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Multi‐attribute Procurement Auctions: Efficiency and Social Welfare in Theory and Practice

Quasi‐linearity of preferences is one of the standard assumptions in auction theory. This assumption is of particular significance in multi‐attribute reverse auctions which are used in procurement. This paper presents an analysis of this assumption and its implications. Building on observations of scholars in economics and decision sciences who note that in practice such preferences may be rare, it shows that in procurement of services and goods that are to be produced, price is often interrelated with costs. When preferences can be represented with convex or concave utilities, the alternatives in which the buyer’s surplus is maximized are different from those that maximize social welfare. The result is that reverse auctions may cause a significant loss of social welfare, which may be of particular significance for public organizations. The analysis of concave efficient frontiers in the utility space which are the result of concave and linear utility functions, shows that it is possible to determine alternatives for which social welfare is greater than for the alternative which is the winning bids. If the winning seller is willing to share the increase in utility with the buyer who faces a loss, then these alternatives can produce for both the buyer and the seller, utility values that are higher than produced by the winning bid.