Rethinking Power Control in Wireless Networks: The Perspective of Satisfaction Equilibrium

In this article, we propose a holistic framework that aims at a paradigm shift in the treatment of the uplink power control problem in wireless networks, under the perspective of games in satisfaction form. Novel satisfaction equilibrium (SE) points of special interest within the considered problem—such as the minimum efficient satisfaction equilibrium (MESE) and the minimum satisfaction equilibrium (MSE)—are introduced, while their benefits, existence, and uniqueness are investigated, considering a realistic and generic user utility function being quasiconcave with respect to its transmission power. It is proven that at the MESE and MSE points, the system achieves the lowest possible cumulative cost, while each user individually is penalized with the minimum cost compared to the corresponding cost of any efficient satisfaction equilibrium (ESE) and of any SE, respectively. A decentralized low complexity algorithm, based on the best response dynamics, is proposed, which converges to the MSE equilibrium, while it can efficiently handle the dynamic behaviors of the users in the network. Numerical results are provided that validate and evaluate the benefits of the proposed novel power control framework, underlining the superiority of the MSE against other equilibrium points.