Congestion Games with Higher Demand Dimensions

We introduce a generalization of weighted congestion games in which players are associated with k-dimensional demand vectors and resource costs are k-dimensional functions c : R->= 0(k) -> R of the aggregated demand vector of the players using the resource. Such a cost structure is natural when the cost of a resource depends on different properties of the players' demands, e.g., total weight, total volume, and total number of items. A complete characterization of the existence of pure Nash equilibria in terms of the resource cost functions for all k is an element of N is given.