Supply-demand function equilibrium for double sided bandwidth-auction games

We consider a cellular based primary network coexisting with a secondary network. The primary network consists of multiple service providers (SP) and there are several independent users in the secondary network. The SP are operating on the different frequency spectrum and a group of secondary users intend to share these spectrum with the primary services. This situation is formulated as a bandwidth auction game where each user bids a demand curve and each SP offers a supply curve. We consider two cases of complete information case and incomplete information case or learning games. For two cases, we derive the optimal strategies of the players and the distributed algorithms are presented to obtain the solution of these dynamic games.