Quality Sensitive Price Competition in Spectrum Oligopoly: Part II
  We investigate a spectrum oligopoly market where each primary seeks to sell secondary access to its channel at multiple locations. Transmission qualities of a channel evolve randomly. Each primary needs to select a price and a set of non-interfering locations (which is an independent set in the conflict graph of the region) at which to offer its channel without knowing the transmission qualities of the channels of its competitors. We formulate the above problem as a non-cooperative game. We consider two scenarios-i) when the region is small, ii) when the region is large. In the first setting, we focus on a class of conflict graphs, known as mean valid graphs which commonly arise when the region is small. We explicitly compute a symmetric Nash equilibrium (NE); the NE is threshold type in that primaries only choose independent set whose cardinality is greater than a certain threshold. The threshold on the cardinality increases with increase in quality of the channel on sale. We show that the symmetric NE strategy profile is unique in a special class of conflict graphs (linear graph). In the second setting, we consider node symmetric conflict graphs which arises when the number of locations is large (potentially, infinite). We explicitly compute a symmetric NE that randomizes equally among the maximum independent sets at a given channel state vector. In the NE a primary only selects the maximum independent set at a given channel state vector. We show that the two symmetric NEs computed in two settings exhibit important structural difference. 
Arnob Ghosh, Saswati Sarkar
cs.GT cs.NI