TY - GEN
T1 - Congestion games with player-specific constants
AU - Mavronicolas, Marios
AU - Milchtaich, Igal
AU - Monien, Burkhard
AU - Tiemann, Karsten
PY - 2007
Y1 - 2007
N2 - We consider a special case of weighted congestion games with player-specific 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.
AB - We consider a special case of weighted congestion games with player-specific 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.
UR - http://www.scopus.com/inward/record.url?scp=38049018063&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-74456-6_56
DO - 10.1007/978-3-540-74456-6_56
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AN - SCOPUS:38049018063
SN - 9783540744559
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 633
EP - 644
BT - Mathematical Foundations of Computer Science 2007 - 32nd International Symposium, MFCS 2007, Proceedings
PB - Springer Verlag
T2 - 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2007
Y2 - 26 August 2007 through 31 August 2007
ER -