Tsukuba Economics Working Papers
No. 2010-009

An Experimental Study of Bidding Behavior in
Subcontract Auctions
by
Jun Nakabayashi and Naoki Watanabe
December 2010

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPAN

An Experimental Study of Bidding Behavior in
Subcontract Auctions∗
Jun Nakabayashi†and Naoki Watanabe‡
December 15, 2010

Abstract
It is commonly observed in practices that prime contractors solicit subcontract
bids, prior to submitting their bids in procurement auctions: the auctioneers insubcontract auctions will become bidders in a procurement auction. This point isremarkably diﬀerent from the standard theory of procurement auction. We presented a simple model of such subcontract auctions and conducted a laboratory
experiment to examine the bidding behavior derived theoretically. We observedthat in the subcontract auction, (1) subjects bid following the equilibrium bidding function derived theoretically, (2) the revenue equivalence between first-priceand second-price mechanisms breaks down, and (3) the first-price mechanism more
likely achieves ex post eﬃcient allocations than the second-price mechanism.
JEL Classification Numbers: C91, D44, D82
Keywords: procurement auction, subcontracting, experiment∗

The authors wish to thank Kenju Akai, Eizo Akiyama, Nick Feltovich, Mamoru Kaneko, Stephen
Turnbull, and Tao-yi Joseph Wang for their helpful comments. The earlier draft of this paper wasentitled as “Procurement Auctions with Pre-Award Subcontracting: A Laboratory Experiment”, andpresented at the International Conference 2010 at the Kyoto Sangyo University and SAET Conference
2010. This research was supported by the MEXT Grant-in-Aid 22370186 (Nakabayashi) and 21730183(Watanabe). All remaining errors are our own.
†
Graduate School of Humanities and Social Sciences, University of Tsukuba, 1-1-1 Tennodai,
Tsukuba, Ibaraki 305-8571, Japan. E-mail: nakabayashi@dpipe.tsukuba.ac.jp.
‡
Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai,
Tsukuba, Ibaraki 305-8573, Japan. E-mail: naoki50@sk.tsukuba.ac.jp.

11Introduction

It is commonly observed in practices that, to make lower bids in procurement auctions,prime contractors solicit bids and make subcontract agreements with the agents who
can complete subcontractable works with lower costs than the prime contractors doby themselves. Accordingly, the auctioneers in the “upstream” subcontract auctions
will become bidders in a “downstream” procurement auction. This point is remarkably
diﬀerent from the standard theory of procurement auctions. (See, e.g., Rezende (2009)
and references therein.) This paper casts light on how subcontractors behave in sucha subcontract auction in order not only to learn about their bidding behavior but also
to draw relevant policy implications towards practical procurement auctions.
We first present a simple model of subcontract bidding based on Nakabayashi (2009).
It is, however, extremely diﬃcult to collect a complete set of field data of subcontract
bids in many countries: the results of procurement auctions are publicly opened toobserve, whereas in subcontract auctions few agents can observe actual bids. So, byusing the data obtained by the laboratory experiment, we next examine some theoreticalpredictions statistically.
In our model, there are two prime contractors competing for a procurement. Before
the procurement auction, each prime contractor solicits bids from two subcontractors.
These subcontractors cannot submit their bids to the other prime contractor. So, there
are four subcontractors in total. Each subcontractor knows his or her own cost forcompleting the subcontract work, but no one else can observe it. In each subcontract
auction, only the auctioneer and bidders can observe bids, and the lowest bidder makes
a subcontract agreement with the prime contractor. If the prime contractor wins the
procurement, then the subcontractor obtains the subcontract work and is paid by theprime contractor. Otherwise, the subcontractor obtains nothing.
The main observation in our experiment is as follows. (1) In the subcontract auction
with the first-price mechanism, subjects bid following the equilibrium bidding function
derived from our theoretical model, and the second price mechanism successfully induced the bidders’ truth-telling of their cost for the subcontract work. (2) The revenue
equivalence between first-price and second-price mechanisms breaks down even under
the independent private value (IPV) environment, because of the aggressive bidding in
the case of a first-price mechanism. (3) The first-price mechanism more likely achieves
ex post eﬃcient allocations than the second-price mechanism.
The above observation (1) implies that our model captures the bidding behavior in
the subcontract auctions. The observations (2) and (3) are both matched with theoretical predictions. The observation (3) in particular suggests that prime contractors
should employ the first-price mechanism for the subcontract auction, which is recommended also from the viewpoint of the social welfare maximization.
2

We assume in this paper that the prime contractors’ costs for completing nonsubcontractable works are all normalized as zero. Prime contractors are faced withpositive amounts of those costs in practices. This situation is, however, so complicatedthat each subcontractor needs to estimate those costs of all prime contractors in orderto decide his or her subcontract bid, while taking into account information about thecosts of all subcontractors: even if a subcontractor wins a subcontract agreement witha prime contractor, he or she is paid nothing unless the prime contractor wins in
a procurement auction. So, as the first step of this research strand on subcontract
auctions, we simplify the situation by assuming that those costs are zero, and examine
whether or not subjects in the experiment can infer the optimal bidding strategies.
We further assume in our model that any collusive arrangements are not allowed inboth subcontract and procurement auctions. It is sometimes reported in practices thatprocurement oﬃcials use their discretion to decide which firms are qualified to submit
bids. In this case, bidders may oﬀer to those oﬃcers pecuniary incentives or wellpaid private-sector employment after retirement. In our experiment, however, there isno possibility of corruption, because the computer program always selects the lowest
bidders as winners in any auctions.
Collusive bidding is possible in practices, particularly when the auctions are repeatedly conducted. (See, e.g., Aoyagi, M (2003) for more detail.) Limiting number ofbidders can also breed collusive bidding by alleviating competition. Accordingly, ourexperiment is carefully designed so that subjects are supposed to be faced with one-shot
auctions; we draw dice to determine the role of each subject at the beginning of eachsequence of subcontract auctions and the subsequent procurement auction, and thus
each subject cannot identify which role a particular subject is playing as. Moreover,
it is impossible for every subject to communicate with any other subjects during our
experiment.
The remaining part of this paper is organized as follows. Sect. 2 describes ourmodel of procurement auctions with pre-award subcontracting and provides some theoretical predictions. Sect. 3 explains the experiment procedures. Sect. 4 discusses theexperiment results. Sect. 5 concludes this paper showing some future research. The
instruction of the experiment is given in the Appendix B.

2

Theoretical Predictions

Consider a situation where a procurement buyer solicits bids for a project from two
prime contractors (PCs), each of which is indexed by i = 1, 2. In practices, the project
consists of subcontractable works and non-subcontractable ones. In this paper, forsimplicity, there is only one subcontractable work for the project. Prior to submitting

3

a bid in the procurement auction, each PC holds a subcontract auction by soliciting bids
from two subcontractors (SCs) which can complete the subcontract work. Let SCi ={SCi,1 , SCi,2 } denote the set of SCs from which PCi solicits bids in the subcontract
auction. We assume that SC1 and SC2 are disjoint; neither SCi,1 nor Si,2 is allowed tosubmit his or her bid to PC j, where i �= j.
Given the order of decision making as above, a subcontract auction is hereafter
called an upstream auction, and a procurement auction is called a downstream auction.
Let ti,j stand for the SCi,j ’s cost for completing the subcontract work. We assume
that, for all i and all j, ti,j is independently and uniformly distributed over [t, t̄]. For¯
both PCs, the lowest cost for completing the subcontract work is t̄, and thus they
make subcontract arrangement with a subcontractor. As explained in Sect.1. the costfor completing the non-contractible work is normalized to zero for simplicity. Upon
solicitation of bids by PCi , SCi,j draws ti,j and submits a bid si,j in the upstream
auction. Collusive bidding is prohibited.
Each SC knows his or her own cost for completing the subcontract work, but noone else can observe it. In each sealed-bid subcontract auction, only the auctioneer
and bidders can observe bids, and the lowest bidder makes a subcontract agreementwith the prime contractor. If the prime contractor wins the procurement, then the SC
obtains the subcontract work and paid by the prime contractor. Otherwise, the SC
obtains nothing and no amount of money is paid to him or her.
Let pi be the conditional subcontract payment PC i makes to the winning SC in
the upstream auction. The payment is conditional because it is paid if the PC i actually wins in the downstream auction. For simplicity, we assume that the mechanismof the upstream auctions is given and either the first- or the second-price sealed-bid
mechanism. Thus, pi equals the lowest bid in the upstream auction if the first-pricemechanism is used in the upstream auction, while pi is the second-lowest bid if thesecond-price mechanism is used. Furthermore, we assume that each PC sets a reservation price equal to t̄ in the upstream auction. Hence, the lowest-bid SC will be selected
as a winning SC if his bid is equal to or below t̄, and the PC performs the subcontractable work for himself otherwise. Since no other payment than pi has to be made,PC i’s cost is characterized as ci = min{t̄, pi }.
Given ci , PC i submits a sealed-bid bi in the downstream auction which is undertaken with the first-price mechanism. Let V > t̄ be the value of the project to the
procurement buyer. We assume that the procurement buyer sets a reservation priceequal to t̄ in the downstream auction. Hence, the lowest-bid PC will be awarded andreceive a payment equal to his bid if the bid is equal to or below t̄.
Throughout this paper, we assume private values. The SCi,j ’s cost ti,j is known
only to SCi,j . Furthermore, the PC i’s cost ci is known only to PC i (and possibly the4SCs who bid for PCi ), but not to any other agents in the game including the opponent
PCs.
In this setting, a dominant strategy for each SC in upstream auctions is to submit
si,j = ti,j if the second-price mechanism is used in upstream auctions.1 In contrast,
no dominant strategy exists in upstream auctions if the first-price auction is used.
Instead, a symmetric increasing equilibrium bidding function in upstream auctions canbe characterized as follows. Suppose that all SCs other than SCi,j follow an increasingbidding function σ : t → s where t ≥ 0 and s ≥ 0 are the SC’s cost and bid. Suppose
also that all PCs follow a symmetric increasing bidding function in the downstream
auction. Then, SCi,j wins if and only if his subcontract bid si,j is the lowest among all
four SCs’. Hence, his maximization problem is given by��3
max (si,j − ti,j ) 1 − σ −1 (si,j ) .
si,j

(1)

This implies that in the symmetric equilibrium SC will bid as if he competes in a
procurement auction with 4 bidders. To see this, we take the derivative with respect to si,j and replace σ −1 (si,j ) = ti,j . Then, we have the first-order condition(1 − ti,j )3 σ � (ti,j ) − 3 (1 − ti,j )2 σ(ti,j ) = ti,j [1 − ti,j ]2 . Solving the diﬀerential equation
for si,j yields the SC’s equilibrium bidding function as2σ(ti |With DC) = ti +t̄ − ti.
4(2)

The symmetric equilibrium bidding function in the standard (no downstream competition) procurement auction with two bidders is given byσ(ti |Without DC) = ti +t̄ − ti.
2(3)

These illustrate that only the first-price auction induces SCs to bid more aggressively, i.e., bid lower prices, as the downstream competition becomes more intense.
Because of the aggressive bidding, revenue equivalence between the first- and secondprice mechanisms breaks down in the upstream auction.
As for eﬃciency, the first-price mechanism in upstream auctions always leads to an
ex post eﬃcient allocation, whereas the second-price mechanism may not. To illustrate,consider the case in which the realized private signals satisfy t1,1 < t2,1 < t2,2 < t1,2 . In
1

In this setting, revenue equivalence holds between English (ascending) auction and Vickery (secondprice sealed-bid) auction. Revenue equivalence in these two second-price mechanisms breaks down inmore general cases. See, for example, Chew and Nishimura (2003) for more detail.
2
The equilibrium bidding strategy in the upstream auction with the case in which the signal isdrawn from a general probability distribution is shown in Nakabayashi (2009).

5

Treatment

Control

SC1,1

SC1,2

SC2,1

SC2,2

SC1,1

SC1,2

t1,1

t1,2

t2,1

t2,2

t1,1

t1,2

✄
✄ s1,2❈s2,1 ❈❈❈✄✄ s2,2✄✄✎❈s1,1 ❈❈❈✄✄ s1,2✄✄✎❈s1,1 ❈

❈
❈

✄
✎✄
PC1

PC2

PC1

c1 = p 1

c2 = p 2

c1 = p 1

b 1 ❈❈

❈
❈❈

b2 ✄✄
✎✄✄

✄

Procurement Buyer

Figure 1: Experimental design
this case, SC1,1 receives the subcontract if the first-price mechanism is used; however,if the second-price mechanism is used, the cost of PC1 is t1,2 which is greater than thecost of PC2 , which is equal to t2,2 . Therefore, the most eﬃcient SC may not obtain thesubcontract due to the loss of his PC if the second-price auction is used in upstream
auctions.
Theoretically, the ex ante probability with which an ineﬃcient allocation occurs
under the second-price mechanism 1/3. Let tα denote the cost of the SC who actually
receives the subcontracted work. If we measure eﬃciency by computing the ratio of theactual surplus of the allocation obtained by V − tα to the maximum possible surplus
V −min{t1,1 , t1,2 , t2,1 , t2,2 }, the dead weight loss created by the second-price mechanism
in upstream competitions is 8.3 percent3 in expectation.

3

The Experiment Procedures

Our experiment consists of six sessions. Thirty six subjects of undergraduate freshman
students are split into six groups and each session uses one group. There is no previous
research on subcontract auctions, and thus subject’s behavior is unpredictable. To conduct detailed analysis on experimental observations, this research adopts the treatment
in which two PCs compete in the downstream auction in comparison with the control
in which there is a single PC (no downstream competition) as shown in Fig. 1.
Each experimental session is divided into three subsessions. Subsession 1 is a controlled experiment; two subjects out of six are chosen as an SC to compete for a3

See the Appendix for how to obtain the value.

6# of PC(s)Subsession 1
Subsession 2
Subsession 3
Subsession G1
Subsession G2

PC(s) played # of SCs # of subcont.

# of# of subj. usedby machine ?

per PCauctions

periods

per period

Yes
Yes
No
Yes
Yes

2
2
2
3
2

20
10
20
10
10

10
10
20
10
10

4
4
6
6
6

1
2
2
2
3

Subcont. auction Showup fee Earned point Number of
mechanism(JPY)
to JPY ratio subjects

Experiment
date

Mean earnings(JPY)

First-priceSecond-priceFirst-priceSecond-priceFirst-priceSecond-priceFirst-price∗1
Second-price∗1
First-price∗2

Jan. 28, 2010
Jan. 28, 2010
Feb. 6, 2010
Feb. 6, 2010
Feb. 7, 2010
Feb. 7, 2010
Mar. 26, 2010
Mar. 26, 2010
Sep. 24, 2010

1,318
1,599
5,485
5,899
4,927
6,335
2,185
2,154
2,976

1,000
1,000
3,500
3,500
3,500
3,500
1,500
1,500
1,500

.2
.2
1
1
1
1
1
1
1

6
6
6
6
6
6
6
6
6

Note: *1: Subsession (SS) 2 is conducted, followed by SS G1 and by SS G2.
*2: SS 2 is conducted, followed by SS 3 and by SS 1.
Downstream competition is always undertaken with the first-price auction.

Table 1: Features of experimental treatments
subcontract from a PC who has already been received a construction project at a priceequal to 2000. Each subject draws a production cost that is known only to him froma uniform distribution on [1000, 2000] that is known publicly. Then, subjects place asealed-bid on the computer screen and earn payoﬀ if their bid is lower. The subject’s
payoﬀ is calculated based on the mechanism (first-price or second-price) of upstream
auctions which is given and announced by the experimenters. The remaining nineteen
projects are auctioned in the same manner. Two projects are undertaken in a period
so that there are ten periods in Subsession 1.
In Subsession 2, a procurement buyer auctions oﬀ a procurement contract for which
the procurement buyer sets a reservation price equal to 2000. In this downstream
auction, two computer-played PCs are solicited. Prior to bidding, each PC randomly
chooses two subjects as SCs. Note that the subjects chosen by a PC are diﬀerent
from those chosen by another PC so that four subjects in total are chosen in a period.
Similar to Subsession 1, selected subjects draw private information from the same
uniform distribution and submit a bid to a PC. Following an auction mechanism i.e.
the first-price or second-price sealed-bid auction, which is preliminarily and publicly
announced by the experimenters, a computer-played PC selects an SC who submits
a lower bid in the upstream auction and decides the subcontract payment. In otherwords, the cost of the PC to complete the construction project is exactly the same7

as the subcontract payment. Given the production cost that is unknown to both theprocurement buyer and the competitor, the computer-played PC submits a bid in
the downstream procurement auction. The bidding strategy the computer-played PC
follows is the risk-neutral Nash equilibrium strategy provided that the SCs follow (2).
The remaining nine projects are auctioned in the same manner for nine periods.
Subsession 3 is the same as Subsession 2 except that PCs are played by subjects. In
each period, four subjects are randomly chosen as SCs and remaining two are as PCs.
Although PCs are played by subjects, their action space is restricted on submitting
a bid in the downstream auction. That is, the computer program chooses the lowest
bidder in the upstream auction as the SC and makes the subcontract payment according
to the given auction mechanism of the upstream competition.
Other subsessions are conducted in a control experiment in order to check whether
the theoretical prediction holds even in more general cases. In subsession G1, thenumber of PCs is three and each PC solicits 2 SCs in the upstream auction while inSubsession G2, the number of PCs is two and each PC solicits 3 SCs in the upstream
auction.
The minimum unit of sealed-bids subjects can type on the computer is �1. Eachsubject have an initial balance of either �1,000 or �3,500. Subjects who lose more than
the amount of the initial endowment will be bankrupt although nobody got bankrupt
in this experiment.
Since subjects randomly selected as a PC or an SC in each round, they have noidea about whom they compete with in both up- and downstream competitions. Thisis expected to help deterring the subject’s incentive to collude.
At this time, a computer program makes a bid on behalf of each potential PC sothat it maximizes the potential PC’s expected profit, given the amount the PC has
to pay to its SC. We assume that the PC does not do any on the public construction
project; all of the work is done by the SC. So, the cost of a public construction project
for the PC is just the expenses it pays to the SC. So, the points for the PC is thediﬀerence between the amount received from the government and the payment to the
SC. At last the payment to the SC is made by the PC who wins the project. The
payment received by a subject is counted for the sum of the total points the subject
earns in the experimental session plus the showup fee.

4

The Experimental Results

4.1

Overview

Fig. 2 and 3 plot subject’ bids and costs in upstream auctions which take place, respectively, with the forms of the first- and the second-price mechanisms. Fig. 2 illustrates
8

that, in the upstream auction with the first-price mechanism, markups (diﬀerences between bids and costs) are larger in Subsession 1 (no downstream competition) than inother subsessions (a downstream competition between 2 PCs). In contrast, Fig. 3 showthat if the second-price mechanism is used in upstream auctions, subjects tend to bid
truthfully regardless of the situation in the downstream competition.
Bids

Bids

First-price auctions

2000

Second-price auctions

2000

1800

1800

1600

1600

1400

1400

Subsession 1: 1 PC
Subsession 2: 2 computerized PCs

1200

Subsession 1: 1 PC

1200

Subsession 3: 2 human PCs

Subsession 2: 2 computerized PCs

Theoretical Bid Function (1 PC)

Subsession 3: 2 human PCs

Theoretical Bid Function (2 PCs）

1000
1000

1200

1400

Costs

1600

1800

Theoretical Bid Function

1000
1000

2000

1200

Figure 2: First-price auctions

1400

Costs

1600

1800

Figure 3: Second-price auctions

FPA

SPA

Subsession No.

1

2

3

1

2

3

Average

Bids
Costs
Markups

1,592
1,446
146

1,583
1,498
84

1,548
1,457
91

1,461
1,491
-31

1,436
1,480
-44

1,506
1,536
-30

Variance

Bids
Costs
Markups

32,831
76,975
18,11653,70786,291
8,626

46,466
74,1618,240

88,47978,914
5,781

111,809
87,992
7,085

91,446
77,271
4,388

80

80

160

80

80

160

Observations

Table 2: Descriptive statistics
Table 2 reports the descriptive statistics of the results. The third row shows that the
average markups drop significantly in Subsession 2 and 3 (84 and 91, respectively) fromthat in Subsession 1 (146) if the first-price mechanism is used in upstream auctions.
On the other hand, the average markups are almost the same between Subsession 1
and Subsession 2 and 3 (Subsession 1: -31, 2: -44, and 3: -30).
92000

Another statistical analysis also supports this evidence. Table 3 reports the Welch’s
t-test statistics which examine whether the means of bids, costs and markups are different between the paired subsessions described on the first column. These show thatthe means of the markups in upstream auctions are lower with statistical significancein subsession 2 (t-value: 3.360) and 3 (t-value: 3.027) than in Subsession 1 if (and onlyif) the first-price mechanism is used in upstream auctions. The results suggest that, astheoretical model predicts, subjects bid aggressively in upstream auctions taking into
account the increase in the downstream competition if the first-price mechanism is usedin upstream subcontract auctions.
First-price
Costs
Markups

Bids
Subsession 1 vs. 2
Subsession 2 vs. 3
Subsession 3 vs. 1-1.150
1.083
0.280

0.300
1.153
-1.5963.360**-0.522-3.027**

Bids
0.179
-1.026
0.831

Second-price
Costs
Markups
0.349-1.1630.788

0.729-1.0030.076

Note: Null hypothesis that the paired subsessions have the same mean is rejectedwith * significant level at 5%; ** significant at 1%

Table 3: Two sample t-test
For more qualitative analyses, we implement OLS and fixed eﬀect (FE) regression
methods. Observed bids are regressed on costs, and FE controls for subject heterogeneity. The result is reported in Table 4. It shows that the aggressive bids initiatedby the downstream competition are observed only in the upstream auctions held withthe first-price mechanism. Regression (1) and (2) show that the observed bids in Subsession 2 and 3 are 38.89 and 50.82 lower on average than those in Subsession 1 if thefirst-price mechanism is used in upstream auctions. In contrast, Regression (3) and (4)have no statistically significant dummies for Subsession 2 and 3.
Finally, the descriptive statistics of bids and costs for each of 18 subjects used inour experiment are available in Table 5 and 6.

4.2

Aggressive bids in first-price mechanisms

Throughout the experiment sessions, we observe the first-price mechanism induces aggressive bids in upstream auctions. Regression (5) through (7) and (8) through (10)in Table 7 are the results of OLS regressions conducted separately for each experiment session,4 which is conducted with its unique subject group. Subsession 2 and 3
dummies are insignificant in all experiment sessions when upstream auctions are held4

Day 1 experimental session is conducted on conducted on January 28th, 2010, Day 2 session is on
February 6th, 2010, and Day 3 is on February 7th. In each day, we run two sessions; i) the session inwhich the first-price mechanism is used for upstream auctions, and ii) the second-price mechanism isused for upstream auctions. The payment scheme in each day session is shown in Table 1.

10

(1)
(2)
First-price(3)(4)
Second-price

OLS

FE

OLS

FE

Cost

0.7**
(60.28)0.7014**(63.95)1.03**(80.79)1.03**(98.91)Subsession 2 dummy-38.89**(4.21)-41.23**(4.73)-16.66(-1.67)-11.24(-1.4)

Subsession 3 dummy-50.82**(6.36)-53.02**(7.04)-5.76(-0.67)-2.90(-0.42)

Constant

586.10**(32.31)585.58**(32.53)-52.154*(-2.56)-49.182*(-2.44)

Observations
R-squared
No. subject IDs

480
0.89
-

480
18

480
0.93
-

480
18

Note: Absolute value of t-statistics in parentheses;* significant at 5%; ** significant at 1%
Subject ID is taken as fixed eﬀect in regression (2) and (4).

Table 4: Regression result for bids and costs 1
with the second-price mechanism, and except for Subsession 2 in Day 1, these dummies
in all experiment sessions exhibit a statistical significance if the first-price auction isused in upstream competitions. These indicate that, regardless of groups and payment
schemes, subjects in an upstream auction recognize the intensity of the downstream
competition and respond the change of the competitive environment as predicted by
the theoretical model.
Because of the aggressive subcontract bids, the revenue equivalence fails in upstream
auctions. Table 8 shows that the costs of PCs are 10 percent lower on average if thefirst-price auction is used in upstream competition than if the second-price auction is
used.

4.3

Overbidding in the second-price mechanism

As shown in Section 2, truth-telling is a weakly dominant strategy for SCs in upstream
auctions held with the second-price mechanism regardless of their risk attitudes and theintensity of the downstream competition. Nevertheless, subjects in upstream auctions
frequently bid below their costs as illustrated in Fig. 3. It is also noteworthy that the“overbids” are observed regardless of the intensity of the downstream competition.
Furthermore, overbids are continuously observed regardless of whether PCs arecomputerized or played by subjects. Table 3 reports the diﬀerence of mean markups
between Subsession 2 and 3 is statistically insignificant. This evidence may shed light

11

12

0.7508**(13.81)-66.3807†(-1.92)-4.4841(-0.12)453.6981**(4.99)
20
0.93

Cost

Subsession 2 dummy

Subsession 3 dummy

Constant

Observations
R-squared

26
0.95

564.1471**(8.83)-35.0349(-1.35)-30.9366(-1.29)0.7053**(18.28)

2

18
0.96

402.3877**(5.61)-84.0447*(-2.82)-69.2456†(-2.03)0.8198**(16.27)

3

17
0.88

411.3615**(3.31)-128.068*(-2.60)-154.456**(-3.08)0.8484**(9.81)

421
0.84

297.8266*(2)4.6802(0.08)-53.3512(-0.88)0.8731**(9.53)

518
0.99

651.9299**(22.65)-69.7916**(-4.81)-35.863*(-2.50)0.6814**
(35)

6

24
0.95

544.5605**(9.54)

2.2465(0.09)

12.3755(0.46)

0.6974**(18.95)

7-72.631**(-2.94)-78.4707**(-3.11)
583.6617**(9.19)
21
0.94

Subsession 2 dummy

Subsession 3 dummy

Constant

Observations
R-squared

19
0.87

710.9265**(7.95)-88.8808†(-1.91)-59.5574(-1.22)

0.6312**(9.86)

11

17
0.97

399.9216**(6.37)

46.055(1.47)

63.8519*(2.19)

0.7554**(18.96)

12

17
0.94

638.7810**(8.35)-100.738*(-2.36)-79.8105†(-2.11)0.6898**(13.72)

13

23
0.96

621.2752**(12.47)-49.7609†(-2.02)-32.7227(-1.26)

0.6957**(21.01)

14

18
0.97

502.2879**(9.6)-27.1427(-1.26)24.4083(1.04)

0.7225**(20.97)

15

22
0.95

353.6076**(3.86)

101.7514*(2.54)-6.3647(-0.23)0.8129**(15.06)

16

Table 5: Each subjects in first-price upstream auctions

Note: Absolute value of t-statistics in parentheses, † significant at 10%; * significant at 5%; ** significant at 1%

0.7321**(15.69)

Cost

10

Note: Absolute value of t-statistics in parentheses, † significant at 10%; * significant at 5%; ** significant at 1%

1

Subject ID

220.7

891.0282**(6.21)-127.357*(-2.40)-3.0319(-0.06)

0.5435**(5.75)

17

22
0.92

665.2329**(8.06)-113.157**(-3.23)-73.0283*(-2.13)0.6521**(12.89)

8

18
0.86

799.5253**(8.1)-82.8041†(-2.07)-30.8003(-0.69)0.5854(8.83)

18

17
0.87

603.6409**(5.76)-106.261(-1.73)-77.5159(-1.31)0.7190**
(8.8)

9

13

-64.6784†(-1.99)-29.2049(-1.01)-132.846*(-2.23)30
0.97

Subsession 2 dummy

Subsession 3 dummy

Constant

Observations
R-squared

26
0.92-128.919(-1.21)-101.686*(-2.25)-75.3185(-1.41)

1.0447**(15.59)

2

27
0.99

-67.7436(-1.64)93.2345**(4.64)

70.4701**(3.18)**

0.9803**(34.09)

3

31
0.96

-268.288**(-3.33)-0.0524(0)29.3833(0.77)

1.1588**(25.36)

4

23
1

0
(.)

0
(.)

0
(.)

1.0000**
(.)

5

23
0.99

-50.5447(-1.19)14.8787(0.88)-18.7174(-0.98)0.9901**(35.26)

6

27
0.95

-63.4697(-0.76)21.935(0.59)

26.7783(0.58)

1.0447**(19.17)

7

27
0.94

15.0233(0.17)-36.5959(-1.17)-66.0274†(-1.83)0.9894**(18.65)89.5282(0.32)
46.1905(1.62)-144.638*(-2.54)29
0.97

Subsession 2 dummy

Subsession 3 dummy

Constant

Observations
R-squared

291-12.1677(-1.48)0.5843(0.21)-3.311(-0.95)

1.0074**(210.56)11

20
1-7.9444(-1.14)-5.1481†(-1.81)-5.2028(-1.31)1.0084**(226.96)1230
132.2414**(3.22)-20.0374**(-5.97)-17.7103**(-4.15)0.9918**(153.83)

13

26
0.98

108.9002*(2.49)-16.9798(-0.87)-38.6731(-1.57)0.9717**(32.45)

14

32
0.9

116.3042(1.16)-54.0736(-1.25)-110.744*(-2.12)0.9983**(15.24)1521
150.4509*(2.68)-9.1776(-1.49)11.6079†(1.8)

0.9728**(84.75)

16

Table 6: Each subjects in second-price upstream auctions

17

25
0.96

-158.158(-1.71)110.1054**(2.95)

67.3693(1.58)

1.0730**(20.74)

Note: Absolute value of t-statistics in parentheses, † significant at 10%; * significant at 5%; ** significant at 1%

1.0243**(29.84)

Cost

10

Note: Absolute value of t-statistics in parentheses, † significant at 10%; * significant at 5%; ** significant at 1%

1.0847**(27.34)

Cost

1

26
0.99

97.7049*(2.15)-40.4766*(-2.27)-6.2779(-0.33)0.9642(36.29)

18

28
0.93

-283.945**(-2.83)34.6084(0.98)

34.2005(0.88)

1.1573**(18.18)

9

(5)

(6)
First-price

(7)

(8)

(9)
Second-price(10)

Session No.

1

3

5

2

4

6

Cost

0.67**(32.58)0.68**(39.12)0.77**(36.05)0.98**(50.49)1.05**(54.32)

1.07**(51.55)Subsession 2 dummy-22.38(-1.35)-38.90**(2.72)-53.41**(3.38)-26.94(-1.87)-11.63(-0.78)-14.05(-0.82)

Subsession 3 dummy-49.43**(3.46)-48.59**(3.93)-51.90**(3.78)-17.75(-1.42)8.71(0.68)-13.03(-0.88)Constant

648.17**(19.99)613.54**(23.46)474.96**(14.03)80.99**(2.62)-98.64**(-3.15)-145.94**(-4.47)

Observations
R-squared

160
0.88

160
0.91

160
0.90

160
0.94

160
0.95

160
0.95

Note: Absolute value of t-statistics in parentheses * significant at 5%; ** significant at 1%

Table 7: Regression result for bids and costs 2
Subcont. Auc. Form

Mean

S.D.

MedianMaxMin

1st-price
2nd-price

1595.366
1740.758

237.884242.024

1555.51788.5

2000
2000

1100
1002

Total

1668.062

250.595

1659.5

2000

1002

Table 8: Costs of PCs
on the theoretical explanation for overbidding in second-price auctions.
There are a group of studies which attempt to explain overbidding in second-priceauctions theoretically (e.g., Morgan, Steiglitz and Reis’ (2003)). A majority of thesestudies assume that bidders have the non-standard preferences, which are broadly categorized into either spite or joy of winning.
In Subsession 3 of our experiment, three subjects form a team in which one plays a
PC and remainders play SCs to compete with another team. A team, on the other hand,consists of two SC subjects in Subsession 2. Hence, in subsession 3, a lower subcontractbid is a spite to the opponent SC but, at the same time, is a goodwill to the PC subject
since the PC subject will have more cost advantage in the downstream competition. In
contrast, no goodwill eﬀect exists in a lower subcontract bid in Subsession 2 where PCs
are computerized. If SC subjects not only care about the payoﬀ of the rival SC but also
about the payoﬀ of the PC subject, subcontract bids should be higher in Subsession 3
than in Subsession 2. However, we do not observe any diﬀerence in subcontract bids
in between Subsession 2 and 3. From this evidence, overbids are in general attributed

14

more plausibly to joy of winning.

4.4

Eﬃciency

Our laboratory data show that the first-price mechanism in upstream auctions contributes more likely to the realization of an ex post eﬃcient allocation. To measure
allocative eﬃciency, we use the ratio between the sample mean of realized social surplus (the social value of the project minus the cost of the awarded SC) and the sample
mean of maximum-possible social surplus (the social value of the project minus the
production cost of the lowest SC). All the descriptive statistics are reported in Table 9.
The numerator of the ratio is denoted by (A) and the denominator is denoted by (B).

Social Surplus Social Surplus
Variance
t-statistics
Realized (A) Maximum (B) (A)/(B) of (A)/(B) FPA vs. SPA
Subsession 1
FPA Subsession 2
Subsession 3

671.9
778.9
792.8

699.2
798.6
820.9

96.1%
97.5%
96.6%

0.84%
0.25%
0.54%

Subsession 1
SPA Subsession 2
Subsession 3

673.1
772.8
660.0

677.9
835.9
755.3

99.3%
92.4%
87.4%

0.14%
1.72%
3.64%

2.4885**
1.9914*3.7110*** significant at 5%; ** significant at 1%

Table 9: Eﬃciency
Two-sample t-test statistics in the table compare eﬃciency between the first- andthe second-price auction in upstream auctions for each subsession. It is shown that thefirst-price mechanism improves eﬃciency with 1 percent significant level for Subsession
1 and 3 and 5 percent significant level for Subsession 2. In addition, Table 10 describing
the ratio for each experimental session and for each subsession reports that the firstprice mechanism in Subsession 2 and 3 always yields higher eﬃciency than the secondprice mechanism (e.g., 97.4 percent vs. 93.2 percent in Subsession 2 on Day 1). On
the other hand, there is no such tendency in Subsession 1. The eﬃciency in Subsession
1 on Day 1 under the first-price auctions is approximately 6 percent lower than that
under the second-price auctions while on Day 2 that is approximately 7 percent higher
under the first-price auctions.

4.5

Risk Attitude

Although observed subjects’ strategies are oﬀ the theoretical bidding functions, thediscrepancy can be well-explained by the subject’s risk attitude. As presented in Cox,
15

Session No.
Subsession 1
Subsession 2
Subsession 3

1
93.2%
97.4%
97.3%

First-price3
5
99.1% 95.8%
98.7% 96.6%
95.6% 96.8%

Second-price2
4
6
98.2% 92.6% 99.6%
93.2% 92.0% 92.2%
92.6% 89.3% 80.6%

Table 10: Eﬃciency rate for each experiment session
Smith, and Walker (1982), bidders bid more aggressively as they are more risk-averse.
Suppose the bidder i’s utility function is expressed as a power function:
Ui (y) = y ri ,where y is the experimental payoﬀ and (1−ri ) represents the Arrow-Pratt measurementof constant relative risk aversion. Then, (2) becomes 5
bi = ti +t̄ − tiri .
4bi = ti +t̄ − tiri .
2whereas (3) becomes

These imply that both strategies move toward the 45 degree line although these arenever coincident with each other. In other words, regardless of the SC’s risk attitude,
the aggressive bidding caused by the downstream competition will be observed only inthe case where the first-price auction is used in the upstream competition.
Our experimental result was fully consistent with such theoretical prediction. The
mean value of r obtained in our data was 0.76 with the standard deviation is .010,
indicating that subjects are risk averse. Nevertheless, they tend to bid lower prices in
the upstream first-price auction if there is a downstream competition. We thus conclude
that risk attitude is not the cause of the aggressive bidding in the upstream auction.

4.6

Unserious Subjects

For subjects to be serious throughout the session, some experiments for auctions introduce the procedure in which the subject’s actual earning is the sum of the payoﬀsearned in some limited rounds which have randomly chosen by the computer. Subjects
are informed of the randomization but do not know which rounds are chosen. We donot, however, employ such a random payment procedure for the following reason. In
5

See Cox, Smith, and Walker (1982) for more detail.

16

our experiment subjects are randomly assigned to be an SC or to have a rest. Therefore, they do not know how many times they will be able to submit a subcontract bid
at any period in every session. This design helps them play seriously in every period.
In fact, we have no evidence that subjects’ bidding behavior changes significantly
through subsessions. Regression (11) through (16) in Table 11 are conducted to compare
the subjects’ bidding behaviors in the first- vs. the last-half periods. The fact that the“first-half” dummies are statistically insignificant in five out of six regressions suggeststhat subjects behave the same in between the first and the last half rounds in mostsubsessions.
(11)

(12)
First-price

(13)

(14)

(15)
(16)
Second-price

Subsession No.

1

2

3

1

2

3

Cost

0.59**(22.12)0.74**(33.98)0.73**(49.12)0.96**(33.47)

1.06**(43.31)1.05**(62.67)First-half auc. dummy-33.88*(-2.31)-3.14(-0.25)1.96(0.24)

29.6(1.84)-14.8(-1.07)-17.4(-1.91)

Constant

759.5**(18.42)490.5**(14.43)495.2**(22.37)37.54(0.86)-102.9*(-2.82)-83.05**(-21.62)

Observations
R-squared

120
0.81

120
0.91

240
0.91

120
0.91

120
0.94

240
0.94

Note: Absolute value of t-statistics in parentheses* significant at 5%; ** significant at 1%

Table 11: Comparison between the first- and last- half rounds
It is thus hardly concluded that subjects turn to be less serious to play in our
experiment as sessions go on due to a suﬃciently large amount of showup fees or to thelack of the random payment procedure.

4.7

More PCs or more SCs

Aggressive subcontract bids as a result of the increased downstream competition are
observed in more generalized settings. We conduct a supplemental experimental session
which begins with the control subsession where 2 PCs bid in the downstream auctionin 10 rounds and each PCs solicits 2 SCs in the upstream auction. Then, in the next
treatment subsession (Subsession G1), the number of PCs is raised to three keeping
other things constant. In the final control subsession (Subsession G2), the number of17

PC’s costs

PC’s profit

Subsession 2,3mechanism
mean
N
First-price
1,439.1 180
Second-price 1,655.8 180
Total
1,547.4 360

sd
153.47250.14233.92

Subsession 2, 3
mechanism
mean
N
First-price147.21
90
Second-price 163.07
90
Total
155.14 180

sd
77.20
111.0495.69

mechanism
First-priceSecond-price
Total

Subsession 2
mean
N1,459.8
60
1,618.2
60
1,539.0 120

sd176.31
264.88237.74

Subsession 2
mechanism
mean
N
First-price211.7730
Second-price 178.20
30
Total
194.98
60

sd
36.51
72.15
59.16

mechanism
First-priceSecond-price
Total

Subsession 3
mean
N1,428.7 120
1,674.6 120
1,551.7 240sd140.33241.38232.37

Subsession 3
mechanism
mean
N
First-price114.93
60
Second-price 155.50
60
Total
135.22 120

sd
71.80
125.96104.10

Table 12: Mean winning bid and PC’s profit
PCs is back to two while the number of SCs for each PC to solicit becomes three.
Throughout the session, subjects bid as SCs. Since the number of necessary subjects
are four in the first subsession, two subjects out of six are randomly selected in eachround to stay away from bidding.
Regression 17 through 24 in Table 13 report the statistical results. In the odd
numbered regressions, the first subsession (i.e., 2 PCs with 2 SCs for each PC), is
identified by putting Dummy 1 and 2 on the subsequent subsessions while in the evennumbered regressions, the second subsession (i.e., 3 PCs with 2 SCs for each PC),
is identified by putting Dummy 2 and 3 on the other subsessions. The t-statistics ofDummy 1 and 3, which are 4.28 in regression 17 and 18 and 2.01 in 21 and 22, imply thatthe increase in the number of PCs from two to three in the downstream auction induces
lower subcontract prices if (and only if when considering only the first- and second-pricesealed-bid auction) the first-price auction is used in upstream competitions. Dummy 2
in both regression 17 and 19 is significant and that in both regression 18 and 20 are not,which supports the theoretical argument that SCs follow the same equilibrium bidding
strategy in both cases i) 3 PCs, each soliciting 2 SCs and ii) 2 PCs, each soliciting 3
SCs.6 Similar results are also obtained when the subject IDs are controlled as fixed��The SC’s winning probability in the upstream auction is 1 − σ −1 (si,j ) in Subsession G1 and�
2
1 − σ −1 (si,j ) in Subsession G2. The conditional probability that his PC wins in the downstream
�
�4
�
�3
auction given that the SC bids si,j is 1 − σ −1 (si,j ) in Subsession G2 and 1 − σ −1 (si,j ) in Subsession G2. Hence, in both cases, the SC’s objective function is��5max (si,j − ti,j ) 1 − σ −1 (si,j ) .
6

�

si,j

The optimal bidding strategy is thus identical in both cases.

18

eﬀect.
(17)

(18)
(19)
1st-price
OLS

(20)
FE

0.8041** 0.8041** 0.806** 0.806**(63.49)(63.49)(68.57)(68.57)
Dummy 1-40.86**-42.15**
3 PCs (2 SCs)
(4.28)(4.77)
Dummy 2-49.40**-8.53-50.71**-8.56
2 PCs (3 SCs)
(5.17)(-1)(5.74)(-1.09)Dummy 340.86**
42.15**
2 PCs (2 SCs)
(4.28)(4.77)
Constant
416.28** 375.41** 414.71** 372.56**(20.43)(18.70)(20.08)(18.23)
320
0.93
-

320
0.93
-

320
12

(22)
(23)
2nd-price
OLS

Cost

Observations
R-squared
Number of IDs

(21)

320
12

(24)
FE

0.9877** 0.9877** 0.9942** 0.9942**(43.36)(43.36)(47.84)(47.84)32.70*
27.44(2.01)(-1.86)
26.68
-6.01
21.69
-5.76
(-1.64)(-0.41)(-1.47)(-0.44)-32.70*-27.44(2.01)(-1.86)-41.67-8.978-46.32-18.87(-1.13)(-0.25)(-1.28)(-0.53)
320
0.86
-

320
0.86
-

320
12

320
12

Note: Absolute value of t-statistics in parentheses, * significant at 5%; ** significant at 1%
Subject ID is taken as fixed eﬀect in regression (18), (19), (23), and (24).

Table 13: 3 PCs with 2 SCs for e.a., 2 PCs with 3 SCs for e.a.
Now, we compare the first subsession in this experiment with Subsession 2 in theprevious experiment; in both subsessions, there are 2 PCs, each soliciting 2 SCs in the
upstream auction. We regress the observed bids on the private signals. The dummy isequal to one if the dependent and independent variables are picked from the previous experiment Subsession 2 and is equal to zero otherwise. Unlike the theoretical prediction,
the regression result in Table 14 shows that it is statistically significant that subjects
in Subsession 2 bid lower prices than those in the first subsession in this supplemental
experiment. Taking into account the fact that all subject groups are randomly selected,
it is hard to conclude that this diﬀerence comes from the subject heterogeneity. Hence,the subject’s bidding behavior may be aﬀected by the competitive environment of theprevious subsession. However, subjects in upstream competition do recognize the competition in the downstream auction and bid diﬀerently if the first-price mechanism is
used.

4.8

Change in the order of subsessions

We conclude this section by reporting the result that the aggressive bids are observed
regardless of the order of subsessions. In the final experimental session, we begins by
Subsession 2 in which 2 PCs solicit 2 SCs for each upstream competition based on
the first-price mechanism. Then, we conduct Subsession 3 followed by Subsession 1 inwhich a paired subjects bid for a PC and there is no downstream competition. The
regression result of the observed bids on the costs in Table 15 shows that the order of
19

(25)

(26)

(27)
(28)
2nd-price

OLS

FE

OLS

FE

0.722**(37.89)-38.6841**(3.44)
578.108**(17.18)0.722**(39.01)-32.6429**(2.71)
571.006**(17.05)0.9969**(28.27)16.4836(-0.8)-72.1702(-1.13)1.0027**(36.48)8.6942(0.16)-65.6597(-0.73)

160
0.9

160
-

160
0.84

160
-

1st-price

Cost
Dummy
Constant
Observations
R-squared

Note: Absolute value of t-statistics in parentheses, * significant
at 5%; ** significant at 1%
Subject ID is taken as fixed eﬀect in regression (26), (28).

Table 14: 2 PCs, 2 SCs for e.a. PC
subsessions does not aﬀect our previous results; subjects bid lower prices in Subsession
2 and 3 even if Subsession 1 is conducted afterward.
(29)

(30)
1st-price

Cost
Subsession 1 dummy
Subsession 2 dummy
Subsession 3 dummy
Constant
Observations
R-squared

(31)

(32)

2nd-price

OLS

FE

OLS

FE

0.769**(51.49)-26.139*(2.17)-40.186**(-3.84)459.448**(19.66)

0.769**(51.49)-26.139*(2.17)-40.186**(-3.84)459.448**(19.66)

0.769**(51.49)40.186**(3.84)
14.046(1.35)
419.263**(17.86)

0.769**(51.49)40.186**(3.84)
14.046(1.35)
419.263**(17.86)

160
0.94

160
-

160
0.94

160
-

Note: Absolute value of t-statistics in parentheses, * significant at 5%;** significant at 1%
Subject ID is taken as fixed eﬀect in regression (30), (32).

Table 15: Changing subsession orders

5

Concluding remarks

In this paper, we conduct a laboratory experiment to examine the bidding behavior
in upstream subcontract auctions that take place prior to a downstream procurement
auction.
To answer the following three questions, we conduct a laboratory experiment; 1)20

whether subjects play the symmetric equilibrium the theoretical research by Nakabayashi(2009) proposes, 2) whether the revenue equivalence breaks down in the upstream auction, and 3) which mechanism yields higher eﬃciency, the first- vs. second-price auction.
As suggested by the theoretical model, subjects tend to bid more aggressively in
upstream competitions if upstream auctions are held with the first-price mechanism.
Although the observed bids in our experiment has a discrepancy from the theoreticalbid functions due presumably to the subject’s risk attitude, the aggressive biddingin the first-price upstream auction is indeed observed with statistical significance thatcauses the failure of the Revenue Equivalence in upstream auctions. On the other hand,
despite the theoretical prediction that expected profits of PCs who use the first-pricemechanism to select an SC is higher than those who use the second-price counterpart,the subject’s earnings as a PC in our experiment are lower if they use the first-pricemechanism in the upstream auction.
Unlike the existing experimental research regarding the eﬃciency on auctions, we
obtain a clear ranking in upstream auctions. Eﬃciency is higher if the first-price auction is used in the upstream auction. Although the second-price mechanism tends
to yield higher eﬃciency in our controlled experiment, the existing of the downstream
competition overcompensates the eﬃciency created by the first-price upstream auction.
An extension from this study can be the examination of the case where a PC uses
the first-price sealed bid auction to select an SC while another PC uses the secondprice sealed-bid auction. Dividing two cases; one in which all subjects know every PC’smechanism to select an SC, and the other is that PC’s mechanism is known only tothe relevant subjects (the PC and SCs who bid for the PC), we will investigate theimpact of such mechanism choices on the strategy in the upstream auction and thePC’s profitability as well as the ex post eﬃciency.
Furthermore, the optimal reservation price in the downstream auction can be analyzed in the laboratory experiment. As theory predicted, the downstream auction
satisfies the standard IPV environment since the PC’s cost is drawn from a distribution function which depends on the number of competitors. As a result, the optimalreservation price in the downstream auction depends on the number of bidders. We
will conduct an experimental session for the inspection of optimal reservation price,
the results of which will be attractive for the real-world procurement buyers who havealways wondering such issues.

21Appendix A
The social surplus is equal to
SS F P =4
5

if the first-price mechanism is used in upstream competitions.
To compute the social surplus in the case of the second-price mechanism in upstream
competitions, let ti,j denote the lowest signal among those of the four SCs. Let alsoti,j � ∈ {1, 2} be an index that satisfies j � �= j. Then, the probability with which is not
the highest is 2/3 regardless of the value of ti,j . Therefore, if ti,j � is not the highest andSCi,j gets the subcontract, then the conditional social surplus is given by
4 2
8
· = .
5 3
15
On the other hand, if ti,j � is the highest, then ti� ,(1) gets the subcontract where i� �= i and(1) is the lowest order statistic among 2 signals, t·,1 , t·,2 . Regardless of the values ti,j andti,j � , this situation happens with probability equal to 1/3. Therefore, the conditionalsocial surplus is given by
3 1
3
· = .
5 3
15
Therefore, the social surplus of the second-price mechanism in upstream competitions
is given by
SS SP =

8
3
11
+
= ,
15 15
15

which is 8.3 percent smaller than SS F P .

6

Appendix B: An Experiment in Subcontract Biddingfor Public Works

In this experiment, each subject (starting with you) is initially given 3,500 points.
Throughout the experiment, you may bring in more points, or you may use up all yourinitial points. Each subject will be given a reward according to the total points he or
she has at the end of the experiment at the rate of 1 yen per point.
All the information we pass out here is for use by the subject only. None of theinformation in this instruction is to be shared with any other subject. There is to be
no talking during the experiment. If someone breaks these rules, the experiment will22

be halted at that point.

6.1

Summary of Experiment

In regard to a public construction project, the procurement buyer (government) chooses
a company to commission the project and decides the amount it will pay out to thecompany by means of public bidding, from the standpoint of fairness and cost reduction.
This company is called a “prime contractor”. The prime constructor usually has tocontract much of the project out to the construction agents. Each of these agents iscalled a “subcontractor”, and each part of the project assigned to the subcontractor
is called a job. From the viewpoint of cost reduction, the prime contractor chooses
its subcontractors by having the agents make bids to see which agent has the lowest
estimate of costs for the job, where these bids are not disclosed to the public. This
experiment is done in order to investigate the interactions of these two types of bidding.
We have the subjects play the role of either potential prime contractors or construction agents. The role of the government is played by us. The government firstannounces a public construction project. Then, it is shown on your computer screen
whether you are a potential prime contractor or a construction agent. If you are assigned to a construction agent, you must make a bid for subcontracting the projectindicated by a prime contractor. If you are assigned to a prime contractor, you must
make a bid to the government for the public construction project.

6.2
6.2.1

Process of Experiment
Subsessions and the Order of BiddingThis experiment consists of three sessions. Before each subsession starts, there is a trial
run of 3 periods. The results of the bids in this trial run account for nothing of yourtotal points. Any necessary information is shown on your computer screen.
Subsession 1 has ten periods. At the beginning of each period, two subjects
are randomly chosen as construction agents. The prime contractor is chosen by thegovernment a priori and it is commissioned a public construction project. Thus, there
is no public bidding for any projects. Each of the two construction agents is first
randomly given an integer that ranges from 1001 to 2000 point as its construction costfor the job of the construction project. This construction cost is the agent’s private
information. The agent who makes the lowest bid wins the subcontract bidding andreceives the same amount as the second lowest bid (the sealed-bid second-price auction).
The payment you receives as a subject is counted for your total point, but nothing iscounted unless you are chosen as a subject.

23

Subsession 2 also has ten periods. At the beginning of each period, four subjects
are randomly chosen as construction agents. The government announces a public construction projects and two potential prime contractors participate in bidding for the
project. Prior to this bidding, each potential prime contractor asks two construction
agents to make a subcontract bid. These two construction agents are randomly assigned
to a potential prime constructor, and each construction agent are first randomly given
an integer that ranges from 1001 to 2000 points as its construction cost for the job of
the construction project. This construction cost is the agents private information.
A computer program assigns to each potential prime contractor one subcontractor,
choosing the agent who makes the lowest bid as the subcontractor. Each potential
prime contractor commits to a contract that if the potential prime contractor wins the
public construction project, it will (1) ask the subcontractor to do a job and (2) pay thesame amount as the second lowest bid in the subcontract bidding to the subcontractor.
If the potential prime contractor makes the lowest bid for the project, it wins the
project and receives exactly the same amount as its bid from the government.
At this time, a computer program makes a bid on behalf of each potential prime
contractor so that it maximizes the potential prime contractor’s expected profit, given
the amount the prime contractor has to pay to its subcontractor. We assume that theprime contractor does not do any on the public construction project; all of the work isdone by the subcontractor. So, the cost of a public construction project for the prime
contractor is just the expenses it pays to the subcontractor. So, the points for the prime
contractor is the diﬀerence between the amount received from the government and thepayment to the subcontractor. At last the payment to the subcontractor is made by
the prime contractor who wins the project. The payment you receives as a subject iscounted for your total point, but nothing is counted unless you are chosen as a subject.
Subession 3 proceeds in the same way as Subsession 2 except the following threepoints. (1) Subsession 3 has twenty periods. There is an intermission of one minuteafter ten periods. (2) Each of the two potential prime contractors is handled by asubject, although a computer program assigns to each potential prime contractor one
subcontractor, choosing the agent who makes the lowest bid as the subcontractor.
So, (3) at the beginning of each period, six subjects are randomly chosen. Two of
the subjects are randomly assigned to potential prime contractors, two of them are
randomly assigned to construction agents who can bid only for a designated subcontract
bidding, the remaining two are randomly assigned to construction agents who can bid
only for the other designated subcontract bidding. The payment you receives as a
subject is counted for your total point, but nothing is counted unless you are chosen asa subject (the sealed-bit first-price auction).
Bidder asymmetry by Estache and Iimi (2010): Asymmetric auctions are among24the most rapidly growing areas in the auction literature. although traditional symmetric framework is still attractive for analyzing general bidding behavior in a tractablemanner, it is not always applicable in practice because bidders are potentially heterogeneous in various dimensions. The existence of weak bidders – also referred to as fringeor entrant bidders – is particularly important from a competition policy perspective.
they can promote bidding competition and break hidden collusive arrangement amongstrong bidders–also referred to as incumbent bidders.
6.2.2

More on the Process

The subcontractor’s construction costs are independently drawn from a uniform distribution between 1,001 and 2,000. The closest example is drawing a dice. The probabilityof a two coming up is 1/6, the others also being 1/6. In the same way, the probability
that the construction costs for the subcontractor is 1,033 is 1/1,000. On the computer, the range of bidding for both potential prime contractors and construction agents is
also limited to integers that ranges from 1,001 to 2,000.
The winner of bidding is determined randomly in the case of a tie. Any periods
in any sessions should be completed in 60 seconds. When 60 seconds elapses, we urge
subjects to complete the period as soon as possible. For each period during a session, henecessary information is shown on your computer screen,. Based on this information,
6.2.3

How to Calculate Profits

If you are the potential prime contractor, the profit you make from a public construction
project isyuor profit = the amount you receive from the government−the amount paid to the subcontractor
This profit may be gained if you are awarded the contract by being the lowest bidderin the public construction project. On the other hand, if you are the subcontractor,
the profit you make from a job of a public construction project is
profit = the ayment from the prime Contractor − your construction costThis profit may be gained not only if you are the lowest bidder in the subcontraction
bidding but also if the potential prime contractor you are working with is fortunate
enough to be commissioned the public construction project.

25

6.2.4

Practice Questions

1. Suppose that you are a construction agent and your construction cost is 1,390
points. Now, you bid 1,390 points. How much profit will you gain, when you wins
the subcontract bidding?
2. Suppose that you are a construction agent and your construction cost is 1,202
points. If, in the next period, you are chosen as a construction agent again, whatis the probability of your construction cost being higher than 1,500 points?
3. Suppose that in Subsession 2 or 3, you are a subcontractor of a potential prime
contractor. The diﬀerence between your bid and your construction cost is 265
points. If, later, your potential prime contractor is commissioned a public construction project, what is your profit?
4. Suppose that in Subsession 2 or 3, you are a construction agent and your construction cost is 1,530 points. Now, you won the subcontract bidding at 1,300 points,
but your potential prime contractor lost the bidding for a public construction
project. How much profit will you make?
5. Suppose that in Subsession 2 or 3, you are a construction agent and your construction cost is 1,880 points but you won the subcontract bidding at 1,700 points.
Let’s say that the potential prime contractor you are working with was commissioned a construction project. How much profit will you make?
6. Suppose that you are a construction agent and your construction cost is 1,240
points. What is the probability of your rival construction agent having his oe her
cost of over 1,500 points?
7. Suppose that in Subsession 3, you are a potential prime contractor and yoursubcontractors bid 1,350 points and 1,504 points. How much will be the costs forthe subcontractor you choose?
8. Suppose that in Subsession 3, you are a potential prime contractor and yoursubcontractors bid 1,090 points and 1,950 points. How much will be your expense?
9. Suppose that in Subsession 3, you are a potential prime contractor and yoursubcontractors bid 1,090 points and 1,950 points. If you bid 1,057 points andwere awarded the public construction project, how much profit will you gain?
Morgan et al. (2003)

26

We study auctions where bidders have independent private values but attach a disutility to the surplus of rivals, and derive symmetric equilibria for first-price, secondprice, English, and Dutch auctions. We find that equilibrium bidding is more aggressive than standard predictions. Indeed, in second-price auctions it is optimal to bid
above one’s valuation; that is, bidding ”frenzies” can arise in equilibrium. Further,
revenue equivalence between second-price and first-price auctions breaks down, withsecond-price outperforming first-price. We also find that strategic equivalence between
second-price and English auctions no longer holds, although they remain revenue equivalent. We conclude that spiteful bidding rationalizes anomalies observed in laboratory
experiments across the four auction forms better than the leading alternatives.

References[1] Andreoni, J, Che Y-K, Kim, J (2007). An Asymmetric information about rival’s
types in standard auctions: an Experiment. Games and Economic Behavior 59,
240-259[2] Aoyagi, M (2003). Bid rotation and collusion in repeated auctions. Journal of
Economic Theory 112, 79-105[3] Bajari, P, Ye, L (2003). Deciding between competition and collusion. Review of
Economics and Statistics 85, 971-989[4] Chew, SH, Nishimura, N (2003). Revenue non-equivalence between the English andthe second-price auctions: experimental evidence. Journal of Economic Behavior
and Organization 51, 443-458[5] Cox, J, Smith, V, Walker, J (1982). Auction market theory of heterogeneous bidders. Economics Letters 9, 319-325[6] Cox, J, Smith, V, Walker, J (1988). Theory and individual behavior of first-priceauctions. Journal of Risk and Uncertainty 1, 61-99[7] Goeree, J, Holt, C, Palfrey, T (2002). Quantal response equilibrium and overbidding in private value auctions. Journal of Economic Theory 104, 247-272[8] Kagel, JH, Levin, D (2008). Auctions: Experiments. In: New Palgrave dictionaryof Economics (2nd ed). Blume LE, Derlauf, AN eds.
[9] Nakabayashi, J (2009). Procurement auctions with pre-award subcontracting.
Tsukuba Economics WP 2009-013, University of Tsukuba

27

[10] Lee, I-K (1999). Non-cooperative tacit collusion, complementary bidding and incumbency premium. Review of Industrial Organization 15, 115-134[11] Lee, I-K (2008). Favoritism in asymmetric procurement auctions, International
Journal of Industrial Organization 26, 1407-1424[12] Morgan, J, Steiglitz, K, Reiss, G (2003). Spite motive and equilibrium behavior
in auctions. The BE Journal of Economic Analysis & Polocy 2, Issue 1 (Contributions), Article 10[13] Pesendorfer, M (2000). A study of collusion in first-price auctions. Review of Economic Studies 67, 381-411[14] Porter, R, Zona, D (1993). Detection of bid rigging in procurement auctions. Journal of Political Economy 101, 518-538[15] Porter, R, Zona, D (1999). Ohio school milk markets: an analysis of bidding. Rand
Journal of Economics 30, 263-288[16] Reiss, JP, Schondube, JR (2010). First-price equilibrium and revenue equivalencein a sequential procurement auction model. Economic Theory 43, 99-141[17] Rezende, L (2009). Biased Procurement auctions. Economic Theory 38, 169-185

28