Bayesian Game Formulation of Power Allocation in Multiple Access Wiretap Channel with Incomplete CSI

In this paper, we address the problem of distributed power allocation in a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> user fading multiple access wiretap channel, where global channel state information is limited, i.e., each user has knowledge of their own channel state with respect to Bob and Eve but only knows the distribution of other users' channel states. We model this problem as a Bayesian game, where each user is assumed to selfishly maximize his average secrecy capacity with partial channel state information. In this work, we first prove that there is a unique Bayesian equilibrium in the proposed game and to attain the equilibrium state we propose a convergent iterative algorithm for power allocation. Additionally, the price of anarchy is calculated to measure the efficiency of the equilibrium solution. Finally, the results are validated using simulations.