Combinatorial optimization games
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Cooperative facility location games
Journal of Algorithms - Special issue: SODA 2000
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Limitations of cross-monotonic cost sharing schemes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Network design with weighted players
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Strategyproof cost-sharing mechanisms for set cover and facility location games
Decision Support Systems - Special issue: The fourth ACM conference on electronic commerce
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Selfish service installation in networks
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Mechanism design for set cover games when elements are agents
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Cost sharing and strategyproof mechanisms for set cover games
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Non-cooperative facility location and covering games
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We consider a general class of non-cooperative buy-at-bulk cost sharing games, in which k players must contribute to purchase a number of resources. The resources have costs and must be paid for to be available to players. Each player can specify payments and has a certain constraint on the number and types of resources that she needs to have available. She strives to fulfill this constraint with the smallest investment possible. Our model includes a natural economy of scale: for a subset of players, capacity must be installed at the resources. The cost increase for larger sets of players is composed of a fixed price c(r) for each resource r and a global concave capacity function g. This cost can be shared arbitrarily between players. We consider the quality and existence of pure-strategy exact and approximate Nash equilibria. In general, prices of anarchy and stability depend heavily on the economy of scale and are Θ(k/g(k)). For non-linear functions g pure Nash equilibria might not exist and deciding their existence is NP-hard. For subclasses of games corresponding to covering problems, primal-dual methods can be applied to derive cheap and stable approximate Nash equilibria in polynomial time. In addition, for singleton games optimal Nash equilibria exist. In this case expensive exact as well as cheap approximate Nash equilibria can be computed in polynomial time. Some of our results can be extended to games based on facility location problems.