Spatial Spectrum Access Game

TL;DR

This paper introduces a framework for spatial spectrum access games in wireless networks, analyzing equilibrium existence, efficiency, and proposing a distributed learning algorithm for strategy adaptation.

Contribution

It models spatial spectrum sharing with directed interference graphs, proves equilibrium existence under various conditions, and develops a distributed learning method for strategy optimization.

Findings

Pure Nash equilibrium exists for acyclic graphs and certain tree structures.

The distributed learning algorithm converges to an approximate equilibrium.

The proposed method outperforms random access algorithms in simulations.

Abstract

A key feature of wireless communications is the spatial reuse. However, the spatial aspect is not yet well understood for the purpose of designing efficient spectrum sharing mechanisms. In this paper, we propose a framework of spatial spectrum access games on directed interference graphs, which can model quite general interference relationship with spatial reuse in wireless networks. We show that a pure Nash equilibrium exists for the two classes of games: (1) any spatial spectrum access games on directed acyclic graphs, and (2) any games satisfying the congestion property on directed trees and directed forests. Under mild technical conditions, the spatial spectrum access games with random backoff and Aloha channel contention mechanisms on undirected graphs also have a pure Nash equilibrium. We also quantify the price of anarchy of the spatial spectrum access game. We then propose a distributed learning algorithm, which only utilizes users' local observations to adaptively adjust the spectrum access strategies. We show that the distributed learning algorithm can converge to an approximate mixed-strategy Nash equilibrium for any spatial spectrum access games. Numerical results demonstrate that the distributed learning algorithm achieves up to superior performance improvement over a random access algorithm.