On bidimensional congestion games

Abstract

We introduce multidimensional congestion games, that is, congestion games whose set of players can be partitioned into k + 1 clusters C 0, C 1,..., C k. Players in C 0 have full information about all the other participants in the game, while players in C i, for any 1 ≤ i ≤ k, have full information only about the members of C 0 ∪ C i and are unaware of all the other ones. This model has at least two interesting applications: (i) it is a special case of graphical congestion games in which the game's social knowledge graph is undirected and has independence number equal to k, and (ii) it models scenarios in which players may be of different types and the level of competition that each player experiences on a resource depends on the player's type and on the types of the other players sharing the resource. We focus on the case in which k = 2 and the cost function associated with each resource is linear and show bounds on the prices of anarchy and stability for two different social functions. © 2012 Springer-Verlag.