Spectrum pricing games with random valuations of secondary users

We analyze price competition among primary users in a Cognitive Radio Network (CRN), in which there are a random and unknown number of secondary users. In every slot, each primary has unused bandwidth with some probability, which it would like to lease to a secondary user, and must set a price for this bandwidth. The valuations of the secondary users for unit bandwidth are independent and identically distributed random variables. We analyze this price competition as a game and explicitly compute a Nash Equilibrium (NE), which we show to be unique in the class of symmetric NE. We show that randomness in the valuations of the secondary users results in significant structural differences in the strategies of the primaries in the NE compared to the case in which the valuations of the secondaries are constants.