strategy profiles at equilibrium. Our results indicate that word semantics are instrumental in assessing communication performance when messages carry meanings, and optimal communication strategies are strongly influenced by the communicating parties' beliefs.