Mechanism design for set cover games when elements are agents

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.