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Quality sensitive price competition in spectrum oligopoly over multiple locations

We investigate a spectrum oligopoly market where each primary seeks to sell secondary access to channels 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 the 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. Secondaries select a channel depending on the price and the quality the channel offers. We formulate the above problem as a non-cooperative game theoretic problem. We focus on a class of conflict graphs, known as mean valid graphs which commonly arise in practice. We explicitly compute a symmetric Nash equilibrium (NE) that selects only a small number of independent sets with positive probability. The NE is threshold type in that primaries do not choose independent sets whose cardinality fall below a certain threshold. The threshold on the cardinality increases with increase in quality of the channel on sale.