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Quadratic program solution of communication links under jamming

In this paper we use a game theoretic approach to model a packetized wireless communication link under jamming. In contrast to the widely used zero-sum framework, we use the bimatrix framework. In bimatrix games each player has his own utility function, this in contrary to the zero-sum games where the sum of players payoffs is always zero. Hence, a much larger class of jamming problems, and many other applications, can be modeled using this framework. Furthermore, in many practical situations, players' strategies must satisfy some additional constraints. To consider these situations, in our model we restrict players' strategies to hyper-polyhedrons defined by linear inequalities. We prove that the Nash equilibrium solution of this constrained game corresponds to the global maximum of a quadratic program. Finally, we study jamming of a packetized wireless link and show that the game theoretic analysis of this typical jamming problem yields rather surprising results.