A generalized Nash equilibrium problem for centralized dynamic spectrum leasing

The dramatic increase of wireless devices in telecommunications is underlining the inefficiency of the traditional spectrum allocation system. A novel scheme for resource allocation is the Dynamic Spectrum Sharing (DSS), where primary users, the exclusive owners of the spectrum rights, allow the secondary ones to share their licensed frequency band. In this paper, a time-continuous model is presented for Centralized Dynamic Spectrum Leasing (C-DSL). This kind of model involves the active participation of both the primary and secondary users in order to share the same frequency band. I treat the problem of secondary power allocation like a non-cooperative Generalized Nash Equilibrium Problem (GNEP) where the primary communication system is willing to allow the secondary users to share its spectrum band and consequently adjusts the maximum tolerable interference in order to obtain the greatest gain, while the secondary users play the game by choosing the most convenient powers to be allocated, in order to obtain a good quality signal and avoid an excessive interference. I give mathematical conditions, easy to be verified locally at the secondary receivers, that ensure the existence of a Generalized Nash Equilibrium for the game.