  In this paper, we analyze the problem of power control in a multiuser MIMO
network, where the optimal linear precoder is employed in each user to achieve
maximum point- to-point information rate. We design a distributed power control
algorithm based on the concept of game theory and contractive functions that
has a couple of advantages over the previous designs (e.g. more uniqueness
probability of Nash equilibria and asynchronous implementation). Despite these
improvements, the sum-rate of the users does not increase because the proposed
algorithm can not lead the power control game to an efficient equilibrium
point. We solve this issue by modifying our algorithm such that the game is led
to the equilibrium that satisfies a particular criterion. This criterion can be
chosen by the designer to achieve a certain optimality among the equilibria.
Furthermore, we propose the inexact method that helps us to boost the
convergence speed of our modified algorithms. Lastly, we show that pricing
algorithms can also be a special case of our modified algorithms. Simulations
show a noticeable improvement in the sum-rate when we modify our proposed
algorithm.
