Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Weak monotonicity suffices for truthfulness on convex domains
Proceedings of the 6th ACM conference on Electronic commerce
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Proceedings of the 8th ACM conference on Electronic commerce
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Proceedings of the 9th ACM conference on Electronic commerce
On characterizations of truthful mechanisms for combinatorial auctions and scheduling
Proceedings of the 9th ACM conference on Electronic commerce
Monotonicity and implementability: extended abstract
Proceedings of the 9th ACM conference on Electronic commerce
A Characterization of 2-Player Mechanisms for Scheduling
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An optimal lower bound for anonymous scheduling mechanisms
Proceedings of the 10th ACM conference on Electronic commerce
A Lower Bound for Scheduling Mechanisms
Algorithmica
Characterizing Incentive Compatibility for Convex Valuations
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
A lower bound of 1 + ϕ for truthful scheduling mechanisms
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Extending characterizations of truthful mechanisms from subdomains to domains
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
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We study the geometrical shape of the partitions of the input space created by the allocation rule of a truthful mechanism for multi-unit auctions with multidimensional types and additive quasilinear utilities. We introduce a new method for describing the allocation graph and the geometry of truthful mechanisms for an arbitrary number of items(/tasks). Applying this method we characterize all possible mechanisms for the case of three items.Previous work shows that Monotonicity is a necessary and sufficient condition for truthfulness in convex domains. If there is only one item, monotonicity is the most practical description of truthfulness we could hope for, however for the case of more than two items and additive valuations (like in the scheduling domain) we would need a global and more intuitive description, hopefully also practical for proving lower bounds. We replace Monotonicity by a geometrical and global characterization of truthfulness.Our results apply directly to the scheduling unrelated machines problem. Until now such a characterization was only known for the case of two tasks. It was one of the tools used for proving a lower bound of $1+\sqrt{2}$ for the case of 3 players. This makes our work potentially useful for obtaining improved lower bounds for this very important problem. Finally we show lower bounds of $1+\sqrt{n}$ and n respectively for two special classes of scheduling mechanisms, defined in terms of their geometry, demonstrating how geometrical considerations can lead to lower bound proofs.