Mechanism design for set cover games when elements are agents

Authors:
Zheng Sun;Xiang-Yang Li;WeiZhao Wang;Xiaowen Chu
Affiliations:
Hong Kong Baptist University, Hong Kong, China;Illinois Institute of Technology, Chicago, IL;Illinois Institute of Technology, Chicago, IL;Hong Kong Baptist University, Hong Kong, China
Venue:
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Year:
2005

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Abstract

In this paper we study the set cover games when the elements are selfish agents. In this case, each element has a privately known valuation of receiving the service from the sets, i.e., being covered by some set. Each set is assumed to have a fixed cost. We develop several approximately efficient truthful mechanisms, each of which decides, after soliciting the declared bids by all elements, which elements will be covered, which sets will provide the coverage to these selected elements, and how much each element will be charged. For set cover games when both sets and elements are selfish agents, we show that a cross-monotonic payment-sharing scheme does not necessarily induce a truthful mechanism.