Spectrum pricing games with correlated bandwidth availabilities and demands

We study price competition among primaries in a Cognitive Radio Network (CRN) with multiple primaries and secondaries located in a large region. In a given slot, some of the primaries have unused bandwidth, which they can potentially lease out to secondaries in exchange for a fee. There is uncertainty in whether a given primary has unused bandwidth in a given slot as well as in the number of secondaries that require bandwidth, with the above random quantities being mutually correlated. Each primary tries to attract secondaries by setting a lower price for its bandwidth than the other primaries. Radio spectrum has the distinctive feature that transmissions at neighboring locations on the same channel interfere with each other, whereas the same channel can be used at far-off locations without mutual interference. So in the above price competition scenario, each primary must jointly select a set of mutually non-interfering locations within the region (which corresponds to an independent set in the conflict graph representing the region) at which to offer bandwidth and the price at each location. In this paper, we analyze this price competition scenario as a game and seek a Nash Equilibrium (NE). We analyze the game at a single location as well as the game at multiple locations. We characterize NE for the cases of (i) symmetric bandwidth availability events of different primaries and (ii) asymmetric bandwidth availability events with a special correlation structure.