Quality Sensitive Price Competition in Spectrum Oligopoly:Part 1

TL;DR

This paper analyzes a spectrum leasing market where primaries set prices without knowing competitors' channel qualities, revealing a unique symmetric Nash Equilibrium and the impact of quality on pricing strategies.

Contribution

It explicitly characterizes the unique symmetric Nash Equilibrium in a spectrum oligopoly game considering random channel qualities and analyzes revenue loss and cooperative payoffs.

Findings

High quality channels are priced higher at equilibrium.

Non-cooperation leads to revenue loss asymptotically.

Repeated interactions enable primaries to approach cooperative payoffs.

Abstract

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.