Procuring substitutes with (fine-tuned) first-price auctions

Suppose a firm uses inputs that are substitutes. Each input is supplied by a single contractor. The firm would like to make suppliers compete. However, since inputs are imperfect substitutes, resorting to winner-take-all competition may not be an attractive option. We allow the firm to use a modified first-price auction. It announces demand functions for each input and contractors simultaneously bid unit prices and sell according to announced input demands. We show that the firm has an incentive to announce demands that overstate input substitutability and understate its willingness to pay. In the extreme inputs are treated as perfect substitutes even if goods are independent.