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

Abstract

In this paper 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 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 Satisfaction Equilibrium (SE), respectively. A decentralized low complexity algorithm, based on the Best Response Dynamics, is proposed that 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 evalua