TY - GEN
T1 - Cost-sharing scheduling games on restricted unrelated machines
AU - Avni, Guy
AU - Tamir, Tami
N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.
PY - 2015
Y1 - 2015
N2 - We study a very general cost-sharing scheduling game. An instance consists of k jobs and m machines and an arbitrary weighed bipartite graph denoting the job strategies. An edge connecting a job and a machine specifies that the job may choose the machine; edge weights correspond to processing times. Each machine has an activation cost that needs to be covered by the job assigned to it. Jobs assigned to a particular machine share its cost proportionally to the load they generate. Our game generalizes singleton cost-sharing games with weighted players. We provide a complete analysis of the game with respect to equilibrium existence, computation, convergence and quality – with respect to the total cost. We study both unilateral and coordinated deviations. We show that the main factor in determining the stability of an instance and the quality of a stable assignment is the machines’ activation-cost. Games with unit-cost machines are potential games, and every instance has an optimal solution which is also a pure Nash equilibrium (PNE). On the other hand, with arbitrary-cost machines, a PNE is guaranteed to exist only for very limited instances, and the price of stability is linear in the number of players. Also, the problem of deciding whether a given game instance has a PNE is NP-complete. In our analysis of coordinated deviations, we characterize instances for which a strong equilibrium exists and can be calculated efficiently, and show tight bounds for the SPoS and the SPoA.
AB - We study a very general cost-sharing scheduling game. An instance consists of k jobs and m machines and an arbitrary weighed bipartite graph denoting the job strategies. An edge connecting a job and a machine specifies that the job may choose the machine; edge weights correspond to processing times. Each machine has an activation cost that needs to be covered by the job assigned to it. Jobs assigned to a particular machine share its cost proportionally to the load they generate. Our game generalizes singleton cost-sharing games with weighted players. We provide a complete analysis of the game with respect to equilibrium existence, computation, convergence and quality – with respect to the total cost. We study both unilateral and coordinated deviations. We show that the main factor in determining the stability of an instance and the quality of a stable assignment is the machines’ activation-cost. Games with unit-cost machines are potential games, and every instance has an optimal solution which is also a pure Nash equilibrium (PNE). On the other hand, with arbitrary-cost machines, a PNE is guaranteed to exist only for very limited instances, and the price of stability is linear in the number of players. Also, the problem of deciding whether a given game instance has a PNE is NP-complete. In our analysis of coordinated deviations, we characterize instances for which a strong equilibrium exists and can be calculated efficiently, and show tight bounds for the SPoS and the SPoA.
UR - http://www.scopus.com/inward/record.url?scp=84983775752&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-662-48433-3_6
DO - https://doi.org/10.1007/978-3-662-48433-3_6
M3 - Conference contribution
SN - 9783662484326
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 69
EP - 81
BT - Algorithmic Game Theory - 8th International Symposium, SAGT 2015
A2 - Hoefer, Martin
PB - Springer Verlag
T2 - 8th International Symposium on Algorithmic Game Theory, SAGT 2015
Y2 - 28 September 2015 through 30 September 2015
ER -