Quality Sensitive Price Competition in Spectrum Oligopoly

TL;DR

This paper models a spectrum oligopoly where primary users set prices for secondary access, analyzing the unique symmetric Nash equilibrium and its efficiency in a stochastic channel environment.

Contribution

It introduces a game-theoretic model for spectrum pricing with random channel qualities and derives the unique symmetric Nash equilibrium strategy.

Findings

Existence and uniqueness of the symmetric NE strategy.

Explicit computation of the NE strategy profile.

Analysis of the NE's efficiency through analytical and numerical methods.

Abstract

We investigate a spectrum oligopoly where primary users allow secondary access in lieu of financial remuneration. Transmission qualities of the licensed bands fluctuate randomly. Each primary needs to select the price of its channel with the knowledge of its own channel state but not that of its competitors. Secondaries choose among the channels available on sale based on their states and prices. We formulate the price selection as a non-cooperative game and prove that a symmetric Nash equilibrium (NE) strategy profile exists uniquely. We explicitly compute this strategy profile and analytically and numerically evaluate its efficiency. Our structural results provide certain key insights about the unique symmetric NE.