Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Sharing the cost of multicast transmissions
Journal of Computer and System Sciences - Special issue on Internet algorithms
An approximate truthful mechanism for combinatorial auctions with single parameter agents
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Limitations of cross-monotonic cost-sharing schemes
ACM Transactions on Algorithms (TALG)
Optimal Efficiency Guarantees for Network Design Mechanisms
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Is Shapley Cost Sharing Optimal?
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Quantifying inefficiency in cost-sharing mechanisms
Journal of the ACM (JACM)
Cost sharing methods for makespan and completion time scheduling
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Bayesian algorithmic mechanism design
Proceedings of the forty-second ACM symposium on Theory of computing
Optimal cost-sharing mechanisms for steiner forest problems
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Black-box reductions for cost-sharing mechanism design
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Bayesian incentive compatibility via fractional assignments
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bayesian incentive compatibility via matchings
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We study the design of Bayesian incentive compatible mechanisms in single parameter domains, for the objective of optimizing social efficiency as measured by social cost. In the problems we consider, a group of participants compete to receive service from a mechanism that can provide such services at a cost. The mechanism wishes to choose which agents to serve in order to maximize social efficiency, but is not willing to suffer an expected loss: the agents' payments should cover the cost of service in expectation. We develop a general method for converting arbitrary approximation algorithms for the underlying optimization problem into Bayesian incentive compatible mechanisms that are cost-recovering in expectation. In particular, we give polynomial time black-box reductions from the mechanism design problem to the problem of designing a social cost minimization algorithm without incentive constraints. Our reduction increases the expected social cost of the given algorithm by a factor of O(log(min{n, h})), where $n$ is the number of agents and h is the ratio between the highest and lowest nonzero valuations in the support. We also provide a lower bound illustrating that this inflation of the social cost is essential: no BIC cost-recovering mechanism can achieve an approximation factor better than Ω(log(n)) or Ω(log(h)) in general. Our techniques extend to show that a certain class of truthful algorithms can be made cost-recovering in the non-Bayesian setting, in such a way that the approximation factor degrades by at most O(log(min{n, h})). This is an improvement over previously-known constructions with inflation factor O(log n).