Optimal decision-making with minimal waste: strategyproof redistribution of VCG payments
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Welfare Undominated Groves Mechanisms
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Redistribution mechanisms for assignment of heterogeneous objects
Journal of Artificial Intelligence Research
Redistribution of VCG payments in public project problems
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Journal of Artificial Intelligence Research
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Many important problems in multiagent systems involve the allocation of multiple resources among the agents. For resource allocation problems, the well-known VCG mechanism satisfies a list of desired properties, including efficiency, strategy-proofness, individual rationality, and the non-deficit property. However, VCG is generally not budget-balanced. Under VCG, agents pay the VCG payments, which reduces social welfare. To offset the loss of social welfare due to the VCG payments, VCG redistribution mechanisms were introduced. These mechanisms aim to redistribute as much VCG payments back to the agents as possible, while maintaining the aforementioned desired properties of the VCG mechanism. We continue the search for worst-case optimal VCG redistribution mechanisms -- mechanisms that maximize the fraction of total VCG payment redistributed in the worst case. Previously, a worst-case optimal VCG redistribution mechanism (denoted by WCO) was characterized for multi-unit auctions with nonincreasing marginal values [7]. Later, WCO was generalized to settings involving heterogeneous items [4], resulting in the HETERO mechanism. [4] conjectured that HETERO is feasible and worst-case optimal for heterogeneous-item auctions with unit demand. In this paper, we propose a more natural way to generalize the WCO mechanism. We prove that our generalized mechanism, though represented differently, actually coincides with HETERO. Based on this new representation of HETERO, we prove that HETERO is indeed feasible and worst-case optimal in heterogeneous-item auctions with unit demand. Finally, we conjecture that HETERO remains feasible and worst-case optimal in the even more general setting of combinatorial auctions with gross substitutes.