Spectrum Pricing Games with Spatial Reuse in Cognitive Radio Networks

In Cognitive Radio Networks (CRN), there are multiple primary and secondary users in a region, and primaries can lease out their unused bandwidth to secondaries in exchange for a fee. This gives rise to price competition among the primaries, wherein 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 in a CRN, 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 identify a class of conflict graphs, which we refer to as mean valid graphs, such that the conflict graphs of a large number of topologies that commonly arise in practice are mean valid. We explicitly compute a symmetric NE in mean valid graphs and show that it is unique.