We investigate a spectrum oligopoly market where primaries lease their
channels to secondaries in lieu of financial remuneration. Transmission quality
of a channel evolves randomly. Each primary has to select the price it would
quote without knowing the transmission qualities of its competitors' channels.
Each secondary buys a channel depending on the price and the transmission
quality a channel offers. We formulate the price selection problem as a non
co-operative game with primaries as players. In the one-shot game, we show that
there exists a unique symmetric Nash Equilibrium(NE) strategy profile and
explicitly compute it. Our analysis reveals that under the NE strategy profile
a primary prices its channel to render high quality channel more preferable to
the secondary; this negates the popular belief that prices ought to be selected
to render channels equally preferable to the secondary regardless of their
qualities. We show the loss of revenue in the asymptotic limit due to the non
co-operation of primaries. In the repeated version of the game, we characterize
a subgame perfect NE where a primary can attain a payoff arbitrarily close to
the payoff it would obtain when primaries co-operate.Comment: Accepted for publication in IEEE/ACM Transactions on Networking. 41
pages single column format.Conference version is available at arXiv:1305.335
