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Summary: Closed form solutions for symmetric
water filling games
E. Altman
INRIA Sophia Antipolis, France
Email: altman@sophia.inria.fr
K. Avrachenkov
INRIA Sophia Antipolis, France
Email: k.avrachenkov@sophia.inria.fr
A. Garnaev
St. Petersburg State University, Russia
Email: agarnaev@rambler.ru
Abstract-- We study power control in optimization and game
frameworks. In the optimization framework there is a single
decision maker who assigns network resources and in the game
framework users share the network resources according to Nash
equilibrium. The solution of these problems is based on so-called
water-filling technique, which in turn uses bisection method for
solution of non-linear equations for Lagrange multipliers. Here
we provide a closed form solution to the water-filling problem,
which allows us to solve it in a finite number of operations. Also,
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