Setting Reserve Prices in Repeated Procurement Auctions

1 Introduction

Public procurement markets represent about 12 percent of GDP in developed countries (OECD 2016). In awarding contracts to suppliers, public buyers often rely on first-price auctions where suppliers bid a rebate on the reserve price, and the contract is assigned to the supplier with the highest rebate (i.e. the lowest-price supplier). In this setting, the reserve price – representing the announced maximum price the buyer is willing to pay for the good or service – is key to the design of the auction and the performance of the procurement procedure. Indeed, in the short-term, its level affects competition in the auction and the final price and, in the long-term, the dynamic efficiency of procurement markets.

The optimum reserve price depends on the information the buyer has on suppliers’ production costs. Specifically, in a single – isolated in time – procurement purchase, the buyer can be faced with a large amount of asymmetric information vis-à-vis all suppliers: each supplier knows its production costs and the buyer does not. However, in repeated – over time – procurement purchases of the same good or service, the buyer may be able to collect and update information about the production costs of one or more suppliers,^[1] and use it to set the reserve price and affecting procurement outcomes.

This paper empirically and theoretically investigates the reserve price in repeated – over time – procurement purchases of a standard good/service to document and rationalize how it is set. Using a large database on Russian first-price auctions for the procurement of gasoline, a commodity with minimum quality differentiation, we first provide empirical evidence of variations in reserve prices at the specific buyer-supplier pair level. In particular, we find that, in a non-negligible number of cases, the reserve price chosen by a procurer in auctions awarded to a given supplier is systematically lower than the reserve price set by the same procurer in similar auctions awarded to other suppliers. Running an econometric analysis, we then show that in these auctions both competition and the winning prices are lower than in the remaining part of our dataset. Hence the conjecture, which we have tested empirically, that public buyers exploit additional information gained over time on the characteristics of previous winners.

To rationalize our empirical results, we develop a simple theoretical setting where a procurer aims to purchase an item using a first-price auction. We show that, when the procurer knows the costs of one supplier and this supplier wins the auction, the optimum reserve price set and the winning bid are lower than the ones the buyer would have set and paid without that information. This is in line with the procurer’s traditional trade-off highlighted in the literature (see, e.g. Krishna 2009): on the one hand, setting a lower reserve price decreases the expected winning bid but, on the other hand, it increases the risk of having no suppliers enter the auction.

Our empirical and theoretical findings highlight that repeated procurement purchasing could play a significant role in reducing asymmetric information about suppliers’ costs and related distortions. Specifically, we add to two main strands of the literature. First, we contribute to the empirical literature supporting the benefits of buyer’s discretion in procurement. In our analysis, in repeated procurement auctions, buyer discretion in setting the reserve price leads to a lower number of bidders in the auction, and – unexpectedly – a lower final price. In a similar vein, Coviello et al. (2022); Kang and Miller (2022) show that the procurer’s actions to reduce competition is not always harmful. Using a regression discontinuity design on a dataset of Italian public work contracts, Coviello, Guglielmo, and Spagnolo (2017) find that giving additional discretion to a public buyer does not result in a higher final price and increases the likelihood of the same firm winning multiple contracts from the same buyer. We contribute to this literature with a set of new results based on the investigation of the procurer’s discretion in the manipulation of the reserve price in a repeated setting where the buyer obtains information on at least one supplier’s costs.

Second, we contribute to the literature studying the revenue-maximizing reserve price from the perspective of the auctioneer. In two seminal papers, Myerson (1981) and Riley and Samuelson (1981) show that, in a direct independent private value (IPV) auction – where the highest offer wins – and with risk-neutral bidders, the auctioneer should always set a reserve price that exceeds its true value by an amount that does not depend on the number of bidders entering the auction. Much of the literature limits the scope of this result: when bidders’ values are correlated, the auctioneer’s optimum reserve price approaches its true value as the number of bidders increase^[2] (Levin and Smith 1996); the optimum reserve price comes closer to the buyer’s true valuation when the auctioneer or the bidders are risk-averse (Hu, Matthews, and Zu 2010); finally, the reserve price can be manipulated to deter bidder collusion (Thomas 2005) or to exploit bidders’ bounded rationality (Crawford et al. 2009). Our findings highlight a further setting where the seminal result of Myerson (1981) and Riley and Samuelson (1981) no longer holds, i.e. the case of repeated auctions where the buyer knows the cost of one bidder and exploits it to set the reserve price.

The remainder of the paper is structured as follows. In Section 2 we first describe Russian public procurement auctions and then illustrate the data on which we run our empirical analysis. The methodology and the empirical results are presented in Sections 3. Section 4 develops a simple model to investigate setting the optimum reserve price with or without information about a specific supplier. A discussion of the empirical and theoretical findings is set out in Section 5, along with the conclusions.

2 Data and Institutional Setting

We build a rich dataset of Russian public procurement contracts for gasoline awarded using first-price auctions. Gasoline sold in petrol stations is a largely standardized commodity.^[3] This reduces the potentially confounding effects from unobserved quality differences in the supply.

On the demand side, Russian state agencies at all levels (federal, regional, and local) are subject to the same procurement regulations and subsequent amendments.^[4] Demand and supply in Russian public procurement markets are matched through the online centralized platform containing all publicly awarded contracts: our dataset collects information from such platform.^[5] Specifically, our original dataset includes information at auction level about each public buyer (name and address) awarding a contract to purchase gasoline for petrol stations, the characteristics of the gasoline to be procured (volume and octanes), the reserve price, the procedure chosen, and the delivery time and place. Moreover, it records the auction outcomes, i.e. the number of bidders and the number of bids, the name of the winning bidder and the price, as well as which three firms submitted the lowest bids.

According to Russian public procurement regulations, gasoline can be purchased through sealed bid auctions, electronic open auctions (e-auctions)^[6] or single-source contracts.^[7] We focus on the former two competitive procedures which award contracts to firms bidding the lowest price. All in all, our original dataset covers the period 1/2011–12/2013 and contains 171,784 auctions in 83 Russian regions.^[8] From the original sample we drop (a) outsourced procurement to centralized agencies acting as intermediaries, and (b) observations with an unknown supplier identity, volume or unit reserve price^[9] and (c) singleton observations at buyer-supplier level. As a result, our final dataset includes information on 70,013 auctions.

We also observe the monthly regional market price per liter of gasoline purchased through petrol stations:^[10] we use this information as a proxy for differences in the costs of the raw material at regional level (Table 1).

Descriptive statistics are presented in Table 1.^[11] Sealed bid auctions account for 70 percent of the total number of auctions in our database, and e-auctions account for the remainder; 60 percent of the total number of auctions were conducted by federal agencies. The volume and unit reserve price are on average, respectively, 8,103 L and 29.3 RUB whereas the mean of the market price equals 27.9 RUB. Furthermore, the average reserve price – calculated as the average unit reserve price multiplied by the average volume – is equal to 237,418 RUB (about 5,800 EUR at the exchange rate in that moment). The average number of bidders is 1.6, and in about 50 % of our sample only one firm took part in the auction. Finally, the related contract price mark-up – calculated as the percentage difference between unit contract price and market price – ranges between −0.4 and 0.5.

3 Empirical Strategy and Results

4 A Simple Theoretical Model

The crucial result of our empirical analysis is that, in a non-negligible number of auctions in our dataset, the reserve price shows a regularity, i.e. with a discount if the winning supplier in that auction has had previous interaction(s) with the buyer. This is puzzling, as the reserve price is set before the identity of the winning supplier is known to the public buyer. In auctions exhibiting this reserve price discount, we find that the winning price and participation in the auction are lower than in the remainder of our dataset.

We conjecture that public buyers are exploiting information gained at previous auctions and during the performance of prior or ongoing contracts. This is supported by empirically studying the reserve price in a dynamic framework, taking into account whether the buyer had previously interacted with the winning supplier. Interestingly, our analysis shows that unit reserve prices drop over the transaction time only for buyer-supplier pairs which feature the reserve price discount strategy.

In this section we show that our empirical results are in line with a simple theoretical framework in which the buyer has information about the supplier’s characteristics and exploits them in setting the reserve price. Specifically, we first characterize the optimum reserve price when the buyer has information about a supplier’s costs: we show that when the contract is awarded to the supplier whose costs are known to the buyer, the winning price is lower than the one the buyer would have paid without that information. We then discuss how our results change moving from a single to a repeated interaction setting.^[23]

We consider a risk-neutral public buyer who aims to purchase a single item (i.e. a standard good/service). The buyer assigns a value V to the item and, running a first-price auction (FPA, henceforth), awards the contract to the lowest-price bidder. In designing the FPA, for the single item awarded, the buyer sets a reserve price r, i.e. the public buyer’s announced maximum willingness to pay. All the suppliers’ offers above r are automatically discarded.

We assume two potential suppliers enter the FPA and compete to win the contract.^[24] Supplier i ∈ {1, 2} records a cost c _i to execute and deliver the contract; note that c _i is also the minimum payment required by the supplier i to provide the buyer with the item. Moreover, we assume that c _i is independently and identically distributed on the interval [0, ω] according to the increasing distribution function F; and that F admits a continuous density f = F′ and has full support. Each supplier knows the realization of its cost c _i , and that other bidder’s costs are independently distributed according to F.^[25]

Both suppliers are risk neutral and maximize their expected profits. The winning supplier’s i profit from the procurement contract is given by the difference between its bid b _i and its cost c _i . The bidding function for a FPA in a procurement setting,^[26] given the reserve price r and considering a supplier with cost c _i ≤ r, is:^[27]

Consider now the setting in which the buyer knows the costs of one of the two suppliers (bidders): we denote the observed cost with c ̄ . Note that in this setting – on the one hand – the bidders’ equilibrium strategies are no different from those in a standard FPA (where one supplier’s costs are unknown). On the other hand, the buyer, by observing c ̄ , will consider this cost in choosing r which maximizes its expected payoff Π ^O . With this aim, the buyer can alternatively set a reserve price r ≥ c ̄ or r < c ̄ . Specifically, in the first case, at least the known bidder (with c ̄ ) takes part in the auction, and the probability that it wins the auction is ( 1 − F ( c ̄ ) ) . In the second case, with r < c ̄ , the contract is awarded only if the unknown supplier has a cost equal to or lower than the reserve price: this happens with a probability equal to F(r) and the buyer is expected to pay E[m(c, r)|c < r], where m(c, r) stands for the bid by a supplier with cost c, multiplied by its probability of winning. Formally, when the buyer observes c ̄ , the expected payoff is:

By algebra, we obtain the following first order condition of Π ^O w.r.t. r:

where λ ( r ) = f ( r ) F ( r ) .

Note that (12) is negative defined when r ≥ c ̄ , i.e. for the buyer it is never optimal to set a reserve price higher than c ̄ .

If r < c ̄ , the known supplier does not take part in the auction. Define, if applicable, r ̂ ∈ [ 0 , c ̄ [ as the reserve price r such that ∂ Π O ∂ r = 0 ; note that r ̂ is independent of c ̄ .

We can now proceed in characterizing the reserve price r* that globally maximizes the buyer’s expected revenue Π ^O (r), and how it changes as a function of the known supplier’s cost. We consider the case in which V ≥ c ̄ , i.e. the buyer values the item to be procured more than the production cost of the known supplier.

In this setting, it is possible to prove that r* can have only two values. Specifically:

1. r * = r ̂ if r ̂ ∈ ] 0 , c ̄ [ exists and Π O ( r ̂ ) > Π O ( c ̄ ) ;

2. else, r * = c ̄

Consider a known supplier with costs c ̄ = 0 . Then, r* = 0. In general, as long as c ̄ ≤ r ̂ , then r * = c ̄ . In this case, the more efficient the known supplier, the lower the observed c ̄ , the optimum reserve price r*, and the resulting price paid by the buyer. For less efficient suppliers, i.e. when c ̄ > r ̂ , the buyer faces a choice. On the one hand, it can exclude the known bidder, setting r * = r ̂ . Or it can still set r * = c ̄ . In the former case the expected price paid if the contract is awarded is lower than in the latter, but the risk is that no bidders take part in the auction. Which of the two alternatives should be preferred depends on the models parameters and the actual costs of the known bidder.

Let us consider the case where the buyer knows the supplier’s costs and this supplier is the winning bidder. The reserve price the buyer sets and the winning bid the buyer pays are equal to c ̄ . Both this reserve price and the winning bid are lower than the ones the buyer would have set and paid without the information concerning the supplier’s costs; indeed, they could not be any lower, if the supplier is willing to take part in the auction. Consider now competition in the auction: the winning supplier is, by definition, the most efficient; and no other bidder with costs greater than c ̄ could enter the auction. As a result, auctions awarded to the known supplier have only one participant.^[28]

The simple theoretical setting we have presented is a static, one-shot game. We now consider a dynamic setting, i.e. a setting where the buyer periodically procures the needed item in repeated and sequential auctions. Here, we assume the buyer maximizes its long-term surplus by setting the reserve price in each auction. Accordingly, the optimum reserve price in t = 1, r ₁, depends on the known supplier costs’ c 0 ̄ at t = 0. Similarly, in t = 2, the buyer sets a reserve price r ₂ using the information on c 1 ̄ gained in t = 1, and so on.

In this model, how the buyer learns the t = i winning bidder costs c i ̄ becomes crucial. It can be in one of two ways: either the buyer learns c i ̄ by observing the execution of the contract, or through the winning supplier’s bid in t = i. In the former case, the predictions of the static model above do not change. The intuition behind this is that the buyer’s awareness of c ̄ in t = 1 is independent of the winning supplier’s bid in t = 0. Specifically, consider a setting with two periods, t = {0, 1}. Supplier i with costs c _i wins the auction in the initial period, t = 0. Then, in t = 1, the buyer sets a reserve price r ₁ equal to, at most, supplier i’s costs: r ₁ ≤ c _i ; as a result, whether or not it is awarded the contract, supplier i makes zero profit from this auction. Solving via backward induction, supplier i bidding strategy in t = 0 is equal to the standard bidding behavior in a static FPA.

However, this is no longer true assuming the buyer learns about the supplier’s costs by observing their bids: in this case, a fully rational bidder notices that its bidding behavior in the earlier rounds influences the reserve prices set in later rounds, and so makes the offer strategically (Amin, Rostamizadeh, and Syed 2013). Such a level of bidder sophistication seems highly unlikely given the average contract value in our empirical setting.

5 Conclusions

In a standard one-shot auction for a standard item, the public buyer has no information about supplier costs. Accordingly, the reserve price it sets is uncorrelated with the identity of the winning bidder. In repeated auctions, where the buyer periodically procures the required item and observes – from time to time – the winner’s bid and the execution of the contract, such a lack of correlation seems no longer to apply. Running our analysis on a large dataset of Russian public procurement auctions for gasoline, we provide original evidence in this respect.

Our identification strategy relies first on identifying pairs of buyer j – supplier i in repeated transactions. We then consider the buyer’s reserve price setting in these transactions and define the reserve price discount as the presence of a positive and statistically significant difference between the average reserve price set by a buyer j and the average reserve price set by the same buyer in all the auctions awarded to the supplier i, after considering contract and procurer characteristics.

We find that, in auctions with a reserve price discount, both the winning price and the number of bidders taking part in the auction are lower than in the remainder of our dataset. We posit that, in these auctions, public buyers are exploiting information they have gained from previous auctions. This hypothesis is supported by empirically studying the reserve price in a dynamic framework, taking into account whether the procurer had previously interacted with the winning supplier.

Finally, we propose a simple theoretical setting to explain our empirical results. Specifically, we assume that the buyer gains information on the supplier’s actual production costs in an initial auction, at time t = 0. Then, we assume that the buyer uses this information at time t = 1 to set the reserve price in a new auction. As a result, at t = 1, in auctions where the winning bidder is the firm supplying at t = 0, our model predicts that the reserve price the buyer sets is lower than the one the buyer would have set without the information about t = 0 supplier's production costs. Both the winning price and the level of competition in the auction are lower in the former case than in the latter, which is in line with our empirical evidence.

Our results suggest that repeated procurement purchases increase the information available to public buyers and could, through this channel, play a relevant role in reducing the final price paid with public money. This is a positive outcome in the short term, but the long-term implications are less clear: the reserve price discount reduces the competition in the market and, in the long run, this can lead to lower innovation rate. Indeed, a long and repeated relationship between buyer and supplier in a public procurement setting is not always advisable as it can reduce the possibility to interact with new, innovative and efficient suppliers.

A straightforward policy implication from our analysis is that information on past procurement outcomes should be shared in an easily accessible way between all public buyers. How to share this information in a way that does not reduce competition is left to future investigations.