  In this paper, we present and analyze the properties of a new class of games
- the spatial congestion game (SCG), which is a generalization of the classical
congestion game (CG). In a classical congestion game, multiple users share the
same set of resources and a user's payoff for using any resource is a function
of the total number of users sharing it. As a potential game, this game enjoys
some very appealing properties, including the existence of a pure strategy Nash
equilibrium (NE) and that every improvement path is finite and leads to such a
NE (also called the finite improvement property or FIP). While it's tempting to
use this model to study spectrum sharing, it does not capture the spatial reuse
feature of wireless communication, where resources (interpreted as channels)
may be reused without increasing congestion provided that users are located far
away from each other. This motivates us to study an extended form of the
congestion game where a user's payoff for using a resource is a function of the
number of its interfering users sharing it. This naturally results in a spatial
congestion game (SCG), where users are placed over a network (or a conflict
graph). We study fundamental properties of a spatial congestion game; in
particular, we seek to answer under what conditions this game possesses the
finite improvement property or a Nash equilibrium. We also discuss the
implications of these results when applied to wireless spectrum sharing.
