In this article, we study the set cover games when the elements are selfish agents, each of which 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 strategyproof mechanisms that decide, 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 single-cover set cover games, we present a mechanism that is at least 1/d_(max)-efficient, i.e., the total valuation of all selected elements is at least 1/d_(max) fraction of the total valuation produced by any mechanism. Here, d_(max) is the maximum size of the sets. For multi-cover set cover games, we present a budget-balanced strategyproof mechanism that is 1/d_(max)H_(d_(max))-efficient under reasonable assumptions. Here, H_n is the harmonic function. For the 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 strategyproof mechanism.
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