  This paper considers a game-theoretic formulation of the covert
communications problem with finite blocklength, where the transmitter (Alice)
can randomly vary her transmit power in different blocks, while the warden
(Willie) can randomly vary his detection threshold in different blocks. In this
two player game, the payoff for Alice is a combination of the coding rate to
the receiver (Bob) and the detection error probability at Willie, while the
payoff for Willie is the negative of his detection error probability. Nash
equilibrium solutions to the game are obtained, and shown to be efficiently
computable using linear programming. For less covert requirements, our
game-theoretic approach can achieve significantly higher coding rates than
uniformly distributed transmit powers. We then consider the situation with an
additional jammer, where Alice and the jammer can both vary their powers. We
pose a two player game where Alice and the jammer jointly comprise one player,
with Willie the other player. The use of a jammer is shown in numerical
simulations to lead to further significant performance improvements.
