Refining the Cost of Cheap Labor in Set System Auctions

In set system auctions, a single buyer needs to purchase services from multiple competing providers, and the set of providers has a combinatorial structure; a popular example is provided by shortest path auctions [1, 7]. In [3] it has been observed that if such an auction is conducted using first-price rules, then, counterintuitively, the buyer’s payment may go down if some of the sellers are prohibited from participating in the auction. This reduction in payments has been termed “the cost of cheap labor”. In this paper, we demonstrate that the buyer can attain further savings by setting lower bounds on sellers’ bids. Our model is a refinement of the original model of [3]: indeed, the latter can be obtained from the former by requiring these lower bounds to take values in {0, +∞}. We provide upper and lower bounds on the reduction in the buyer’s payments in our model for various set systems, such as minimum spanning tree auctions, bipartite matching auctions, single path and k-path auctions, vertex cover auctions, and dominating set auctions. In particular, we illustrate the power of the new model by showing that for vertex cover auctions, in our model the buyer’s savings can be linear, whereas in the original model of [3] no savings can be achieved.