Optimal Procurement Design: A Reduced-Form Approach

Abstract

Standard procurement models assume that the buyer knows the quality of the good at the time of procurement; however, in many settings, the quality is learned only long after the transaction. We study procurement problems in which the buyer's valuation of the supplied good depends directly on its quality, which is unverifiable and unobservable to the buyer. For a broad class of procurement problems, we identify procurement mechanisms maximizing any weighted average of the buyer's expected payoff and social surplus. The optimal mechanism can be implemented via an auction that restricts sellers to submitting bids within specific intervals.

Figures (3)

• Figure 1: Illustration of a BRA. Sellers who wish to participate in the auction must submit a bid $b$ within the two bid intervals, $[\underline{b}_1, \overline{b}_1]$ and $[\underline{b}_2, \overline{b}_2]$. In other words, bids strictly between $\overline{b}_1$ and $\underline{b}_2$ are not allowed.
• Figure 2: Illustration of \ref{['p:oia']} for $v(q)=-2q^2+4q$, $q\sim U[0,1]$ and $n=2$. In panel (a), the blue curve is $G$ and the orange curve is its concave hull, $\overline{G}$. In panel (b), the blue curve is $P^*(q)=1-q$ and the red curve is the optimal interim allocation, $\hat{P}(q)$.
• Figure 3: In panel (a), the blue curve is the buyer's quantile virtual surplus $\widetilde{g}$ (here $\widetilde{g}(s)=g(q)$ since $q$ is uniformly distributed), and the orange curve is the ironed quantile virtual surplus $\overline g$. In panel (b), the blue curve is $P^*(q)=1-q$ that appears in Border's condition, and the red curve is the optimal interim allocation $\hat{P}(q)$.

Theorems & Definitions (25)

• Lemma 1
• Lemma 2: Border's condition
• Proposition 1
• Definition 1
• Lemma 3
• Theorem 1
• Corollary 1
• Example 1
• Theorem 1*
• Example 2