Congestion Games with Multi-Dimensional Demands

Weighted congestion games are an important and extensively studied class of strategic games, in which the players compete for subsets of shared resources in order to minimize their private costs. In my Master’s thesis (Congestion games with multi-dimensional demands. Master’s thesis, Institut für Mathematik, Technische Universität Berlin, 2013, [17]), we introduced congestion games with multi-dimensional demands as a generalization of weighted congestion games. For a constant \(k \in \mathbb {N}\), in a congestion game with k-dimensional demands, each player is associated with a k-dimensional demand vector, and resource costs are k-dimensional functions of the aggregated demand vectors of the players using the resource. Such a cost structure is natural when the cost of a resource depends not only on one, but on several properties of the players’ demands, e.g., total weight, total volume, and total number of items. We obtained a complete characterization of the existence of pure Nash equilibria in terms of the resource cost functions for all \(k \in \mathbb {N}\). Specifically, we identified all sets of k-dimensional cost functions that guarantee the existence of a pure Nash equilibrium for every congestion game with k-dimensional demands. In this note we review the main results contained in the thesis.