  We develop a constrained bimatrix game framework that can be used to model
many practical problems in many disciplines, including jamming in packetized
wireless networks. In contrast to the widely used zero-sum framework, in
bimatrix games it is no longer required that the sum of the players' utilities
to be zero or constant, thus, can be used to model a much larger class of
jamming problems. Additionally, in contrast to the standard bimatrix games, in
constrained bimatrix games the players' strategies must satisfy some linear
constraint/inequality, consequently, not all strategies are feasible and the
existence of the Nash equilibrium (NE) is not guaranteed anymore. We provide
the necessary and sufficient conditions under which the existence of the Nash
equilibrium is guaranteed, and show that the equilibrium pairs and the Nash
equilibrium solution of the constrained game corresponds to the global maximum
of a quadratic program. Finally, we use our game theoretic framework to find
the optimal transmission and jamming strategies for a typical wireless link
under power limited jamming.
