The eavesdropping and Jamming Dilemma in multi-channel communications

We consider the game where Alice wants to communicate with Bob secretely, while Eve wants to hinder this objective by either eavesdropping or jamming, though she cannot employ both eavesdropping and jamming simultaneously. Alice is employing a multi-channel communication scheme, such as OFDM, and can control the transmit power allocation of her signal among the channels. If Eve chooses to jam, she can control her jamming power allocation amongst the channels, but in this case cannot eavesdrop. In this paper we examine three different patterns for Alice´s (and Eve´s) behavior: (a) Alice assumes Eve employs either a pure jamming or eavesdropping strategy and determines her optimal mixed strategy under this assumption; (b) assuming a fixed probability with which Eve will jam/eavesdrop, Alice/Eve´s equilibrium power allocation strategies can be determined, and then Eve chooses the probability that maximizes her payoff; (c) Eve chooses between two modes (either to jam or eavesdrop) as well as power allocations simultaneous with Alice´s selection of power allocation. Using a game-theoretic formulation, the equilibrium strategies are found for each model and conditions where players apply mixed strategies are produced.