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In this paper, we address the problem of distributed power allocation in a
$K$ 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 \emph{secrecy capacity} with
partial channel state information. In this work, we first prove that there is a
unique Bayesian equilibrium in the proposed game. Additionally, the price of
anarchy is calculated to measure the efficiency of the equilibrium solution. We
also propose a fast convergent iterative algorithm for power allocation.
Finally, the results are validated using simulation results.
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