Closed Form Expression of the Saddle Point in Cognitive Radio and Jammer Power Allocation Game

In this paper, we study the power allocation problem for a cognitive radio in the presence of a smart jammer over parallel Gaussian channels. The objective of the jammer is to minimize the total capacity achievable by the cognitive radio. We model the interaction between the two players as a zero-sum game, for which we derive the saddle point closed form expression. First, we start by solving each player’s unilateral game to find its optimal power allocation. These games will be played iteratively until reaching the Nash equilibrium. It turns out that it is possible to develop analytical expressions for the optimal strategies characterizing the saddle point of this minimax problem, under certain condition. The analytic expressions will be compared to the simulation results of the Nash equilibrium.

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