From competition to coopetition: Stackelberg equilibrium in 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 these selfish users as a non-cooperative game. We study how a foresighted user, who knows the channel state information and response strategies of its competing users, should optimize its own transmission strategy. To characterize this multiuser interaction, the Stackelberg equilibrium is introduced. We start by analyzing in detail a simple two-user scenario, where the foresighted user can determine its optimal transmission strategy by solving a bi-level program which allows him to account for the myopic user´s response strategies. Therefore, the competition among users is transformed into a cooperative competition (coopetition) since the foresighted user will avoid interfering the myopic user. Since the optimal solution is computationally prohibitive, we propose a low-complexity algorithm based on Lagrangian duality theory. Numerical simulations illustrate that, if a foresighted user has the necessary information about its competitor, the resulting coopetition will benefit both users. Possible methods to acquire the required information and to extend the formulation to more than two users are also discussed.