On the Fictitious Play and Channel Selection Games

TL;DR

This paper models the channel selection problem in decentralized radio networks as a potential game, demonstrating convergence of fictitious play to Nash equilibria and proposing a local information-based implementation method.

Contribution

It proves the channel selection problem is a potential game and introduces a local information-based fictitious play method for decentralized implementation.

Findings

Fictitious play converges to Nash equilibria in the channel selection game.

Mixed strategy convergence can lead to suboptimal cycles.

A local information-based implementation method is proposed.

Abstract

Considering the interaction through mutual interference of the different radio devices, the channel selection (CS) problem in decentralized parallel multiple access channels can be modeled by strategic-form games. Here, we show that the CS problem is a potential game (PG) and thus the fictitious play (FP) converges to a Nash equilibrium (NE) either in pure or mixed strategies. Using a 2-player 2-channel game, it is shown that convergence in mixed strategies might lead to cycles of action profiles which lead to individual spectral efficiencies (SE) which are worse than the SE at the worst NE in mixed and pure strategies. Finally, exploiting the fact that the CS problem is a PG and an aggregation game, we present a method to implement FP with local information and minimum feedback.