A New Look at Multi-User Power Control Games

This paper considers the problem of how to allocate power among competing users sharing a frequency-selective interference channel. We model the interaction between selfish users as a non-cooperative game and analyze their strategic behavior. As opposed to the existing iterative water-filling algorithm, this paper introduces the Stackelberg equilibrium and shows the existence of this equilibrium for the investigated non-cooperative game. We model the two-user case as a bi-level programming problem and derive the necessary optimality conditions. It is analytically shown that a user can improve its performance if it knows the channel state information and the response strategy of the competing user. Due to computationally prohibitive nature of the optimal solution, a practical low- complexity approach is proposed based on the intuition gained from the necessary conditions. Numerical simulations verify the performance improvements.