Quality Sensitive Price Competition in Spectrum Oligopoly: Part 1

We investigate a spectrum oligopoly market where each primary seeks to sell its idle channel to a secondary. Transmission rate of a channel evolves randomly. Each primary needs to select a price depending on the transmission rate of its channel. Each secondary selects a channel depending on the price and the transmission rate of the channel. We formulate the above problem as a non-cooperative game. We show that there exists a unique Nash Equilibrium (NE) and explicitly compute it. Under the NE strategy profile a primary prices its channel to render the channel which provides high transmission rate more preferable; this negates the perception that prices ought to be selected to render channels equally preferable to the secondary regardless of their transmission rates.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.