Congestion games with resource reuse and applications in spectrum sharing

TL;DR

This paper extends classical congestion games to include spatial reuse, modeling wireless spectrum sharing more accurately, and investigates conditions for the existence of Nash equilibria and finite improvement paths in these games.

Contribution

It introduces congestion games with resource reuse (CG-RR) and analyzes their properties, especially regarding Nash equilibria and finite improvement paths in wireless contexts.

Findings

CG-RR models spatial reuse in wireless spectrum sharing.

Conditions for Nash equilibrium existence in CG-RR are identified.

Implications for designing efficient spectrum sharing protocols.

Abstract

In this paper we consider an extension to the classical definition of congestion games (CG) in which multiple users share the same set of resources and their payoff for using any resource is a function of the total number of users sharing it. The classical congestion games enjoy some very appealing properties, including the existence of a Nash equilibrium and that every improvement path is finite and leads to such a NE (also called the finite improvement property or FIP), which is also a local optimum to a potential function. On the other hand, this class of games does not model well the congestion or resource sharing in a wireless context, a prominent feature of which is spatial reuse. What this translates to in the context of a congestion game is that a users payoff for using a resource (interpreted as a channel) is a function of the its number of its interfering users sharing that channel, rather than the total number among all users. This makes the problem quite different. We will call this the congestion game with resource reuse (CG-RR). In this paper we study intrinsic properties of such a game; in particular, we seek to address under what conditions on the underlying network this game possesses the FIP or NE. We also discuss the implications of these results when applied to wireless spectrum sharing