Nash equilibrium in multiple antennas protected and shared bands

Two non-cooperating cells are considered, each with its protected band to provide service to its high priority users. A shared band for the two cells is employed to deliver service to low priority users. We formulate the situation between the two cells as a non-cooperative game and study its Nash equilibrium. We prove that the game belongs to a class of games called supermodular games which have several interesting properties, such as the global stability of a unique Nash equilibrium. We provide a sufficient condition for the existence of a unique Nash equilibrium and study its efficiency by extensive simulations.