Design Multidimensional All-Pay Procurement Auction with Loss-Averse Bidders

Abstract

Procurement auctions involving multidimensional bids, typically consisting of a proposal and a price, are common in various industries. One notable aspect of these auctions is the all-pay component, where bidders must invest time and effort upfront to prepare a proposal, regardless of whether they win the contract. If a bidder loses the auction, the cost of developing the proposal is unrecoverable. Given that individuals tend to be loss averse, meaning they are more sensitive to losses than to gains of the same magnitude, loss aversion is particularly relevant in this setting, especially regarding the all-pay component. We analyze the impact of bidder loss aversion using game theoretical analysis and find that in the unique symmetric equilibrium of this setting, loss aversion consistently reduces equilibrium bid quality. Additionally, the effect on the buyer's equilibrium expected utility depends on the degree of loss aversion and how the buyer values the bidder's proposal. To mitigate the potential negative impact of loss aversion, we investigate two quality compensation policies commonly used in practice and studied in the literature: the proportional and the flat compensation policy. We show that both policies can improve social welfare without harming either side. Furthermore, we find that the flat compensation policy is preferable when the bidder population exhibits low levels of loss aversion. Additionally, we explore the role of competition and suggest that there may be benefits to limiting the number of participating bidders. Moreover, we demonstrate that implementing a compensation policy, along with the ability to restrict the number of bidding bidders, can provide added value to the buyer.

Keywords: multidimensional procurement auction; all-pay quality spending; loss aversion; proportional compensation; flat compensation.