Optimal Strategy in Covert Communication based on Game Theory

Covert communication provides the security for wireless communications via hiding the existence of the transmissions. In this paper, we consider a scenario that the transmitter and the warden do not know the state information of each other. We formulate a power threshold game and a Bayesian game to model the scenario. The optimal strategies are given by the game theory concept solutions, i.e. the Nash equilibrium (NE) and the Bayesian Nash equilibrium (BNE). For the power threshold game, we prove the existence of the NE and give a numerical method to calculate it. We prove that the BNE can be calculated by solving another optimal problem. The method to solve the optimal problem is also proposed. Numerical results are shown to illustrate the stability of the equilibrium and the performances of the optimal strategies.