Spectrum pricing games with arbitrary bandwidth availability probabilities

We consider price competition among multiple primary users in a cognitive radio network with multiple secondary users. Each primary has unused bandwidth with some probability, possibly different for different primaries, which he would like to lease to a secondary. For the case in which all the primaries and secondaries are in a single location, we explicitly compute a Nash equilibrium (NE) and show its uniqueness. Then we consider the game with spatial reuse of spectrum, and for linear conflict graphs, explicitly compute a NE and show its uniqueness in a natural sub-class of NE.