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# Mechanism design in project procurement auctions with cost uncertainty and failure risk

• * Corresponding author: M. Huang

This work has been sponsored by Distinguished Young Scholars Award of NSFC Grant #71325002; Major International Joint Research Project of NSFC Grant #71620107003; Foundation for Innovative Research Groups of NSFC Grant #61621004; the 111 Project Grant #B16009; Fundamental Research Funds for State Key Laboratory of Synthetical Automation for Process Industries Grant #2013ZCX11; Research Funds of Shenzhen University Grant #2018059

• Project procurement has two important attributes: cost uncertainty and failure risk. Due to the incomplete feature of such attributes, a novel mechanism incorporating contingent payments and cost sharing contracts is proposed for the buyer. Constructing models of bid decisions for risk averse and risk neutral suppliers, respectively, closed-form solutions of optimal bid prices are derived. By investigating the properties of bid prices in a first-score sealed-bid reverse auction, we find that when the degree of risk aversion or the variance of unpredictable cost is sufficiently small, bid prices of risk averse suppliers could be lower than those of risk neutral suppliers. Yet risk averse suppliers always bid higher than risk neutral suppliers in a second-score sealed-bid reverse auction. An interesting result verified by numerical experiments is that the classical revenue equivalence theorem no longer holds for the proposed mechanism if suppliers involve risk averse behavior. In this case, the buyer's best choice is to adopt a first-score sealed-bid reverse auction. We also provide decision support for the buyer to achieve optimal expected profit.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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• Figure 1.  Timing of events

Figure 2.  Comparison of ex ante expected payments of the buyer when facing risk averse suppliers in FSRA and SSRA

Figure 3.  Comparison of ex ante expected payments of the buyer when facing risk averse and risk neutral suppliers in FSRA

Figure 4.  Impact of parameters on β and ∆ for the buyer when facing risk averse suppliers in FSRA

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