Congestion Games with Player-Specific Constants

We consider a special case of weighted congestion games with playerspecific latency functions where each player uses for each particular resource a fixed (non-decreasing) delay function together with a player-specific constant. For each particular resource, the resource-specific delay function and the playerspecific constant (for that resource) are composed by means of a group operation (such as addition or multiplication) into a player-specific latency function. We assume that the underlying group is a totally ordered abelian group. In this way, we obtain the class of weighted congestion games with player-specific constants; we observe that this class is contained in the new intuitive class of dominance weighted congestion games. We obtain the following results: Games on parallel links: – Every unweighted congestion game has a generalized ordinal potential. – There is a weighted congestion game with 3 players on 3 parallel links that does not have the Finite Best-Improvement Property. – There is a particular best-improvement cycle for general weighted congestion games with player-specific latency functions and 3 players whose outlaw implies the existence of a pure Nash equilibrium. This cycle is indeed outlawed for dominance weighted congestion games with 3 players – and hence for weighted congestion games with player-specific constants and 3 players. Network congestion games: For unweighted symmetric network congestion games with player-specific additive constants, it is PLS-complete to find a pure Nash equilibrium. Arbitrary (non-network) congestion games: Every weighted congestion game with linear delay functions and player-specific additive constants has a weighted potential. This work was partially supported by the IST Program of the European Union under contract number IST-15964 (AEOLUS). Supported by the International Graduate School of Dynamic Intelligent Systems (University of Paderborn, Germany). L. Kučera and A. Kučera (Eds.): MFCS 2007, LNCS 4708, pp. 633–644, 2007. c © Springer-Verlag Berlin Heidelberg 2007 634 M. Mavronicolas et al.