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With the advance of complex large-scale networks, it is becoming increasinglyimportant to understand how selfish and spatially distributed individuals willshare network resources without centralized coordinations. In this paper, weintroduce the graphical congestion game with weighted edges (GCGWE) as ageneral theoretical model to study this problem. In GCGWE, we view the playersas vertices in a weighted graph. The amount of negative impact (e.g.congestion) caused by two close-by players to each other is determined by theweight of the edge linking them. The GCGWE unifies and significantlygeneralizes several simpler models considered in the previous literature, andis well suited for modeling a wide range of networking scenarios. One goodexample is to use the GCGWE to model spectrum sharing in wireless networks,where we can properly define the edge weights and payoff functions to capturethe rather complicated interference relationship between wireless nodes. Byidentifying which GCGWEs possess pure Nash equilibria and the very desirablefinite improvement property, we gain insight into when spatially distributedwireless nodes will be able to self-organize into a mutually acceptableresource allocation. We also consider the efficiency of the pure Nashequilibria, and the computational complexity of finding them.

Congestion Games on Weighted Directed Graphs, with Applications to Spectrum Sharing