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Atomic Congestion Games on Graphs and its Applications in Networking

In this paper, we introduce and analyze the properties of a class of game, the atomic congestion game on graphs (ACGG), which is a generalization of the classical congestion game. In particular, the ACGG captures the spatial information which is often ignored in the classical congestion game. This is useful in many networking problems, e.g., wireless networks where interference among the users heavily depend on the spatial information. In an ACGG, a player’s payoff for using a resource is a function of the number of players who interact with it and use the same resource. Such spatial information can be captured by a graph. We study fundamental properties of the ACGG; under what conditions this game possesses a pure strategy Nash equilibrium (PNE), or the finite improvement property (FIP), which is sufficient for the existence of a PNE. We show that a PNE may not exist in general, but that it does exist in many important special cases including tree, loop, or regular bipartite networks. The FIP also exists for important special cases including systems with 2 resources or identical payoff functions for each resource. Finally, we present two wireless network applications of an ACGG: power control and channel contention under IEEE 802.11.