A New Theoretical Evaluation Framework for Satisfaction Equilibria in Wireless Networks

In this paper, a theoretical evaluation framework regarding the $\mathit{\text{Satisfaction}}\mathit{\text{Equilibrium}}\mathit{\text{(SE)}}$ in wireless communication networks is introduced and examined. To study these equilibria operation points, we coin some new concepts, namely the $\mathit{\text{Valued}}\mathit{\text{Satisfaction}}\mathit{\text{Equilibrium}}$, the $\mathit{\text{Price}}\mathit{\text{of}}\mathit{\text{Efficiency}}$ and the $\mathit{\text{Max}}\mathit{\text{Price}}\mathit{\text{of}}\mathit{\text{Satisfaction}}$, which can be used for measuring the efficiency of the obtained equilibria solutions. The aforementioned framework is analyzed and evaluated in a wireless communication environment under the presence of the Gaussian Interference channel (GIC). Within this setting, a non-cooperative game among the users is studied, where users aim in a selfish manner to meet their Quality of Service (QoS) prerequisite. However instead of maximizing the QoS which is generally energy costly, we evangelize that better energy-efficiency is achieved by targeting satisfactory QoS levels only. The sufficient and necessary conditions that lead to the $\mathit{\text{Satisfaction}}\mathit{\text{Equilibrium}}$ are provided for the two-user case and the $\mathit{\text{Efficient}}\mathit{\text{Satisfaction}}\mathit{\text{Equilibrium}}\mathit{\text{(ESE)}}$ is determined, where the users satisfy their QoS constraints with the lowest possible cost. Moreover, specific measures for evaluating the efficiency of various satisfaction equilibria, in a formal and quantitative manner, expressing the tradeoff with respect to the achieved utility or a given objective function and corresponding cost, are defined and analyzed.