Investments in First-Price and Second-Price Procurement Auctions

This paper is about a procurement auction setting with two sellers in which before the auction seller i can make an investment which improves the ex ante probability distribution of his cost; seller j observes seller i's investment decision before bidding occurs. Under somewhat restrictive assumptions on the pre- and the post-investment cost distributions, Arozamena and Cantillon (2004) prove that in the first price auction seller i's investment induces seller j to bid more aggressively. This negative strategic effect contributes to AC's result that the investment incentive for seller i is stronger in the second price auction than in the first price auction. We prove that under weaker but economically significant assumptions, and discretely distributed costs, an investment by seller i may actually induce seller j to bid less aggressively in the first price auction (i.e., the strategic effect may be positive), and the investment incentive may be stronger in the latter auction. Moreover, in some cases the buyer prefers the first price auction precisely because it provides a stronger investment incentive, even though the second price auction is preferable when no investment is possible. We prove that the two auctions are not equivalent in a setting in which each seller has the option to invest and the sellers are ex ante symmetric, and that the second price auction gives a stronger investment incentive to the initially stronger seller than to the other seller (this increases asymmetries), but such result does not necessarily hold in the first price auction.