The beauty of Dutch: Ex-post split-award auctions in procurement markets with diseconomies of scale

Highlights

• We provide an equilibrium analysis of 3 combinatorial first-price auction formats.

• First-price sealed-bid and Dutch auction formats are not strategically equivalent.

• The information revealed during the Dutch auction formats helps bidders coordinate.

• In markets with only two bidders, equilibria involving high pooling prices emerge.

• With additional bidders such high-cost equilibria do not exist anymore.

Abstract

Ex-post split-award auctions are frequently organized as combinatorial procurement auctions in which the demand for some quantity to be procured is split into multiple shares and suppliers can bid on individual shares and the package. With two shares the auction selects either a single- or dual-source allocation. Markets with diseconomies of scale make the environment strategically challenging, because suppliers need to coordinate on a split outcome in the efficient equilibrium. We provide an equilibrium analysis of three combinatorial formats, namely, the first-price sealed-bid, the Dutch and the Dutch-FPSB split-award auction. We show that, unlike in single-object auctions, first-price sealed-bid and Dutch combinatorial auction formats are not strategically equivalent. While the FPSB auction exhibits a coordination problem for bidders, the Dutch formats have only efficient equilibria. The price information revealed during the Dutch auction formats helps bidders coordinate. In markets with only two bidders equilibria involving high pooling prices emerge in all three formats. However, no such strategy exists anymore when the number of bidders exceeds the number of shares. As a result, qualifying one more supplier has a significant impact as the expected procurement costs are reduced substantially.

Introduction

The analysis of procurement auctions is a rich and growing field of study. Different environments and auction mechanisms have been analyzed recently (Lorentziadis, 2008, Mishra, Veeramani, 2007, Xu, Feng, He, 2017). We focus on a simple but wide-spread market environment in which a buyer wants to minimize procurement costs and he can either buy the demand from a single supplier (sole source award) or split the demand in two indivisible lots (aka. shares) by buying from different suppliers (dual sourcing).

If the scale economies in the market are known by the buyer, it is easy to select an appropriate auction format: with economies of scale it is efficient to select a single supplier, and the procurement manager can employ a single-lot auction in which bidders are only allowed to bid on the package of all lots (Kokott, Bichler, & Paulsen, 2018b). Diseconomies of scale are wide-spread due to capacity constraints and stepwise-fixed costs in the production (Bichler, Schneider, Guler, Sayal, 2011, Gallien, Wein, 2005, Jin, Wu, Erkoc, 2006). In microeconomic textbooks short-run marginal cost functions are typically U-shaped (Baumol, 1987). With diseconomies of scale the allocation to two suppliers (split award) is efficient and the procurement manager could use ex-ante split-award auctions (Bichler, Guler, Mayer, 2015, Chaturvedi, Beil, Katok, 2018). In this auction, the split is determined before the auction and a supplier can win at most one of the two shares. If a buyer knew the scale economies in the market, he could use the appropriate auction design for each efficiency scenario. While it is reasonable to assume that suppliers know the scale efficiencies for the production of a good, this is often not true for the buyer. Procurement managers are typically responsible for many products and they do not always have detailed knowledge about the production technologies and supplier capacities. However, if an ex-ante split-award auction is employed in a market with economies of scale, the outcome is inefficient and can lead to high procurement costs. The same applies for a single-unit auction in a market with diseconomies of scale.

We analyze combinatorial ex-post split-award auctions which allow suppliers to bid on the individual lots and the package. The mechanism determines ex-post, i.e., after all bids have been collected, whether the sole source award is selected or each lot is awarded to a different supplier. Procurement auctions are largely organized as first-price sealed-bid auctions (FPSB) (Bogaschewsky, 2016). Whether first-price combinatorial auctions indeed yield the efficient outcome in equilibrium is an open question. This is particularly challenging with diseconomies of scale, because suppliers need to coordinate such that each of them wins one lot in the efficient equilibrium rather than just outbidding each other on the package of two lots. So far, there is limited research on combinatorial first-price auctions.

Bernheim and Whinston (1986) studied the equilibrium of a combinatorial FPSB auction under complete information. No general closed-form Bayesian Nash equilibrium bidding strategy is known for the analysis of the incomplete-information game, however, and this has been an open problem for several decades now. One way forward is the analysis of more specific environments. An article by Anton and Yao (1992) provided a Bayesian Nash equilibrium analysis for a procurement market with two objects, two bidders, and strong diseconomies of scale. They showed that there are multiple and also inefficient equilibria in a combinatorial FPSB procurement auction. The theoretical analysis hinges on the assumption of two bidders only and it cannot easily be generalized to n > 2 bidders, because in the two-bidder case one bidder can unilaterally veto the split-award with a very high bid on a single lot. Kokott, Bichler, and Paulsen (2018a) provided equilibrium predictions and also experimental results for a split-award auction with two objects and n > 2 bidders who have economies of scale. It was shown that combinatorial first-price auctions yield high efficiency and low procurement costs both in equilibrium and in the lab compared to sequential auctions. The equilibrium analysis of markets with diseconomies of scale was left open in their paper, as it constitutes a strategically different environment. The results are complementary to this article.

Markets with diseconomies of scale are interesting for a number of reasons. First, in the efficient equilibrium the winning bidders need to coordinate on the split which is strategically more challenging than competing just for a package. Second, environments with diseconomies of scale are relevant for a large number of procurement markets. In this article, we study procurement setting with two and more than two bidders having diseconomies of scale. Furthermore, not only the FPSB but also the Dutch and Dutch-FPSB split-award auction format are analyzed and it is shown that not only the allowed bid types but also the auction process matter.

First, we introduce three ex-post split-award auctions including two shares (50% and 100%) and derive equilibrium bidding strategies for them. The FPSB format, in which all bidders simultaneously submit a quote for the 50% and 100% share, is the most common one. Additionally, we introduce the Dutch and Dutch-FPSB split-award auctions as dynamic formats. Phase 1 is the same in both auction formats. Beginning from low starting prices for both shares a price clock is increasing in phase 1. When a bidder accepts the price for the 100% share, the auction is over and a single-source allocation is installed. In case of an acceptance of the 50% share in phase 1, the auction continues and both bidders have the chance to win the remaining share in a subsequent phase. Dependent on the auction format, phase 2 is either a Dutch or a FPSB auction for the remaining share. A dual-source allocation is the outcome when the remaining share is won by a different bidder than the winner of phase 1.

Second, we derive the equilibrium strategies. Perfect Bayesian equilibria are provided for the dynamic formats with two bidders. In contrast to the FPSB auction, in which efficient and inefficient equilibria emerge, there is a unique and efficient equilibrium in the Dutch auction and multiple efficient equilibria in the Dutch-FPSB auction both involving pooling prices. The analysis shows that this strategic differences comes from the different possibilities for the winner of phase 1 to pose threats to his opponent in order to prevent him from deviating from equilibrium in phase 2. We provide Bayesian Nash equilibrium strategies as closed-form solutions for the FPSB auction with two shares and n > 2 bidders. Like in the setting with two suppliers there is a coordination problem for the bidders in the FPSB format, because efficient and inefficient equilibria emerge. This equilibrium selection problem vanishes in the Dutch and Dutch-FPSB split-award auctions for which we prove that only unique and efficient equilibria exist. In contrast to the setting with two bidders only, these equilibria are competitive and do not involve pooling. This can be seen as a reduction of the strategic complexity for the bidders compared to the FPSB auction.

Finally, we compare the different formats with respect to efficiency and costs. It is shown that procurement prices can be reduced significantly by adding an additional bidder as equilibria involving pooling are not feasible in the setting with three bidders any more.