The Dutch construction cartel : bidding in the pre-auction

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The Dutch Construction Cartel:

Bidding in the Pre-auction

Master’s Thesis

Abstract

This study compares bidding behavior in the low price, sealed-bid pre-auction/knockout of a bidding ring organized in a manner comparable to the Dutch construction cartel with that of a fully competitive scenario within the framework of (finite) repeated interaction. By assuming perfect information and symmetry across both firms’ cost prices and projects, the model examined in this thesis captures the main gist of how capacity constraints - leading to higher cost prices - and discounted side transfers on bidding behavior.

It is found that the pre-auction bids submitted in equilibrium are lower, implying more aggressive bidding behavior, than in the competitive setting. That is, because arising side transfers are not paid out to the full. This implies that the winning pre-auction bids do not serve as an accurate benchmark for the price paid by the procurement agent in case of full competition. Furthermore, imposing the condition that firms’ cost prices increase after winning only results in less aggressive bidding behavior if, at some point, all firms but one experience an increased cost price.

Max Hesseling

Student Number 10767010

University of Amsterdam Master of Science in Economics

Markets & Regulation

Supervisors: Prof. Dr. Maarten Pieter Schinkel and Leonard Treuren July 15, 2018

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Statement of Originality

This document is written by Student Max Hesseling who declares to take full responsibility for the con-tents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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List of Figures

1 Equilibrium bids as a function of discount rate β . . . 35

2 Equilibrium bids as a function of α . . . 36

List of Tables

1 Side Transfers (Example) . . . 12

2 Balances after Project 1-4 (Example) . . . 13

3 Winning bids in equilibrium . . . 33

4 Total payoffs each player receives in equilibrium . . . 34

5 Critical discount factor in various settings . . . 41

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1 Introduction

Early in November 2001, Dutch public broadcasting corporation VARA revealed the existence of illegal collu-sive behavior, bid rigging, double-entry bookkeeping and other corrupt practices among Dutch construction companies and civil servants in an episode of its documentary series Zembla. Among others, secret financial accounts, a so-called shadow bookkeeping, from major construction company Koop Tjuchem was disclosed in the documentary. This shadow bookkeeping consisted of over 250 A3 pages covering approximately 3500 rigged bids (Dorée, 2004; Van Bergeijk, 2007). This concurrence of events led to political and social con-troversy, resulting in extensive investigations by the Cabinet, the Department of Justice and the Dutch Competition Authority (NMa). It was the beginning of a long-winding legal affair (Van den Heuvel, 2005).1

In the Netherlands, procurement of infrastructure projects is conducted trough auctions. In these auc-tions, participating companies simultaneously bid a price for which they would be willing to carry out the project of interest. The company submitting the lowest price ultimately carries out the project and receives his bid from the procurement agent (usually the government) (NMa, 2005; Parlementaire Enquête Commissie (PEC), 2003). Such an auction is generally defined as a low price, sealed-bid auction (Boone, Chen, Goeree and Polydoro, 2009; Hubbard and Paarsch, 2009).

It was found that the construction companies colluded by organizing secret meetings prior to the official procurement auction - so-called pre-auction or knock-out meetings - in which the official low price, sealed-bid auction was replicated. The company winning the pre-auction was the designated winner of the official auction (Boone et al., 2009; NMa, 2005; PEC, 2003; Pheiffer and Langendijk, 2003). Subsequently, in the official auction, each company rigged their bid such that the pre-auction winner obtained the right to carry out the project at a price close to the maximum budget of the procurement agent. Thereafter, the difference between the price paid by the procurement agent (the marked up/rigged bid) and the lowest pre-auction bid, labeled as the calculation fee by the cartel, was divided among its members (Boone et al., 2009; NMa, 2005; PEC, 2003; Pheiffer and Langendijk, 2003). Hence, due to these collusive practices, procurement agencies did not benefit from the competition that existed between construction companies.

Cartels using private knockouts to prevent competition in the target auction have a long history, partic-ularly in markets for collectibles, such as rare books, art, rugs, stamps, coins, and antiques (Asker, 2010). Asker (2010) examines bidding in over 1,700 knockout auctions used by a cartel of stamp dealers in the 1990s. Other observed variations in ring implementation belonging to this class are recorded by Charles Smith (1989), Ralph Cassady (1967) and Robert Wraight (1974) in markets for farm land, collectible guns, rugs, antiques and paintings respectively, with the earliest recorded example of such a ring being in 1830, in a sale for books (Freeman and Freeman, 1990). Moreover, such practice in auctions for fish, timber,

1_{The Lower House of the Dutch Parliament decided to conduct a parliamentary inquiry (Parlementaire Enquête}

Com-missie (PEC), 2003). After conduction of these preliminary investigations, public hearings were held 2002. These hearings and the Final Report confirmed that the entire sector was involved in the illegal practices and that authorities helped to per-petuate the system (Van den Heuvel, 2005). The first round of dealing involved six major cases of anticompetitive behavior in the civil engineering and infrastructure sector. Public authorities instituted almost 300 arbitration procedures against nu-merous construction companies for damages incurred as a result of alleged bid-rigging (Hettema and Van Thermaat, 2004). In 2004, Dutch media revealed the existence of yet another shadow bookkeeping, which led to a flood of 486 leniency ap-plicants (Van Bergeijk, 2007). In 2010, the NMa imposed personal fines varying between 10,000 and 250,000 euros on three executives of two construction companies for their involvement in the cartel (Dolmans and Snelders, 2011).

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industrial machinery, and wool has been described by Cooper (1977), Graham and Mar- shall (1987), and Arthur Halpern (1985).

There also exists theoretical literature on bidding rings with features that are relevant for the Dutch construction cartel. In their analysis of a bidding cartel with a somewhat comparable knockout mechanism, Graham, Marshall and Richard (1990) find that cartel members have an incentive to bid higher in the knockout than their actual valuation. This is because side transfers players receives are an increasing function of in their knockout bids, however, which was not an feature of the mechanism applied by the Dutch construction cartel. McAfee and McMillan (1992) find that the system of knockouts only creates efficiency, in the sense that the player with the highest valuation for the auctioned product wins it, in case the cartel makes use of side transfers. Within the heterogeneous independent private values model, Marshall and Marx (2006) analyze bidder collusion at first-price and second-price auctions, allowing for within-cartel transfers. They conclude that cartels unable to control the bids of their members cannot eliminate all ring competition at second-price auctions, but not at first-price auctions. In case the cartel can control its, members’ bids, competition is also suppressed in first-price auctions. Aoyagi (2003) examines a bidding cartel in which members interact over an unlimited number of rounds. In his paper, a bid rotation scheme which coordinates bids such that that a players’ chance of winning increases as the number of rounds he has not won increase is proven to be an equilibrium.

The affair of widespread collusion between construction companies is presumably one of the most im-portant cases in the history of Dutch competition policy. Nevertheless, there exist relatively little academic literature on this subject, especially from a game-theoretical point of view. Before the illegal collusive behav-ior in the Dutch construction sector became publicly acknowledged, Bremer and Kok assessed the industry’s attempts to reform tendering arrangements on a more competitive basis back in 2001. A broadly-based post mortem of methodologies that were applied earlier to detect malfunctioning markets in the Netherlands, but failed to identify the construction sector as problematic, is presented by Van Bergeijk (2007). He concludes that these studies were seriously flawed. Furthermore, Dorée (2004) uses industrial organization theory to discuss the characteristics of the Dutch construction market that facilitate collusion. Priemus (2004) claims that the illegal practices in the Dutch construction market were precipitated by the structure of the build-ing industry, inadequate governance policies and enforcement. Moreover, Van den Heuvel (2005) tries to illustrate the relationship between collusion and corruption among civil servants in the Dutch construction cartel case. Rensman and Toet (2003) point out that the difference between the final price paid by the client and the winning pre-auction bid, as documented in the shadow bookkeeping, does not serve as an accurate estimate of the damages incurred by the client due to the collusive agreements made by the cartel. Namely, they state, firms had different incentives in the pre-auction than they would have in case of full competition. This study compares bidding behavior in the low price, sealed-bid pre-auction/knockout of a bidding ring organized in a manner comparable to the Dutch construction cartel with that of a fully competitive scenario. For this purpose, a model is considered where n players interact over m rounds. At least at the start of the game, players are presumed to be symmetric in their cost prices. All players are perfectly informed

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about each other’s cost prices and the maximum price set by the procurement agent - which is endorsed by the findings of the NMa (2005) and PEC (2003). These sources also claim that firms were constraint in their capacity once they already carry out a project, causing their cost price regarding additional projects to increase. To account for this phenomenon, it is studied how two variants of changes in players’ cost prices after winning influence competitive conduct. These variants include: 1) one where a player experiences an increase in his cost price for the rest of the game after his first win and 2) one where a player’s cost price increases for only one round after winning.

Two variations of the model are examined: a collusive setting and a competitive scenario. In the col-lusive setting, ring members’ bidding behavior in the pre-auctions is considered. In these pre-auctions, the designated winner of the official auction is determined. The cartel rigs its members’ bids such that the designated winner always obtains the project at the maximum price set by the procurement agent. In line with the findings of the NMa (2003) and PEC (2005), all players including the winner receive an equal share of the difference between the price paid by the procurement agent and the winning pre-auction bid. Since the winner initially receives the full payment, side transfers from the winner to all losing players arise. The NMa (2005) and PEC (2003) declare that payable side transfers were in practice not settled to the full, which is confirmed by whistle-blower A. Bos in a personal interview (May 10, 2018).2 Therefore, is assumed that side transfers are paid out at a discount rate β, where 0 < β < 1. Since the NMa (2005) and PEC (2003) point out that there existed rotation among the members regarding the winner of various pre-auctions, the focus lies, in the collusive setting, on equilibria where there is a rotating winner scheme.3 _{In in contrast to}

the analyses conducted by Aoyagi (2003), bidder rotation is not stimulated by a bid coordination center. As for the competitive scenario, the is assumed to be no cartel and players bid competitively in the target auction.

It is found that the pre-auction bids submitted in the collusive equilibrium are lower, implying more aggressive bidding behavior, than in the competitive setting. This is, however, only because arising side transfers are not fully paid out (0 < β < 1). In case the side transfers are not discounted (β = 1), pre-auction bids match the bids submitted in case of full competition in equilibrium. As mentioned above, however, the NMa (2005), PEC (2003) and A. Bos (personal communication, May 10, 2018) point out that side transfers were indeed not paid out out the full (0 < β < 1). This indicates that the winning pre-auction bids are not an accurate benchmark for what bids would have been submitted in a counter-factual competitive scenario. Furthermore, the condition imposed that the cost price of a player increases for the rest of the game after his first win causes competition to be less intense in terms of bidding, only in case the number of players is lesser or equal to the number of rounds. In case players’ experience an increase in their cost price for one round after winning, bidding behavior is only less aggressive if there are exactly two payers.

The thesis proceeds as follows. In the next section, some relevant aspects of the mechanism applied by the

2_{Ad Bos is a former employee of the Dutch construction company Koop Tjuchem and is familiar with the inner workings}

of the cartel from close quarters. Moreover, he revealed the existence of a shadow bookkeeping of his former employer and made part of these bookkeeping publicly available. A report of the interview (in Dutch) is provided in the Appendix.

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Dutch construction cartel are discussed in detail. Subsequently, the model is examined in section 3, as well as the equilibrium outcomes in the collusive setting. In section 4, equilibrium outcomes in the counter-factual competitive scenario are discussed. The results for the collusive and competitive scenarios are compared in section 5. Section 6 provides an analyses on the incentive compatibility of the cartel. Concluding remarks finalize the thesis in section 7.

2 Cartel Mechanism

Prior to every official procurement auction, denoted as the target auction from now onwards, the cartel used a secret pre-auction/knockout to coordinate their bidding behavior in the target auction. Replicating the format of the target auction, the knockout was conducted using a low price, sealed-bid auction where the lowest bidder wins. Subsequently, once the pre-auction winner was determined, the cartel decided on what the level of each member’s bid should be in the target auction. All target auction bids were rigged in a manner that ensures the pre-auction winner would win the project against a price close to the maximum budget the procurement agent. That is, the cartel made sure that the lowest bid submitted in the target auction approximated the reserve price (A. Bos, May 10, 2018; NMa, 2005; PEC, 2003; Pheiffer and Langendijk, 2003).

The difference between winning target auction price and the lowest knockout bid, the calculation fee, was shared among the members through the use of side transfers (PEC, 2003; NMa, 2005). McAfee and McMillan (1992) conclude that the use of side transfers in a bidding cartel ensures efficiency in the sense that the member valuing the product for auction the most actually wins it. This ensures that the cartel earns total profits equal to the difference between the highest valuation and the reserve price. A cartel that is not able to divide some of the profits made trough side transfers can do no better than having its members who value the product more than the reserve price submit identical bids (McAfee and McMillan, 1992).

In the remainder of this section, some relevant aspects of the mechanism by which the Dutch construction companies organized their cartel are discussed in detail. Thereafter, an fictional example covering the determination of side transfers and documentation of inter-company payments is provided for illustrative purposes.

2.1 Ascertaining the reserve price

It is claimed by the PEC (2003), Bos (May 10, 2018) and Pheiffer and Langendijk (2003), that the cartel members were usually to a large extent aware of the clients’ maximum budget/reserve price regarding a certain project. In some cases, the reserve price was publicly announced. Alternatively, especially in cases where the Dutch government or local municipals requested a tender, arrangements were made with corrupt civil servants who then provided an indication of the maximum budget available.4 _{Furthermore, the reserve}

4_{Companies invested, on an individual basis, in their relationship with civil servants. Usually, there were one or two}

members who were able to gather information regarding a certain project. This then gave these members a favorable negoti-ating position over the other members while determining the side payments. Each large construction company had its "own" pool of civil servants (A. Bos, May 10, 2018; PEC, 2003).

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price could be estimated on the bases of prices charged in the past regarding comparable projects.

2.2 Individual determination of pre-auction bids

2.2.a Cost price

The expected cost price of the project was the starting point for the pre-auction bids. Construction com-panies, especially the ones eager to win, spent substantial time and effort to calculate their expected cost price for the project. It was declared by several construction companies that these costs served as one of the main reasons why the cartel existed. Namely, construction companies considered the compensation received from procurement agencies for incurring these calculation costs were to low. As a response, these companies arranged pre-auction meetings in which information about cost estimations was shared and a rigged price at which the project was awarded was ensured. For this reason, the cartel labeled the difference between the winning pre-auction bid and the price actually paid by the procurement agent the calculation fee (A. Bos, May 10, 2018; NMa, 2005; PEC, 2003).

2.2.b The expected cost prices of other players

The cost price regarding a certain project differed between firms. Cost determinants that could vary across firms, thereby causing inter-company cost price differences, include, among others, available capacity and degree to which the project of interest matches a company’s field of specialization. To a large extent, companies present at the pre-auction meeting were aware of other firms’ costs (A. Bos, May 10, 2018; NMa, 2005; PEC, 2003). Thus, although firms were not perfectly informed about others, cost prices were not completely private either. It is evident that each company tried to win at the highest possible bid. Thus, in line with existing literature regarding comparable bidding rings (Grahamet al., 1990; McAfee and McMillan, 1992), a company has the incentive to submit a bid just below what it expects to be the lowest lowest cost price among all other firms, conditional on its own cost price being the lowest.

2.2.c Receivable side transfers

Graham et al. (1990) conclude that ring members have the incentive to bid above their value in the knockout auction. This is due to the feature of the mechanism applied in their model that the side transfer a member receives positively depends on his pre-auction bid. In the case of the Dutch construction cartel, since it concerns low price auctions, this implies that players would have the incentive to bid below their cost price. Although side transfers did not depend on players’ cost price in case of the Dutch construction cartel, members did bid below their own cost price in some cases. It is pointed out by the NMa (2005) and PEC (2003), as well as Pheiffer and Langendijk (2003), that firms lowered their pre-auction bids with part of side transfers generated in previous knockouts still receivable from other companies - an practice referred to as blanking by the cartel. Moreover, it is indicated that companies lowered their bids with the expected level of the side transfer arising in the pre-auction of interest. This was to anticipate on the fact that payable side transfers were usually not settled to the full, an phenomenon which aggravated as amounts payable of

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different firms diverged. It rationale firms lowered their pre-auction bids to anticipate on the notion that side transfers are not paid out to the full. Namely, winning becomes relatively more attractive in case arising side transfers from the winner to all losing players are not fully settled in practice.

In some instances, this led to pre-auction bids below players’ cost prices. The notion is that it was important to avoid having a reputation of being expensive and inefficient. Namely, tis could imply that a firm would not be invited to submit a tender by procurement agents in the future (NMa, 2005; PEC, 2003). This provides the incentive to bid below cost price occasionally, since doing so ensures a company avoids experiencing long periods without carrying out a project.

The use of receivable side transfers to lower a firm’s pre-auction bid is declared to be "the core of the system" by the NMa (2005). A. Bos (May 10, 2018), however, states that this practice was carried out occasionally. According to A. Bos, only in knockouts regarding big projects yielding a high value, receivable side transfers were used to lower a parties’ pre-auction bid and higher the chance of winning the right to carry out the project.5

2.3 Determination of the calculation fee and target auction bids

2.3.a Calculation fee

At the start of the pre-auction, members jointly determined the level of the calculation fee. The calculation was the amount that was added to the winning pre-auction bid to form the lowest bid the cartel would ultimately submit in the target auction. This should be seen as a concept version, since it was usually refined once the winning pre-auction bid was known, to make sure the lowest target auction bid approximated the client’s maximum willingness to pay. In this process, information regarding the (estimated) maximum budget of the procurement agent, project-specific risks and cost projections were shared. Moreover, some indication of each firm’s preliminary pre-auction bid was provided in this stage (NMa, 2005; PEC, 2003).

2.3.b Designated winner

Subsequently, firms had the opportunity to revise the preliminary version of their pre-auction bids determined beforehand. Thereafter, pre-auction bids were submitted. All bids were revealed to the participants and compared. The participant submitting the lowest bid was the designated winner of the target auction, which would ultimately carry out the project of interest. The winning participant had the opportunity to withdraw his bid, in case of wrongly estimated costs (PEC, 2003; Boone et al., 2009). It could occur that the winning participant, after observing that his bid was significantly lower that all other bids, realized he underestimated the cost price of the project.6 This phenomenon is commonly acknowledged in auction literature, where it is referred to as the winner’s curse and was claimed by several construction firms to be one of the reasons to organize the pre-auction meetings (Boone et al., 2009).

5_{By carrying out a large project, a long stream of cash flows is secured. Moreover, large projects yielded higher profit}

margins (A. Bos, May 10, 2018). As a result, firms were usually more eager to win in knockouts regarding these projects.

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2.3.c Target auction bids

After determining which firm would be the designated winner of the target auction, it was decided which bid each participant should submit in that target auction. These target auction bids were set such that the pre-auction winner submitted the lowest bid in the target auction. This bid equaled the winning pre-auction bid, plus the calculation fee. The calculation fee was usually revised somewhat as the level of the winning pre-auction bid became clear. That is, the cartel aimed for the lowest target auction bid to approximate the maximum budget/reserve price of the procurement agent. Generally, the winning bid in the target auction was determined by the cartel to be approximately 10 percent lower than the procurement agent’s reserve price. The definitive calculation fee was defined as the difference between this bid and the lowest pre-auction bid (A. Bos, May 10, 2018; NMa, 2005; PEC, 2003). This calculation fee was usually added to other players’ pre-auction bids to determine their designated target auction bid. Sometimes, this resulted in excessively high target auction bids, causing the firms submitting these bids to obtain a reputation of being expensive and inefficient, which implies not being invited to future target auctions by procurement agents. A firm’s target auction bid was often adjusted downwards in these cases to avoid this.

2.4 Dividing the calculation fee

Contrary to the ring mechanism analyzed by McAfee and McMillan (1992), the calculation fee was not equally shared among all members present at the pre-auction of interest. The cartels studied by Graham et al. (1990) and Asker (2010) let the side transfers each player receives depend on their knockout bids. The division of cartel profits occurred in a more arbitrary way in case of the Dutch construction cartel. In every pre-auction, participants negotiated on what share of the calculation fee each member would receive (A. Bos, May 10, 2018). As mentioned earlier, members providing information regarding the client’s maximum budget in a certain pre-auction were able to extract a relatively larger share of the corresponding calculation fee. Moreover, a companies’ bargaining power was usually increasing in its size. Thus, pre-auction winner ultimately received its pre-auction bid, his share of the calculation fee. All losing players received their share of the calculation fee as a side transfer (A. Bos, May 10, 2018; PEC, 2003; Pheiffer and Langendijk, 2003).

2.5 Punishment in case of defection

In contrast to what is assumed in most common literature regarding cartel workings and stability (Belle-flamme and Peitz, 2015; Motta, 2004; Norman, Pepall and Richards, 2014), the Dutch construction cartel did not collapse in case a firm defected from the agreement. Bos (May 10, 2018) claims the use of fines was embedded in the cartel mechanism, rather than a scenario where the entire cartel collapses and all firms start bidding competitively in the target auction forever after one member defected from his prescribed target auction bid. The level of these fines were usually not determined in advance. The defecting firm was generally confronted with its action by the designated winner in the target auction of defection, which was

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essentially the victim of the defection, in or in advance of, the first pre-auction the two firms met again.7

Without real negotiations, the victimized firm then revealed the level of the fine demanded from the defector. Despite the uncertainty about the absolute level of these fines, firms could quite accurately estimate a range for which levels the fine would take (A. Bos, May 10, 2018). The system of fines ensured the willingness of victimized firms to keep participating in pre-auctions and contributed to the stability of the cartel (A. Bos, May 10, 2018). This more mild way of punishment to ensure the continuity of the cartel, even after the occurrence of defection is also observed by David Genesove and Wallace Mullin (2001), who use notes on cartel meetings to examine the internal operation of the US sugar cartel, which operated until 1936. Significantly, they find that defection did occur but was met with only limited punishment.

2.6 Documentation and shadow bookkeepings

The (pre-auction) winner initially obtains the full rigged price form the procurement agent. As a result, amounts payable, consisting of the side transfers determined earlier, from the pre-auction winner to each other cartel member arise. These side transfers were not paid out instantly. That is, each member of the cartel documented the amounts payable to, and receivable from, each other firm in a shadow bookkeeping. Approximately once a year, the net amounts payable/receivable between all firms were settled (A. Bos, May 10, 2018; PEC, 2003; Pheiffer and Langendijk, 2003).

2.7 An Illustration

To illustrate the workings of the cartel, consider the following example, where firm/player A, B and C successfully rig four project auctions within a year. In line with the claims made by the NMa (2005), the PEC, 2003 and Pheiffer and Langendijk (2003), the calculation fee is assumed to be shared equally among all members.

Project 1 Firm A, B and C are invited to participate in a procurement auction regarding a infrastruc-ture project. In advance, the three firms organize a pre-auction meeting in which the designated winner and the bid each firm submits in the target auction, will be determined. The maximum willingness to pay of the auctioneer is known to equal 1,150.8 In the pre-auction, the lowest and therefore winning bid is submitted by firm A: 800. Subsequently, the firms agree to submit the following bids in the target auction: firm A bids 1,100, firm B bids 1,250 and C bids 1,300. The target auction was successfully rigged. Pre-auction winner A obtained the project at a price just below the budget price of the auctioneer.9 _{The arising calculation fee}

of 300, the difference between the winning target auction bid and winning pre-auction bid, is shared equally among the three participating firms. Since firm A initially receives the full 1,100 form the auctioneer, this

7_{The composition of participating firms differed across pre-auctions. It could occur that the defector and the firm}

vic-timized by his defection met again after several knockouts had already passed. The cartel did not necessarily exclude certain firms from participation as in the analyses on endogenous cartel formation conducted by Bos and Harrington (2010). Partici-pants were rather determined by which firms received an invitation to take part the procurement auction.

8_{All numbers in this subsection are fictional and in thousands of guilder.}

9_{As mentioned earlier, the cartel coordinated firms’ bids such that the winner obtained the project at a price just below}

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firm owes a side transfers of 100 both firm B and C. The process of determining side transfers is summarized in Table 1. In the "Participants" column, the pre-auction winner (which is the target auction winner as well) regarding each project is underlined.

As mentioned earlier, arising side transfers were documented, rather then paid out instantly. The resulting impact on debtor an creditor accounts after each project are depicted in Table 2. The (net) amounts payable/receivable from one firm to the other firms is depicted in the corresponding column.10 After the first project, firm A owes a side payment of 100 to firms B and C.

Table 1: Side Transfers (Example) Project Participants Price

Target Auction

Winning Bid Pre-auction

Calculation Fee Side Transfer

1 A, B and C 1100 800 1100-800=300 300₃ = 100

2 A, B and C 800 620 800-620=180 180₃ = 60

3 A, B and C 900 660 900-660=240 240₃ = 80

4 A and C 700 600 700-600=100 100₂ = 50

Project 2 A second procurement auction is upcoming. Firm A, B and C are again all invited to submit a bid. Firms are aware of the fact that the reserve price of the auctioneer equals 850 and arrange a pre-auction, in which player C wins with a bid of 620. In the target auction, bids are rigged to ensure that player C wins at a price of 800. The resulting side transfer payable from firm C to firms A and B amounts to 60. As a consequence, the net payable amount from firm A to C now equals 100 − 60 = 40. As follows from Table 2, the total account receivable for firm B, which has not yet carried out a project, amounts to 160 (100 from firm A and 60 from firm B).

Project 3 Regarding the third target auction, again all three firms are invited to participate in the procurement auction. The client’s budget equals 930, which the firms are able to infer from the price at which comparable projects were carried out in recent years. Since firm B has not yet carried out a project, it is eager to win this pre-auction and does so at a bid amounting to 660. The firms agree to rig the bids that will be submitted in the target auction such that firm B wins at a price of 900, yielding side transfers of 80 from firm B to firms A and C. Each firm now has won a pre-auction once. Amounts payable and receivable are smaller, compared to the situation after the first project. The liability of firm A to firm B now only amounts to 100 − 80 = 20. On its turn, firm B owes firm C an net amount of 80 − 60 = 20 as well.

Project 4 For the fourth procurement auction, only firm A and C are invited. The firms know that the maximum price the agent is willing to pay equals 750. A and C arrange a pre-auction, in which firm C submits the winning bid, which amounts to 600. The firms decide to set their target auction bids such that

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firm C wins the right to carry out the project at a price of 700. Since only firm A and C participate in this (pre-)auction, the calculation fee of 100 is shared among these two firms. The arising side transfer equals 50, payable from firm C to firm A.

Over the four projects, amounts the amounts payable and receivable declined gradually, due to the rotating pre-auction winner. Most of the payment liabilities arisen in different project cancel each other out. As a result, limited amounts of cash have to be paid out at the end of the year. After the fourth project, the net liability of firm A to firm C equals 50 − 40 = 10. The net amount payable from A to B still still equals 20, just as the amount firm B owes firm C. After the fourth project, all these debtors and creditors are settled and paid out in cash.

Table 2: Balances after Project 1-4 (Example)

(a) Project 1 A B C A 100 100 B -100 C -100 Total -200 100 100 (b) Project 2 A B C A 100 40 B -100 -60 C -40 60 Total -140 160 -20 (c) Project 3 A B C A 20 40 B -20 20 C -40 -20 Total -60 0 60 (d) Project 4 A B C A 20 -10 B -20 20 C 10 -20 Total -10 0 10

3 The model and collusive setting

In this section, a game-theoretical approach is deployed to describe the behavior of a bidding cartel using a mechanism which is analogous to that of the Dutch construction cartel, as described elaborately in the previous sections. In short, the construction cartel used secret knockout auctions prior to the official/target auction to to assign a designated winner in the target auction, coordinate their bidding behavior and elim-inate competition in the target auction. Cartel profits were divided among the cartel members trough side transfers. As declared by the NMa (2005) and PEC (2003), there some rotation among the cartel members regarding the winner of different pre-auctions. Therefore, I will particularly search for an equilibrium where each consecutive pre-auction round (and, as a result, each target auction round) has a different winner.

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The model is designed as follows. A total number of n players form a (complete) cartel and participate in both a pre-auction and a target auction each round. Players interact over m rounds in total. Both m and n are assumed to be larger or equal to two. The pre-auction takes place prior to the target auction. Both the pre-auction and the target auction are low price, sealed-bid auctions. That is, participants simultaneously submit a bid, without any information on other players’ bids. The participant submitting the lowest bid (b) wins the auction. Note that the target auction is the official one, where it is determined which player carries out the project against what price - which is paid by the auctioneer/procurement agent. Under the cartel agreement, the winner of the pre-auction is the designated winner of the target auction. Hereby, the bids submitted by the cartel members in the target auction are rigged such that this pre-auction winner obtains the project in the target auction at the highest price the auctioneer accepts, the reserve price, denoted as p. Since, in the Dutch construction market, it was important to participate in target auctions on a regular basis to ensure being invited for future tenders, cartel members losing in the pre-auction still take part in the target auctions, despite being designated to lose. Thus, the pre-auction winner bids p in the target auction, while the other player(s) submit some bid > p in the target auction. Note that, under the cartel agreement, players compete in the pre-auction, but make sure there is no competition in the target auction. As a consequence, the auctioneer never benefits from the existing competition among the players.

Each player, including the pre-auction winner, receives an equal share of what the Dutch construction cartel labeled the calculation fee: the difference between the winning pre-auction bid and the price at which the target auction was won. For the rest of this section, it will be assumed that the latter equals the reserve price of the procurement agent.11 _{In line with the claims made by the NMa (2005), PEC and Pheiffer and}

Langendijk, )2003), the calculation fee is assumed to be divided equally among all players. Since the pre-auction winner initially obtains all the cartel profits, side payments from the pre-pre-auction winner to the other players arise. That is, if player z wins the pre-auction in round k (where k = 1, 2, . . . , m) at bid bzk = bk,

he transfers side payment p−bk

n to all n − 1 other players. In this manner, the cartel divides the payoffs

generated among all members.

Note that the arising side transfers were, in the case of the Dutch construction cartel, not immediately paid out in cash. In contrast, the side transfers parties owed to each other were documented in a shadow bookkeeping. Subsequently, the arising debtors and creditors were redeemed once a year. Usually, parties were not able to collect the full amount receivable from other cartel members (A. Bos, May 10, 2018; PEC, 2003; Pheiffer and Langendijk, 2003). Therefore, it is presumed that side transfers are paid out against discount rate 0 < β < 1 (of which players are aware at the start of the game). The discounted side transfer will be referred to as the side payment for now on.

Each player i, where i = 1, . . . , n, choses two bids strategically in every round k (where k = 1, . . . , m): its pre-auction bid and its target auction bid. Note that, in case player i complies with the cartel agreement, its target auction bid is determined by the outcome of the corresponding pre-auction. Namely, if he wins

11_{In reality, the cartel coordinated their bids such that the winning target auction bid did not exactly equal the reserve}

price of the procurement agent to avoid suspicion. This aspect, however, does not have any noteworthy game-theoretical im-plications and will therefore be ignored for simplicity reasons.

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(loses) the pre-auction in round k, his target auction-bid equals p (>p) in round k. Throughout this section, it is assumed that the cartel agreement is incentive compatible and, therefore, no player will deviate in the target auction from the bid he gets assigned on the basis of the pre-auction outcome. Presuming this, player i sets one bid in every round k in the collusive setting: bikC.

This section examines whether an equilibrium exists where every player submits the same pre-auction bid in each round and there is a rotating winner scheme.12 The condition that each player submits the same bid implies that, for every round k, ¯bk = bkiC = bkjC, where i 6= j and i, j = 1, . . . , n. Without loss of

generality, a rotating winner scheme is defined as follows. In each consecutive round, a different player wins and as many players as possible win alternately. That is:

• If n=m:

Every round k has a different winner and each player i wins once, where k = 1, . . . m and i = 1, . . . n. • If n<m:

Player i winning in round k wins again in round k + n if m_{> k +n and does not win again if m < k +n,} where k = 1, . . . m and i = 1, . . . n. Note that in this case, players can win several times, depending on the proportion of m to n. Since n < m, at least one player wins more than once.

• If n>m:

Every round k has a different winner, where k = 1, . . . m. As a result, m players win once and n − m players do not win.

An example of a rotating winner scheme is the following: player 1 wins in round 1, player 2 wins in round 2, . . ., player n wins in round n. In case m > n, player 1 wins again in round n + 1, player 2 wins for the second time in round n + 2 (if applicable), et cetera.

Throughout, player i incurs costs cik by carrying out the project for auction in round k. Each project is

presumed to be equally costly for every player: cik= 1 for all i = 1, . . . , n in every k = 1, . . . , m, unless stated

otherwise. All players are assumed to be perfectly informed and are therefore aware of the level of p, β and other players’ cost prices, including the conditions imposed on these cost prices.13 Furthermore, the reserve price of a project is set equal to p for all rounds, where p > 1. Thus, player i winning and thus carrying out the project for auction in round k at price p, incurring costs cik, earns payoff p − cik, of which βp−b_n−1k

is paid out to each of the n − 1 other players as a side transfer. The payoff player i receives from winning (losing) the pre-auction in round k is depicted as πikw (πikl).14 However, while deciding on their pre-auction

bids in round k, players take into account the impact of their decision on future payoffs. The payoff player i obtains from winning (losing) in round k, including the cumulated payoffs that will be obtained in future rounds (these might depend on the outcome of, and therefore the bid of player i in, round k) is depicted as

12_{"Every player submits the same pre-auction bid" implies that the winning player bids a negligible amount higher than}

the other players.

13_{According to Bos (May 10, 2018), the NMa (2005) and the PEC (2003), construction companies were to a great extent}

aware of the production costs and available capacity of other firms, as well as the procurement agent’s reserve price p.

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Πikw (Πikl), where Πikw= πikw+P_v=k+1m πiv andPm_v=k+1πiv might depend on the outcome of round k.15

Cumulated profits obtained by player i in equilibrium are defined as ΠiC for all i = 1 . . . , n.

In the upcoming subsections, bids and payoffs will be examined for which the equilibrium discussed earlier can emerge under the following conditions regarding players’ costs:

1) Cost price does not change after winning

The cost price regarding the project for auction in each round k equals cik= 1 for every player i, where

i = 1, . . . , n and k = 1, . . . , m.

2) Cost price increases to α for the rest of the game after winning, where p > α > 1

At the start of the game, the cost price regarding the project for auction in each round k equals cik= 1

for every player i, where k = 1, . . . , m and i = 1, . . . , n. However, if a player wins a certain project, his cost price increases to α for the rest of the game, where p > α > 1. Thus, cik= 1 if a player did not

win in any of the rounds 1, . . . , k − 1 and cik= α otherwise.

3) Cost price increases to α for one round after winning, where p > α > 1

At the start of the game, the cost price regarding the project for auction in each round k equals cik= 1

for every player i, where k = 1, . . . , m and i = 1, . . . , n. However, if a player wins a certain project, his cost price increases to α, where p > α > 1, for the next round. Thereafter, his costs "recover" and equal 1 again in all subsequent rounds (conditional on not winning again). Thus, cik = α if player i

won in round k − 1 and cik= 1 otherwise.

Once a construction company obtains the right to carry out a (large) project, it experiences some capacity constraint. It might occur that such a company does not have enough capital or staff available to internally carry out a second project. It then has to hire new capital in order to be able to do so or outsource part of it (NMa, 2005 and PEC, 2003). To account for this phenomenon and analyze how this changes players’ bidding behavior, two variations of the condition that a player’s cost price starts to exceed 1, once it has won a previous auction and is therefore already carrying out a project, are imposed, each examined in a different subsection. Note that in this manner, the impact available capacity had on the determination firms’ pre-auction bids is integrated in this model trough the effect of capacity constraints on cost prices. Throughout, players with cost price 1 can be referred to as the low cost players, whereas players with cost price α can be referred to as the high cost players.

LEMMA 1:Consider the following variations of conditions imposed on players’ cost prices: 1. Cost price does not change after winning.

2. Cost price increases to α for the rest of the game after winning, where p > α > 1. 3. Cost price increases to α for one round after winning, where p > α > 1.

15_{Note that, since m is the last round, Π}

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For each of these cases, it holds that, if there are at least two players with cost price 1 in round m, there are as well in each round 1, . . . , m − 1

PROOF:

See the Appendix.

3.1 Cost price does not change after winning

Start with considering a situation where the project in every round k = 1, . . . , m yields cost price cik = 1

for every player i = 1, . . . , n, regardless of previous rounds’ outcomes.

PROPOSITION 1: In case the cost price regarding the project for auction in every round k equals cik= 1

for each player i, where i = 1, . . . , n and k = 1, . . . , m, the following is an equilibrium: - bikC = bjkC = bk= p − p−1_β , where i 6= j, k = 1, . . . , m and i, j = 1, . . . , n.

- There is a rotating winner scheme. - ΠiC= m_n(p − 1) for all i = 1, . . . , n.

PROOF:

See the Appendix.

Proposition 1 states that the bids submitted and payoffs received are equal across all rounds and players and there is a rotating winner scheme. This is an equilibrium, since all players are completely symmetric in each individual round and there is perfect information. This causes the outcome of every round to have no influence on players’ competitive position in any future rounds: there exists perfect symmetry across players anyway. As a result, players continuously maximize their round-specific payoffs. In an equilibrium where all players submit equivalent bids in each round, therefore, it should hold that all players receive the same bid in every round. Essentially, competitive conduct in the pre-auction is as severe as it can get and no player is able to extract a higher profit than any other player. It holds for every round that the winner and all losing players receive equivalent payoffs and each player is therefore indifferent between winning and losing. As a consequence, each player is indifferent between all possible winner schemes and an equilibrium in which the winner rotates exists.

Whereas competitive conduct in the pre-auction is severe, all competition in the target auction is elimi-nated by the collusive agreement. In each of the m rounds, the winner receives the maximum price p from the procurement agent and incurs costs of 1 by carrying out the project, resulting in profits amounting to p − 1. Subsequently, a Proposition 1 states, the cartel shares these profits equally among all n members. This is intuitive, since all players are symmetric and should therefore receive equivalent payoffs in an equilibrium where each player submits the same (pre-auction) bid in all rounds.

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k (where k = 1, . . . , m) decreases as p increases: δbk

δp = 1 − 1

β < 0 for all β < 1 and k = 1, . . . , m. This is intuitive, since:

δπikw δp = 1 − n − 1 n β and δπikl δp = 1 nβ for all i = 1, . . . , n and k = 1, . . . , m, where

δπikw

δp > δπikl

δp for all 0 < β < 1.

That is, since the arising side transfers are not paid out to the full, payoffs from winning are more increasing in p than the payoff from losing. Thus, as p increases, winning becomes relatively more attractive compared to losing. Players are aware of this and, as a result, bid more aggressively as p gets higher. Put differently, the (winning) bid for which the winner and all losing players receive equivalent payoffs, which should be satisfied for the bidding strategies defined under Proposition 1 to be an equilibrium, is a decreasing function of p.

The assumption that side transfers are not paid out to the full (β < 1), however, is endorsed by the NMa (2005), the PEC (2003) and A. Bos in a personal interview on May 10, 2018. Note that players bid below their cost prices in equilibrium, since 0 < β < 1 < p. In this case, the notion that side transfers will not be paid out to the full increases the relative attractiveness of winning. Moreover, it can be inferred that the equilibrium bids, given some value of p above 1, are increasing in β and approach players’ cost prices as β gets close to 1:

δbk

δβ = p − 1

β2 > 0 for all 0 < β < 1 < p, where k = 1, . . . , m.

It is easily observed that the payoff function of the winning (losing) player(s) is strictly decreasing (increasing) in β: δπikw

δp < 0 and δπikl

δβ > 0 for all 0 < β < 1, i = 1, . . . , n and k = 1, . . . , m. That is, the lower β gets, the

smaller the proportion of the arising side transfers that are actually paid out from the winner to all losing players. As a result, winning becomes relatively more attractive compared to losing as β increases. Players therefore have the incentive to bid more aggressively as β increases. This is in line with the NMa (2005), the PEC (2003), which state that firms lowered their pre-auction bids with part of the side transfers still receivable from other players (blanking), to anticipate on the fact that these are not fully settled in practice - a phenomenon that aggravated as dis-balances in payable amounts across players increased.

If β = 1, bids submitted in the equilibrium defined in Proposition 1 equal players’ cost prices. In this case, side transfers are paid out the the full. Proposition 1 states that, in each round the winner and losing

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players should receive equivalent payoffs in equilibrium, which translates into the following condition: πikw = p − 1 − β n − 1 n (p − bk) = β 1 n(p − bk) = πikl where i = 1, . . . , n and k = 1, . . . , m. In case β = 1, this simplifies to:

πikw = p − 1 − n − 1 n (p − bk) = 1 n(p − bk) = πikl ↔ p − 1 = p − bk ↔ bk = 1.

Side transfers are paid out to the full if β = 1. Recall from Proposition 1 that, in each round, players have the incentive to undercut each other up to the point where the winning bid is such that the winner and all losing player receive equivalent payoffs. If β = 1 and players are symmetric in their cost prices, this is achieved at a winning bid that equals players’ cost prices.

The setting discussed above serves as a useful starting point to make an inference on players’ bidding behavior in the pre-auction. However, the role of capacity constraints experienced by a company already carrying out a project is not taken into account. This is done in the upcoming two subsections.

3.2 Cost price increases to α for the rest of the game after winning

As mentioned earlier, construction firms usually experience some capacity constraint once they already carry out a project. As a result, these firms need to hire or purchase extra capital to be able to carry out an additional project, or are forced outsource part of it (NMa, 2005; PEC, 2003). This causes the cost price of firms recently having won a procurement auction regarding upcoming projects to increase. In this subsection, a setting is considered where players experience a constraint in their capacity, resulting in a cost price increase to α, where p > α > 1, for the rest of the game after winning for the first time.

LEMMA 2: If the outcome of round u has no impact on any future payoffs, and there is at least one player with cost price 1, all players bidding bu can only be an equilibrium if a player with cost price 1 wins.

PROOF:

Round u has no impact on any future payoffs. As a result, it is optimal for players to maximize their round-specific payoffs in round u. Since α > 1, players with cost price α, the "high cost players", are less eager to win than players incurring costs of 1, the "low cost players", by carrying out the project. Namely, given bu, the payoff players with cost price α receive from winning is lower than that of a player with cost

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cost players. From this, it follows that, in case there is at least one other player with cost price 1, a player incurring costs α by carrying out the project will never win in equilibrium. That is, the minimum bid b∗_c=α for which a high cost player is just indifferent between losing and winning by undercutting b∗_c=αexceeds that of a low cost player (b∗_c=α>b∗_c=1). As a result, a low cost player will always undercut each high cost player and win in equilibrium.

As the competitive conduct of the game in this setting changes in the proportion of m to n, the following cases are considered separately: a) n > m and b) n_{6 m.}

3.2.a The number of players exceeds the number of rounds First, consider the setting where n > m.

PROPOSITION 2.1: In case the cost price of each player i regarding the project for auction equals cik= 1 if

he has not won in any of the previous rounds and equals cik= α otherwise in every round k, where i = 1, 2,

k = 1, . . . , m, and n > m, the following is an equilibrium:

- bikC = bjkC = p −p−1_β , where i 6= j, k = 1, . . . , m and i, j = 1, . . . , n.

- There is a rotating winner scheme. - ΠiC= m_n(p − 1), for all i = 1, . . . , n.

PROOF:

See the Appendix.

Bids and payoffs in the equilibrium examined under Proposition 2.1 are equivalent to that of the equi-librium defined under Proposition 1. In round m, and therefore any other round (Lemma 1), there are at least two players with cost price 1 in this setting. As a result, the condition imposed that a winning player experiences an increase in his cost price does not change competitive conduct compared to the setting where players’ cost prices do not change. Namely, in every round, there are at least two players with cost price 1 each round k (where k = 1, . . . , m) that compete over the project, who should be indifferent between winning and losing for no player to have the incentive to deviate from bidding bk. The players with cost

price α obtain the same payoff as the players with cost price 1. That is, the high cost players benefit from the competitive, downward pressure the low cost players put on the (winning) equilibrium bid bk. As under

Proposition 1, in all m rounds, a player with cost price 1 wins and receives p from the auctioneer. Hence, total cartel profits equal m(p − 1), which is equally shared among the n members.

3.2.b The number of players is lesser or equal to the number of rounds First, consider the setting in which the number of players matches the number of rounds.

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he has not won in any of the previous rounds and equals cik= α otherwise in every round k, where i = 1, 2,

k = 1, . . . , m, and n 6 m, the following is an equilibrium:

- bikC = bjkC = p −p−α_β , where i 6= j, k = 1, . . . , m and i, j = 1, . . . , n.

- A player with cost price 1 wins in round 1, . . . , n and a player with cost price α wins in round n+1, . . . , m. - There is a rotating winner scheme.

- ΠiC= p − 1 + m−n_n (p − α), for all i = 1, . . . , n.

PROOF:

See the Appendix.

Proposition 2.2 states that no player has the incentive to deviate from bidding bk = p − p−α_β in every

round k (where k = 1, . . . , m and there is a rotating winner scheme. Moreover, a player with cost price 1 wins in round 1, . . . , n and a player with cost price α wins in round n + 1, . . . , m. This equilibrium yields each player i a payoff amounting to p − 1 +m−n_n (p − α), where i = 1, . . . , n.

In case n_{6 m, the game can be divided into two sub-games: 1) rounds 1, . . . , n and 2) rounds n+1, . . . , m.} The capacity constraint, resulting in a higher cost price, a player experiences after winning for the first time causes competition to be less intense in rounds 1, . . . , n. That is, in contrast to the setting where n > m, there is one player left with cost price 1 in round n. At the start of the game, players are ware of the competitive advantage the last player with cost price 1 in round n has. Namely, since he is the only player left with cost price 1, this player has the opportunity to win at a bid equal to p −p−α_β (none of the players with cost price α has the incentive to undercut him in this case), yielding a round-payoff which is α − 1 higher than the payoff all other players receive (see the proof in the Appendix). This difference in payoff received is equal to the difference in the cost price of the single-most efficient player and the other players, and could therefore be interpreted as a sort of efficiency premium. As a result, players only have cost price α in case they have already won, winning at a bid lower than p −p−α_β in any of the rounds 1, . . . , n − 1 is not attractive for a player with cost price 1, since this player then misses out on the opportunity to be the only low cost player who extracts the efficiency premium in round n.

Put differently, for the bidding strategies defined under Proposition 2.2 to be an equilibrium, the winning player in all of the rounds 1, . . . , n should receive a α − 1 higher round-specific payoff than all other players. This is due the incentive of the nth_{-round winner to utilize its competitive advantage and win the project}

at a lower pre-auction bid, such that its payoff exceeds that of the losing players. Since the competitive disadvantage these players experience is the result of the fact that they have won in one of the previous rounds and therefore experience an increase in their cost price, they also require a higher payoff - and thus lower winning bid - in the round they win to not be willing to deviate. A player with cost price 1 only receives a α − 1 higher payoff by winning than all losing players in case the winning bid equals:

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↔ p − 1 − βn − 1 n (p − bk) − β 1 n(p − bk) = α − 1 ↔ bk= p − p − α β .

If α equals p, the bids submitted in equilibrium - in rounds 1, . . . , n - equal p as well. That is, if α = p, the efficiency premium equals p − 1, which is the profit margin the winner with cost price 1 initially extracts from the procurement agent. As a result, the condition that the winner in each of the rounds 1, . . . , n obtains a α − 1 higher payoff than all losing players is only satisfied if the winning bid equals p and there are no side payments.

Note that the equilibrium bids in rounds 1, . . . , n provided that 1 < α < p and 0 < β < 1, are increasing in α:

δbk

δα = 1

β > 0 if 0 < β < 1 < α < p, where k = 1, . . . , m.

That is, the gap between the payoff obtained in equilibrium by the last player with cost price 1 in round n and the payoff all other players receive, which equals α − 1, gets larger as α increases. As a result, winning in one of the rounds 1, . . . , n − 1 is relatively less attractive for higher values of α.

In rounds n + 1, . . . , m, all players have cost price α. Analogous to the setting where at least two players have cost price 1 in round m, players maximize their round-specific payoffs and the payoff from winning and losing should be equal in an equilibrium where each player submits the same bid each round. This is satisfied if bk = p − p−α_β , for all k = n + 1, . . . , n. In these rounds, equilibrium bids are an increasing function of α

as well. The explanation for this is different than in round 1, . . . , n, however. In round n + 1, . . . , m, players maximize round-specific payoffs and the round-specific payoffs from winning is a decreasing function of α in these rounds: δπikw δα = −1 < 0 and δπikl δα = 0

for all k = n + 1, . . . , m. As a result, winning becomes relatively less attractive compared to losing as α increases. This gives players the incentive to bid less aggressive for higher values of α. Stated differently, as α increases, the value of bk for which no player has the incentive to deviate from bidding bk increases as well

(where k = n + 1, . . . , m). In case α equals p, the bids submitted in this equilibrium equal p as well. That is, players’ cost prices increase to the level of the maximum budget of the procurement agent. For round 1, . . . , n, this implies that

Overall, no player has the incentive from bidding bkin every round k if bk = p −p−α_β , where k = 1, . . . , m.

In this equilibrium, each player receives an equal share of the cumulated profits the cartel extracts over all rounds, resulting in cumulated payoffs amounting to p − 1 +m−n_n (p − α) for each player. Up to and including round n, there is at least one player with cost price 1, who ultimately wins in equilibrium and receives p

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from the procurement agent, each round. Thus, in each round k, where k = 1, . . . , n, the cartel generates a profit of p − 1, resulting in total cartel profits amounting to n(p − 1) over the first n rounds, which is equally divided among all n members. Thereafter, each player has already won the auction once. As a result, in the subsequent m − n rounds, the player who wins the pre-auction and carries out the project incurs costs amounting to α, whereas p is extracted from the procurement agent. Thus, over rounds n + 1, . . . m, the cartel generates total profits of (m − n)(p − α), which is again equally divided among the n members.

It can be inferred from the shadow bookkeeping of construction firm Koop Tjuchem and the report published by the PEC in 2003 that the number of procurement auctions/projects within a year usually exceeded the number of (frequently participating, large) firms. This indicates that the case where n < m corresponds most to reality.

3.3 Cost price increases to α for one round

In this section, a setting is considered where a players’ cost price increases to α (where p > α > 1) for one round after winning, rather than the rest of the game. Put differently, a player is able to carry out a project within a time span of one round after winning, making him constraint in his capacity (which is the cause of the increase in his cost price) for only that period.

Since the recovery of players’ cost prices only has an effect compared to the setting considered in the previous subsection if there are at least three rounds, it is assumed that m_{> 3. The main discrepancy in} competitive conduct, in this scenario, arises between the following settings, which will therefore be examined separately: a) n > 2 and b) n = 2 and m > 2.

3.3.a There are more than two players

he has not won in round k −1 and equals cik= α otherwise in every round k, where i = 1, . . . , n, k = 1, . . . , m

and n > 2, the following is an equilibrium:

- bikC = bjkC = p −p−1_β , where i 6= j, k = 1, . . . , m and i, j = 1, . . . , n.

- There is a rotating winner scheme. - ΠiC= mn(p − 1) for all i = 1, . . . , n.

PROOF:

See the Appendix

The proposition defined above states that no player has the incentive to deviate from bidding p −p−1_β in each round and there is a rotating winner scheme in equilibrium, where each player receives an equal share of the total profits generated by the cartel. Thus, in case n > 2, the short-term increase in players’ cost prices does not affect competitive conduct.

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each round. Players realize that these players with cost price 1 will compete over the project and drive the winning bid downwards. Namely, in the last round, these all players maximize their round-specific payoffs and, as a result, the low cost players will undercut each other up to the point they are indifferent between winning and losing. Since all players therefore receive the same payoff in round m, the outcome of round m − 1 does not affect any future payoffs and an exactly equivalent situation emerges. Inducing backwardly, one can infer that in every round k (where k = 1, . . . , m), players maximize their round-specific payoffs and a player with cost price 1 should be indifferent between winning and losing. As a result, for all players bidding bk to be an equilibrium, bk should equal p −p−1_β .

The player having won in round k −1, who therefore has a cost price of α in round k, essentially "benefits" from the competitive pressure the players with cost price 1 put on the bid submitted. As a result, no player takes into account the competitive disadvantages he will experience the next round after winning now while bidding, since the players with cost price 1 will ensure competitive pressure on the winning bid, such that the winner and all losing players receive equivalent payoffs each round (just as in the equilibria defined under Propositions 1 and 2.1).

As a result, each player is indifferent between all possible winner schemes and there exist an equilibrium where the winner rotates. In this equilibrium a player with cost price 1 wins and receives price p from the procurement agent in all m rounds. Over the course of the game, the cartel therefore extracts profits amounting to m(p − 1), of which all n members receive an equal share in this equilibrium. This is again intuitive, because all players are symmetric at the start of the game.

3.3.b There are two players

he has not won in round k − 1 and equals cik= α otherwise in every round k, where i = 1, 2, k = 1, . . . , m,

and m > 2, the following is an equilibrium:

- bikC = bjkC = p −p−2α+1_β for all k = 2 . . . , m − 1, where i 6= j and i, j = 1, . . . , n.

- bikC = bjkC = p −p−α_β in case k = 1, m, where i 6= j and i, j = 1, 2.

- There is a rotating winner scheme. - ΠiC= m_n(p − 1), for all i = 1, . . . , n.

PROOF:

See the Appendix.

The proposition defined above states that, since there is a rotating winner scheme, both players win alternately. Moreover, equilibrium bids in the first and last round exceed the equilibrium bis submitted in a comparable setting where n > 2, whereas equilibrium bids in rounds 2, . . . , m − 1 are even higher.

In round m, there is one player who has lost in the previous round, incurring costs of 1 by carrying out the project and one player with a cost price amounting to α, that has won in the previous round. As derived under Proposition 4.3, neither of the two players have the incentive to deviate from bidding p −p−α_β in this

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case. Thus, the player with cost price 1 has a competitive advantage in round m, resulting in a payoff which is α − 1 higher than the payoff obtained by the player with a cost price of α.

Inducing backwardly, it is shown in the Appendix that in this equilibrium, in every round k, where k = 2, . . . , m − 1, the player with cost price 1 obtains α − 1 higher cumulated payoffs over rounds k, . . . , m. Thus, in all of these rounds, the following holds. The relative attractiveness of winning for the player with cost price α is driven downwards by two forces: 1) the competitive disadvantage and the α − 1 lower payoff obtained as a consequence that arises from being a high cost player in the next round and 2) the fact that he has already won in the previous round and therefore incurs higher costs by carrying out the project, whereas, the side transfer, conditional on bk being the winning bid, remains the same. The player with cost price

1 is aware of this and sets his bid bk such that the cost price α player is just indifferent between winning

and losing, which is satisfied if bk = p − p−2α+1_β . The latter one therefore has no incentive to deviate from

bidding bk as well.

In round 1, both players have a cost price amounting to 1. As a result, both players should be indifferent between winning and losing in round 1 for neither being able to profitably deviate from bidding b1. This

implies that the winner and loser of round 1 should receive the same payoff over the entire game. The winning player, however, will have a cost price of α in round 2, yielding α − 1 lower cumulated payoffs over rounds 2, . . . , m. Cumulated payoff equivalence is achieved in round 1 if b1 = p − p−α_β , since the winner is

then compensated for the lower payoff received over the rest of the game as a result of winning in round 1. Note that: δbk δα = 2 β for all k = 2, . . . , m − 1 and δbk δα = 1 β in case k = 1, m

where 0 < β < 1. Thus, an increase in α causes equilibrium bids to increase twice as much in rounds 2, . . . , m − 1 as it does in round 1 or m. Recall that the two forces driving bids up in rounds 2, . . . , m − 1 both originate from the increase in cost price to α a player experiences in the rounds after winning and have therefore greater impact as α increases. In round 1 and m, only one of these two forces enter into effect. In round 1, both players have cost price 1 and therefore only the α − 1 lower cumulative payoff generated over all future rounds by the winner causes players to bid less aggressive. In round m on the other hand, since there are no future rounds to account for, only the fact that one of the players incurs costs of α rather than drives up the bids submitted in equilibrium.

In case n = 2, the condition imposed that players experience an increase in their cost price for one round after winning does result in higher equilibrium bids, in contrast to the n > 2 setting. That is, the fact that cost price increases only lasts for one round after winning ensures there is just one player with cost price α each round k, where k = 2, . . . , m. If n exceeds 2, this implies that there are always at least two players with cost price 1 left that compete over the project and drive the equilibrium bids down. If n = 2, however, there is only one player left with cost price 1 in rounds 2, . . . , m, who can benefit from the lower attractiveness of

The Dutch construction cartel : bidding in the pre-auction