GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.54

Auctions for Public Construction with Corner-cutting

Kenju Akai, Tatsuyoshi Saijo, and Shigehiro Serizawa

May 2009

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Auctions for Public Construction with Corner-cutting
Kenju Akaia,b, *, Tatsuyoshi Saijob,† , Shigehiro Serizawab,†aJapan Society for the Promotion of Science, 1-6 Chiyoda-Ku, Tokyo 1028471, Japanb
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki,
Osaka 5670047, JapanMay 13, 2009
Abstract: This paper reports the theoretical and experimental results of auctions for
public construction in which firms cut corners. We show that winning bids and qualities of
the constructed buildings are both zero in equilibria if there are at least two firms whose
initial cash balances are zero. The experimental results support that firms with zeroinitial cash balance win and that the winning bids and the qualities of the constructedbuildings are considerably low.
JEL classification: C92; D44; L15
Key words: Corner-cutting; Public procurement; First-price auction; Experiment;*Corresponding author: k-akai@iser.osaka-u.ac.jp, Institute of Social and Economic
Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 5670047, Japan. Tel.: +81-66879-8552; Fax: +81-6-6879-8584.
†
E-mail: saijo@iser.osaka-u.ac.jp (T. Saijo), serizawa@iser.osaka-u.ac.jp (S. Serizawa)1. Introduction
Auctions are a transparent and fair method of public procurement, and are commonly
employed in the public sector. Corner-cutting is a critical issue to consider in construction contracts. In this context, corner-cutting refers to the construction of low-quality
buildings to save costs and/or time. Corner-cutting may have serious consequences inconstruction, including even the high death toll1 . However, most of the literature on auction do not take it into account. This article aims to explicitly introduce corner-cutting
into procurement auctions, theoretically investigate its eﬀect, and examine the theoreticalpredictions through experiments.
In our model, the firms chosen by auction as contractors have the option to cut corners
in construction. The more the contracting firms cut corners, that is, the more they save
construction cost, the lower the qualities of the constructed buildings, which result in
the higher probability that corner-cuttings are detected. If corner-cutting is detected,
a contracting firm is required to pay a penalty in accordance with the scale of cornercutting. However, the penalty payment is limited by the firm’s initial cash balance owing
to bankruptcy. Thus, the profit maximizing level of corner-cutting depends on the costof constructing buildings of the specified quality, penalty rates, initial cash balances, andcontract prices (winners’ bids).
We assume that there are at least two firms whose initial cash balances are zero. In
this paper, we focus on problems that will occur when the auction authorities of public
sectors do not limit participant qualification and auctions are opened to any firms. The
cash balances of firms on the brink of bankruptcy are virtually zero. If several such
firms participate in the auctions, the above assumption holds. During recessions, many
construction firms become bankrupt. Thus, if auctions in public sectors are made open to
any firms during that time, then the above assumption becomes reasonable. Even in nonrecessionary periods, statistically some construction firms go bankrupt. If the auctions
are open to any firms, the firms on the brink of bankruptcy would be more eager toparticipate in the auctions, and the assumption would be plausible.
We find that if the above assumption holds, then in equilibria, zero-initial cash balancefirms win auctions by bidding zero amount, and construct buildings of zero quality. Our
experimental results support this theoretical result, and indicate that the firms with zero
initial cash balance win and that the winning bids and the quality of the constructedbuildings are considerably low.
There are many special rules in public construction auctions to prevent corner-cutting,most of which are ignored in auction theory. For example, many public procurement authorities in Japan and European countries such as Belgium, Italy, Portugal, Spain, andGreece set a minimum price to exclude or detect abnormally low tenders. Alternatively,
only designated bidders–as deemed qualified on the basis of factors such as locality, technological ability, and initial cash balance–are invited to procurement auctions. Althoughsuch special rules curb competition in auctions and are often criticized for aﬀecting thetransparency and fairness of auction, our results suggest the necessity of these special
rules in public procurement auctions.
1
For example, the New York Times (September 4, 2008, China Admits Building Flaws in Quake)
reported the following: “Chinese government committee said on Thursday that a rush to build schools
during the country’s recent economic boom might have led to shoddy construction that resulted in thedeaths of thousands of students during a devastating earthquake in May. It is well known that construction
firms and other companies often cut corners in China’s rapidly growing economy.”2

Calveras et al. (2004) show that when cost is common but uncertain for firms, firms
with a small amount of initial cash can make a profit by bidding low and declaring
bankruptcy if the cost is found to be high in the second-price auction. By conducting
experiments, Cox et al. (1996) discover that too-low bids in the first-price auction underpost-auction cost uncertainty lead to cost overruns. These articles also suggest the necessity of the above special rules in public procurement auctions. However, to the best of
our knowledge, our article is the first to introduce corner-cutting into an auction modeland to analyze its eﬀect.
The remainder of the paper is organized as follows. Section 2 develops the theoreticalmodel. Section 3 analyzes the equilibrium. Section 4 details the experimental procedures.
Section 5 analyzes the results, and section 6 summarizes the conclusions.
2. Model Description and Notations
There are n construction firms, from which a public sector chooses a contractor forconstruction. Each firm i has an initial cash balance wi . Each firm i also has a “propercost” di . This means that the firm needs to spend di to construct a building of the quality
specified by the public sector. Firms’ initial cash balances and proper costs represent
their financial conditions and technological competence, respectively.
The public sector employs the first price auction in choosing a contractor. Each firmi submits its bid bi to the procurement authority of the public sector. The firm with theminimum bid wins and is awarded the contract. Ties are broken with equal probability.
The contract price is the winner’s bid.
The firm chosen as a contractor, say firm i, does not necessarily spend its proper coston construction. Instead, the contractor might “cut corners” and spend a smaller amount.
Denote by ci the actual cost firm i spends on construction. We assume that the scaleof corner-cutting is represented by di − ci , and the quality of the constructed building isdetermined by qi = ci /di . For example, suppose that di = 100, but firm i spends only
ci = 80 for construction. Then, the scale of corner-cutting is 20, and the quality is 0.8.
After the contractor constructs a building, the procurement authority investigates thequality of the building. The lower the quality of the constructed building, the higher the
probability of the authority detecting corner-cutting. If qi = 1, that is, if the contractor
does not cut corners, then the probability of detection is zero. Conversely, if qi = 0,
that is, if the contractor does not spend cost for construction at all, the probability ofdetection is one. For simplicity, we assume that the probability that the authority detects
corner-cutting is 1 − qi = (di − ci )/di .
If the authority detects corner-cutting, it imposes a penalty on the contractor. The
greater the scale of corner-cutting, the larger is the amount of penalty. For simplicity, we
assume that the penalty is proportional to the scale of corner-cutting, and the penalty
rate is given by r > 1. That is, if the scale of corner-cutting is di − ci , the penalty isr · (di − ci ).
If the contractor who has cut corners and has been detected has enough cash balance
to pay the penalty–that is, if penalty r · (di − ci ) is less than or equal to the contractor’s
cash balance, wi + bi − ci , at that point of time–then he pays the penalty. Otherwise,
the contractor goes bankrupt and pays only the cash balance wi + bi − ci .
The contract procedure in the public sectors can be summarized as follows.
Stage 1 (Auction Stage): Each firm submits bid bi to the authority. The firm with theminimum bid wins and is chosen as the contractor. The contract price is the winning bid.
3

Stage 2 (Construction Stage): The contractor determined in Stage 1, say firm i, receives the contract price bi and chooses spending ci for construction.
Stage 3 (Investigation Stage): The procurement authority investigates if the contractor
cuts corners in construction. The probability of corner-cutting being detected is (di −ci )/di .
Stage 4 (Penalty Stage): If corner-cutting di − ci is detected in stage 3, a penaltyr · (di − ci ) is imposed on the contractor. If wi + bi − ci ≥ r · (di − ci ), the contractor paysr · (di − ci ). Otherwise, he goes bankrupt and only pays wi + bi − ci .
The profit of a firm is defined as its final cash balance minus its initial cash balance.
It is computed as follows: Suppose firm i bids bi . (i) If firm i does not win the auction,then its final cash balance is equal to its initial cash balance, and its profit is zero. (ii)
If firm i wins the auction, spends ci on construction, and corner-cutting is not detected,
then its final cash balance is wi + bi − ci , and its profit is bi − ci . (iii) If firm i wins, spends
ci on construction, and corner-cutting is detected but it does not go bankrupt, then the
final cash balance is wi + bi − ci − r · (di − ci ), and the profit is bi − ci − r · (di − ci ).
(iv) If firm i wins, spends ci on construction, and corner-cutting is detected and it goesbankrupt, then the final cash balance is 0 and its profit is −wi .
3. Theoretical Analysis
We analyze firms’ behavior backward. In other words, we first analyze their behavior
in Stage 2 and then in Stage 1.
3.1. Contractor’s choice of spending
Firms enter Stage 2 only if they win the auction in Stage 1. Thus, the firms in Stage 2
are already contractors. We analyze how much a contractor spends for construction given
its initial cash balance wi and contract price bi . In this subsection, since we focus on the
behavior of one contracting firm and ignore the others, we omit appending subscripts to
wi , di , bi , and ci for simpler notation.
When corner-cutting is detected, and the deficit is greater than the limit, i.e., c + r ·(d − c) − b > w, the contractor becomes bankrupt. Thus, if corner-cutting is detected,
the constructor’s payoﬀ is max{b − c − r · (d − c), −w}.
When the contractor spends the cost c, since the probability of the detection is 1−d/c,
his expected payoﬀ is
π=

c
d−c
· (b − c) +· max{b − c − r · (d − c), −w}.
dd

We assume that the firms are risk-neutral and seek to maximize the expected profit π as
defined above. Note thatb − c − r · (d − c) ≶ −w ⇔ c ≶ [r · d − (b + w)]/(r − 1).
Thus, a contractor goes bankrupt when corner-cutting is detected, if and only if its spending c is less than c ≡ [r · d − (b + w)]/(r − 1).
Given w, d, and b, let c∗ (w, d, b) be the optimal spending for w and b, i.e., the spendingthat maximizes the expected profit, and let Π(w, d, b) = π(c∗ (w, d, b)).
Proposition 1 below characterizes the optimal cost and maximal expected profit given
b and w.
4

√
Proposition 1: Let b = 2d − w − d/ r. Then,½(b + w)/2
if b ≤ b∗c (w, d, b) =(1 − 1/2r) · d otherwise,½[(b + w)2 − 4dw] /4d if b ≤ b
Π(w, d, b) =b − d + d/4r
otherwise.
The proof is provided in Appendix. Proposition 1 states the following: (i) If thecontract price b is smaller than threshold level b, then the contractor’s optimal choice c∗does not depend on its proper cost d. (ii) On the other hand, if the contract price b isgreater than b, then the contractor’s optimal choice c∗ does not depend on its initial cash
balance w or contract price b. A contractor chooses to go bankrupt when detected, if andonly if b < b.
Note that at b = b = 2d − w − √dr ,
¤
d
1 £
b+w
1
· (b + w)2 − 4dw = b − d + , and< (1 − ) · d.
4d
4r
2
2r

That is, the contractor’s maximized expected profit Π(w, d, b) is continuous with respect
to b, but the optimal spending c∗ (w, b) is not.
We consider a firm’s bid b0 such that if the firm wins the auction by bidding b0 , his
expected profit will be zero in Stage 2. That is, b0 is a bid such that Π(w, d, b0 ) = 0.
We term such a bid b0 a “zero-profit bid.” If d −√d/4r ≥ b, then b0 = d − d/4r, and if
d − d/4r < b, then by (b0 + w)2 − 4dw = 0, b0 = 2 dw − w. Note that¡ √¢2d − d/4r R b ⇔ w R d · 2 r − 1 /4r.

Since Π(w, d, b) is increasing in b, Π(w, d, b) R 0 ⇔ b R b0 . Therefore, we have Lemma 1
below.
√
2
Lemma 1: (i) If w ≥√d · (2 r − 1) /4r, then b0 = d − d/4r, and if w < d ·√2(2 r − 1) /4r, then b0 = 2 d · w − w. (ii) Π(w, d, b) R 0 ⇔ b R b0 .
In an ordinal auction model for public construction, i.e., a model in which firms haveno option of corner-cutting, once a firm wins the auction in Stage 1, it is required to spend
its proper cost in Stage 2; hence, the distinction between a firm’s proper cost and the costit actually spends is meaningless. In the ordinal model, the expected profit of a firm is
positive if and only if it wins the auction by bidding greater than its cost. (ii) of Lemma
1 implies that zero profit bids have similar properties in our model where firms have theoption of corner-cutting. This fact plays an important role in analyzing the equilibria of
the auction in Stage 1.
3.2. Equilibria
In this subsection, we analyze firms’ bidding behavior in Stage 1 by employing theresults of subsection 3.1. We assume that firms know only their own initial cash balancesand proper costs, but not those of the others. We analyze firms’ bidding behavior in Stage
1 in the framework of incomplete information games.
Since initial cash balances and proper costs vary, we depict firms’ bidding behaviors
as bidding functions. A bidding function of firm i is a function bi (·, ·) of its initial cash
balance wi and its proper cost di . bi (wi , bi ) denotes firm i’s bid in Stage 1 when its initial
cash balance is wi and its proper cost is di .
5

We denote the initial cash balance profile by w = (w1 , . . . , wn ), the proper cost profile
by d = (d1 , . . . , dn ), and the bid function profile by b(·, ·) = (b1 (·, ·), . . . , bn (·, ·)). Further,
W denotes the class of initial cash balance profiles, and D the class of proper cost profiles.
For each firm i, let Wi be the projection of W
Q on the ith coordinate,
Q Di be the projectionof D on the ith coordinate, and let W−i = j6=i Wj and D−i = j6=i Dj .
Let Pr(·) be a probability distribution on W ×D. That is, Pr(W ×D) = 1, and further,
for an event X ⊂ W × D, Pr(X) is the probability of the event, i.e., the probability that(w, d) ∈ X. For firm i, given its initial cash balance wi and proper cost di , Pr−i (·; wi , di ) is
the conditional probability on W−i ×D−i . That is, Pr(W−i ×D−i ) = 1, and further, for an
event X−i ⊂ W−i × D−i , Pr−i (X−i ; wi , di ) is the probability of the event of X−i under thecondition that firm i’s initial cash balance is wi and its proper cost is di . The conditional
expected payoﬀ of firm i is E(bi , b−i (·, ·); wi , di ) when firm i bids bi , the other firms follow
b−i (·, ·), and firm i’s initial cash balance and proper cost are wi and di , respectively.
The Bayesian Nash equilibrium defined below is a standard equilibrium concept ofincomplete information games.
Definition: A bid function profile b(·, ·) = (b1 (·, ·), . . . , bn (·, ·)) is a Bayesian Nashequilibrium if for all firm i, all its cash balance wi , all its proper cost di , and all its bid bbi ,E(bi (wi , di ), b−i (·, ·); wi , di ) ≥ E(bbi , b−i (·, ·); wi , di )In this paper, we pay a special attention to the event that there are at least two firms
whose initial cash balances are zero. This event is formally defined as W ∗ × D,
where W ∗ = {w ∈ W : ∃i & ∃j such that i 6= j and wi = wj = 0}.
In Proposition 2 below, we assume that the probability of this event is one, that is,
Pr(W ∗ × D) = 1.
To state Proposition 2, we introduce a zero winning-bid profile. This is a bid function
profile b∗ (·, ·) = (b∗1 (·, ·), . . . , b∗n (·, ·)) such that for all firm i, all initial cash balances wi ,and all proper costs di , if wi = 0, b∗i (0, di ) = 0, and if wi > 0, b∗i (0, di ) > 0. Note that if theabove assumption holds and firms follow a zero winning-bid profile, then with probability
one, the winner is a firm with a zero initial cash balance and the winning bid is zero.
Further, note that if the winner is a firm with a zero initial cash balance and the winningbid is zero, then it follows that in Stage 2, the winner spends nothing for construction,and so the quality of the constructed building is zero.
Proposition 2: Assume that there are at least two firms whose initial cash balances
are zero with probability one. Then, a zero winning-bid profile is a Bayesian Nash equilibrium. At this equilibrium, the winner is a firm with a zero initial cash balance, and thewinning bid and the quality of the building constructed by the winner are both zero.
The proof is simple. By Lemma 1, the zero-profit bids of firms with zero initial cash
balance are zero, and those of others are positive. At a zero winning-bid profile, theconditional expected profits of all firms are zero. A firm with a zero initial cash balancecannot win by a positive bid since another firm else bids zero. Thus, firms with zero
initial cash balance cannot obtain a greater conditional expected profit by deviating fromthe zero winning-bid profile. If a firm with a positive initial cash balance bids zero,then it wins with positive probability, but winning by zero bid makes its expected payoﬀ
negative. Thus, firms with positive initial cash balances do not deviate either from thezero winning-bid profile.
6

It is worthwhile to remark the robustness of the equilibria of Proposition 2. Typically,
Bayesian Nash equilibria of the first price auction of Bayesian models depend on the detailsof the prior probability distribution of private information. In addition, the symmetry of
the prior distribution is often assumed to derive symmetric equilibria. On the other hand,the equilibria of Proposition 2 do not depend on such details. In this sense, the equilibria
of Proposition 2 are more robust than Bayesian Nash equilibria. This robustness is rather
similar to that of ex-post Nash equilibrium, another equilibrium concept of incomplete
information games.
Definition: A bid function profile b(·, ·) = (b1 (·, ·), . . . , bn (·, ·)) is an ex-post Nashequilibrium if for all initial cash balance profile w = (w1 , . . . , wn ), all proper cost profiled = (d1 , . . . , dn ), for all firm i, and all its bid bbi ,ui (b(w, d); wi , di ) ≥ ui (bbi , b−i (w−i , d−i ); wi , di ).

The concept of ex-post Nash equilibrium is independent of the probability distribution of private information such as initial cash balances and proper costs. In other words,
ex-post Nash equilibria are Bayesian Nash equilibria for any probability distribution ofprivate information. Similarly, although Proposition 4 requires the assumption of a probability of one for the event that there are at least two firms whose initial cash balances arezero, the zero winning-bid profiles are the Bayesian Nash equilibria for any probability
distribution of private information that satisfy these assumptions. In the next section, we
provide experimental procedures to examine Proposition 2.
4. Experimental Procedures
The experiment was consisted of two sessions. It was programmed and conducted withthe software z-Tree (Fischbacher, 2007). The subjects were undergraduate and graduate
students from Osaka University. They were invited to sign up at the designated websites
through flyers posted around campus and email solicitations sent to those students who
had signed up for other experiments before. None of the subjects participated in morethan one session.
Upon arrival, the subjects were seated at separate computer terminals, and no communication was permitted throughout the session. The subjects listened to prerecorded
instructions, while simultaneously following the same from their own copies.2 In the instructions, they were told that their roles were those of producers producing a good eachand selling them to the experimenter3 . The subjects were prohibited from asking anyquestions in verifying their understanding of the procedures in an examination.
The top twenty subjects who passed the examination participated in the subsequent
proceedings4 . After we announced the correct answers of the examination to the subjects,
the identification numbers of producers were determined through a lottery.
Each session consisted of 16 periods. At the beginning of each period, the subjects
are automatically assigned into five groups, each comprising four subjects5 . Each subject
received his ready reckoner of the all payoﬀs with respect to all his bid and costs. Eachsubject knew only his own initial cash balances and proper costs from that reckoner. We
2

Instructions are available from the authors upon requests.
We use "producers" instead of firms in the experiment.
4
In each session, we invited more than 20 subjects including a few extra subjects in order to ensure
the necessary number.
5
The instructions are available from the authors upon request.
3

7

set initial cash balances, wi , as 0, 0, 50, and 100, and the proper cost di , as 24, 30, 36,
and 42 for each group. Throughout the 16 periods, every subject was assigned to all
combinations of 4 initial cash balances and 4 proper costs, but this fact was not informed
to the subjects. The subjects entered their proper costs and initial cash balances into theirrecord sheets distributed along with the instructions. Apart from their own initial cash
balances and proper costs, they are informed that each group has at least two producers
whose initial cash balances were zero in the instruction.
In each group, the first-price auction was implemented. Subjects were allowed to enter
their actual costs and bids into the interface and calculate their profits and probabilities
of corner-cutting being detected as many times as desired before they made their final
decisions. They, however, decided their costs and bids simultaneously within 6 minutes.
The subjects were not allowed to change their costs after the winner was decided. It was
mandated that their bids would be no more than the ceiling price of 58 set by us, andthat their actual costs would be no more than their proper costs. Further, the costs weremandated to be no more than the sum of the bids and initial cash balances so as to avoid
bankruptcy before the experimenter investigated the quality of the produced good.
The penalty ratio, r, is 2. When the winner was detected to have cut corners, his final
cash balance was equal to his initial cash balance plus bid minus his cost and penalty if
he was able to pay the all amounts of penalty, and it was zero if he was not. Winner’s
profits were his final cash balance minus initial cash balance; those of others were zero.
After the winner was decided, each subject’s computer screen displayed whether or
not he won along with his own profits. The subjects enter these results into their record
sheets.
The subjects were paid in cash in accordance with their total experimental points
under the conversion rate of 7 yen (8 cents)6 for each point. To cover the loss of thesubjects, we added 40 points at the end of each period. Each session lasted roughly 3
hours. The average payments to subjects were 4,554 yen ($50.6). No one had negative
total experimental points.
5. Experimental Results
First, we focus on the market outcomes and examine Proposition 2. Table 1 summarizes the means and standard errors of qualities of produced goods, winning bids, winners’
cost spending, and the ratio of the winning of producers with zero initial cash balance. On
average, the quality of produced goods is less than 0.4. the ratio of the winning of producers with zero initial cash balance is more than 0.9. These results suggest that producers
with zero initial cash balance win and cut corners in large scale. Both of the qualities
of produced goods and winning prices are not significantly diﬀerent between sessions inboth t-tests (two-tailed p-values are 0.20 and 0.35, respectively) and Wilcoxon rank-sum
tests (two-tailed p-values are 0.17 and 0.52, respectively).
––––––––––––—
Table 1 is around here.
––––––––––––—
6$1 = 90 yen at that time.

8Both the qualities of produced goods and winning prices, however, are higher than thetheoretical prediction of zero. Next, we focus on the dynamics of these values and examine
whether the learnings of subjects in the laboratory induce the theoretical prediction.
Figure 1 presents all the qualities of the produced goods and the OLS regression linesof the qualities of the produced goods for the periods in each session and for the twosessions taken together. In each figure, circles and diamonds represent the qualities of
the goods produced by producers with zero initial cash balance and those with positive
initial cash balances, respectively. The quality of produced goods, however, are censoredvariables between 0 and 1, inclusively; hence, we employ a Tobit regression of all qualitiesof the produced goods on periods. Table 2 summarizes the results of this regression. The
coeﬃcient on period is negative and significant at the 1% level in both sessions and forthe two sessions taken together. According to F-tests of the hypothesis of no changes in
the intercepts and the coeﬃcients of periods across the two sessions, both of them are
not significantly diﬀerent (two-tailed p-values are 0.212). Therefore, we conclude that thequalities of the produced goods tend toward the theoretical prediction of zero as subjects
learn more.
––––––––––––––––Figure 1 and Table 2 are around here.
––––––––––––––––—
Figure 2, on the other hand, presents all the winning prices and the OLS regression
lines of the winning prices on the periods in each session and the two sessions taken
together. All winning prices are less than 30. Winning prices are also censored variables
between 0 and 58 of the ceiling price, inclusively, and hence, we employ a Tobit regressionof all winning prices on periods. Table 3 summarizes the results of this regression. The
coeﬃcient on period is negative and significant at the 1% level in both sessions and inboth taken together. According to the F-tests of the hypothesis of no changes in theintercepts and the coeﬃcient of period across sessions, both sessions are not significantly
diﬀerent (two-tailed p-values are 0.246). Therefore, we conclude that the winning prices
tend toward the theoretical prediction of zero as subjects learn more.
––––––––––––––––––
Figure 2 and Table 3 are around here.
––––––––––––––––––
Proposition 2 also suggests that the proper costs of producers with zero initial cash
balance do not aﬀect both the winning prices and the qualities of the produced goods.
In order to examine this suggestion, we add the proper cost as a variable to the above
Tobit regression of winning prices and that of qualities of the produced goods and conduct
separate Tobit regressions. Table 4 summarizes the results of these regressions. Since there
are no significant diﬀerences in the winning prices and the qualities of the produced goods
between sessions as described in the F-tests above, we use pooled data across sessions ineach regression. In these regressions, the coeﬃcients on proper cost are not significant
9

in the winning prices, but are negative and significant at the 1% level in the qualitiesof the produced goods. These findings suggest that the proper costs of producers withzero initial cash balance do not aﬀect the winning prices but aﬀect the qualities of the
produced goods in the laboratory.
––––––––––––—
Table 4 is around here.
––––––––––––—
The average of the qualities of produced goods for the proper costs of 24, 30, 36, and
42 are 0.41, 0.37, 0.27, and 0.24, respectively. In the experiment, the subjects must choose
integer costs, so that producers with zero initial cash balance and with higher proper costs
have more choices with regard to their cost spending. Since the quality is inversely related
to proper cost, the higher the proper cost, the lesser is the quality. Our results suggestthat theoretically non-binding proper costs may aﬀect the qualities of the produced goods.
It is similar to the results of the market experiments in Smith and Williams (1981), Isaac
and Plott (1981), Coursey and Smith (1983), and Gode and Sunder (2004), who discoverthat theoretically non-binding price controls also aﬀect trading prices.
Next, we focus on individual behaviors and examine the relation between bids andcosts as described in Proposition 1. Table 5 summarizes the results of OLS regressionof costs on bids for each proper costs in the region bi < b. Since there are only data ofproducers with zero initial cash balance on this region, we set wi = 0. The coeﬃcients on
price are more than 0.5 and significant at the 5% level for each proper cost. According
to the F-test of the hypothesis that ci = bi /2, the experimental results are significantly
diﬀerent from the risk-neutral theoretical prediction for each proper cost. This result
suggests that subjects spend more than the theoretical risk-neutral level relative to thebid if bi < b.
––––––––––––—
Table 5 is around here.
––––––––––––—
Table 6 summarizes, on the other hand, the results of the OLS regression of costs onbids for each proper costs on the region bi ≥ b. The coeﬃcient on price is more than
0 and significant at the 5% level for the proper costs 24 and 42. According to the Ftest of the hypothesis that ci = 3di /4, the experimental results are significantly diﬀerent
from the risk-neutral theoretical prediction for each proper cost. In this region, however,
the adjusted R2 is very low. Therefore, we need more experiments to obtain a precise
conclusion with regard to whether or not the subjects are risk averse.
––––––––––––—
Table 6 is around here.
––––––––––––—

10

6. Conclusions
In this paper, we analyzed corner-cutting by firms who participate in procurement
auctions. Theoretically, in the first-price auction, if there are at least two firms with zero
initial cash balance, the winning bids and the qualities of the constructed buildings in theBayesian Nash equilibria are both zero. In the laboratory, we find that (i) the winners
are firms with zero initial cash balance, (ii) the qualities of the constructed buildings
are considerably less than 1 and decrease as periods proceed, (iii) winning prices are
considerably less than their proper costs and decrease as periods proceed, (iv) the proper
costs of firms with zero initial cash balance do not aﬀect the winning prices but aﬀect thequalities of the constructed buildings, and (v) cost spendings relative to bids are higher
than the risk-neutral predictions.
The decreasing qualities of the constructed buildings and winning prices are consistent
with Dufwenberg and Gneezy (2002), who find that winning prices converge to the Nashoutcomes when they inform the subjects of which participant wins without uncertainty of
the cost. Our results, however, do not reach the Bayesian Nash outcome of zero in boththe qualities of the constructed buildings and winning prices. Upon examining the relation
between cost spendings and bids in Proposition 1, the risk attitudes of subjects is likely
to cause cost spending to diverge from theoretical level. Although more experiments areneeded to investigate why subjects spend and bid higher than the risk-neutral predictions,
we can conclude that firms with zero initial cash balance win and cut corner in considerable
scale.
This paper is a first step of analyzing corner-cutting. As we pointed out in the introduction, auction authorities prescribe special rules to prevent corner-cutting, such as
setting minimum prices in order to exclude the abnormally low bids and stipulating thenecessary levels of initial cash balances for firms. Although our findings suggest thatfirms cut corners in considerable scale if no such regulation exists, the eﬀects of theseregulations are yet to be assessed. Thus, a next step is to evaluate those regulations. Our
goal is to design best regulation to maximize social benefits in models where firms cut
corners.
Acknowledgements
This research was support by the Japanese Ministry of Education, Culture, Sports,
Science and Technology (the COE program of Behavioral Macrodynamics based on Surveys and Experiments; the Grant-in-Aid for Scientific Research on Priority Areas). We
wish to acknowledge the helpful comments and suggestions of Ryuji Kutsuzawa, Kosuke
Oya, and participants at the meeting of the Society for Social Choice and Welfare and at
the seminar at Kyoto University. We also thank Keiko Aoki, Takanori Kudo, and Kenta
Onoshiro for assistance conducting the experiment.
References
Calveras, A., Ganuza, J., Hauk, E., 2004. Wild Bids. Gambling for resurrection in
procurement contracts. Journal of Regulatory Economics 26, 41-68.
Coursey, D., Smith, V.L., 1983. Price controls in a posted oﬀer market. American
Economic Review 73, 218-221.
Cox, J. C., Isaac, R. M., Cech, P., Conn, D., 1996. Moral Hazard and Adverse
Selection in Procurement Contracting. Games and Economic Behavior 17, 147-176.
Dufwenberg, M., Gneezy, U., 2002. Information disclosure in auctions: an experiment.
Journal of Economic Behavior & Organization 48, 431—444.
11

Fischbacher, Urs., 2007. z-Tree: Zurich Toolbox for Ready-made Economic Experiments, Experimental Economics 10(2), 171-178.
Gode, D. K., Sunder, S., 2004. Double auction dynamics: structural eﬀects of nonbinding price controls. Journal of Economic Dynamics & Control 28, 1707-1731.
Plott, C. R., Salmon, T. C., 2004. The simultaneous, ascending auction: dynamics ofprice adjustment in experiments and in the UK3G spectrum auction. Journal of Economic
Behavior and Organization 53, 353—383.
Smith, V.L., Williams, A.W., 1981. On nonbinding price controls in a competitivemarket. The American Economic Review 71, 467-474.
Appendix
Proof of proposition 1: First, we compute the maximizer c∗ of π on the two
subdomains, Subdomain 1: {c ≥ c} and Subdomain 2: {c ≤ c}.
Subdomain 1:
On this subdomain, since b − c − r · (d − c) ≥ −w,cd−c· (b − c) +· {b − c − r · (d − c)}dd2r − 1dr· d]2 + b − d += − · [c −d2r4rπ(c) =d· d of this quadratic function, we have: π(c1 ) = b − d + 4r.
At the singular point c1 = 2r−1
2r
Note
r
b+w
3r − 1
2r − 1c1 R c ⇔·d−(·d−)R0⇔bR· d − w.
2r
r−1
r−1
2r

Therefore, by letting b1 ≡ 3r−1
· d − w, we have:2r½
c1 = 2r−1· d if b ≥ b1
2r
arg max{π(c) : c ≥ c} =cotherwise,½
db − d + 4r
if b ≥ b1
max{π(c) : c ≥ c} =
r
2r−1
d
2
− d · [c − 2r · d] + b − d + 4r otherwise.
Subdomain 2:

On this subdomain, since b − c − r · (d − c) ≤ −w,cd−c· (b − c) −
·w
d
d
∙
¸2
¤
1
1 £
b+w
= − c−+· (b + w)2 − 4dw .
d24dπ(c) =At the singular point c2 =[(b + w)2 − 4dw]. Note
c2 R c ⇔b+w
2of this quadratic function, we have: π(c2 ) =

r
b+w
2r
b+w
−(
·d−
)R0⇔bR· d − w.
2
r−1
r−1
r+1

2r
Therefore, by letting b2 ≡ r+1· d − w, we have:arg max{π(c) : c ≤ c} =12½

c2 if b ≤ b2
c otherwise,1·
4dmax{π(c) : c ≤ c} =
Note:

½ 1

· [(b + w)2 − 4dw]
4dc
· (b − c) − d−c·wddif b ≤ b2
otherwise.

3r − 1(r − 1)22r· d − w) − (· d − w) =
· d.
r+1
2r
2r(r + 1)
Thus, by r > 1 and d > 0, b2 > b1 . This implies that we have, Case A: b ≤ b1 < b2 , Case
B: b1 < b < b2 , or Case C: b1 < b2 ≤ b. In the following, we compute the maximizer of π
in each case.
1
Case A:
Since c1 < c and c2 ≤ c holds, max π(c) = π(c2 ) = 4d
· [(b + w)2 − 4dw].
dCase B:
Since c2 < c < c1 holds, max π(c) = π(c1 ) = b − d + 4r
or max π(c) =12π(c2 ) = 4d · [(b + w) − 4dw].
We need to compute which of π(c1 ) or π(c2 ) is bigger. Note
¶
µ
1 −1
d2
2
2
2
.
π(c1 ) − π(c2 ) = d · 4bd − 2bw + 4dw − b − 4d − w +4rb2 − b1 = (Thus, by d > 0,d2π(c1 ) R π(c2 ) ⇔ 4bd − 2bw + 4dw − b − 4d − w +
R 0.
r
2

2

2

Also note
4bd − 2bw + 4dw − b2 − 4d2 − w2 +d2d2
= − (b − (2d − w))2 + .
rr
2The solutions of the equation − (b − (2d − w))2 + dr = 0 are b = (2d − w) ± √dr . Thus,
4bd − 2bw + 4dw − b2 − 4d2 − w2 +ddd2
≥ 0 ⇔ 2d − w − √ ≤ b ≤ 2d − w + √ .
rrr

Therefore, we have:ddπ(c1 ) ≥ π(c2 ) ⇔ 2d − w − √ ≤ b ≤ 2d − w + √ .
rrNote that

By d > 0,

µ
¶
µ
¶
1
r
d
− b2 = d · √ − 2
2·d−w+ √
+2 .
r+1
r
r
r
1
d
+ 2 ≥ 0.
2 · d − w + √ ≥ b2 ⇔ √ − 2
r+1
r
r

r
+ 2 > 0, and so b2 < 2d − w + √dr holds. Also note
By r > 1, √1r − 2 r+1
¶
µ
d √
d
− b1 =
2d − w − √· ( r − 1)2 > 0.
2rr

Thus, 2d − w − √dr ≥ b1 . Also note
¶
µ
√
d
d
√ · (r − 2 r + 1).
=
b2 − 2d − w − √r(r + 1) r
13

By d > 0 and r > 1,√db2 ≥ 2d − w − √ ⇔ r − 2 r + 1 ≥ 0.
r√√
d
By r > 1, dr(r − 2 r + 1) = 1 − √1r > 0. Thus, since, r − 2 r + 1 = 0 at r = 1,b2 > 2d − w − √dr . Accordingly, we have:ddb1 < 2d − w − √ < b2 < 2d − w + √ .
rrThis implies that in Case B, we have:dπ(c1 ) ≥ π(c2 ) ⇔ 2d − w − √ ≤ b.
r
Therefore,
max π(c) =Case C:½

1π(c2 ) = 4d
· [(b + w)2 − 4dw] if b ≤ 2d − w − √drdπ(c1 ) = b − d + 4rotherwise.

dSince c2 ≥ c and c1 > c holds, max π(c) = π(c∗ ) = b − d + 4r
.

14

QED

Table 1. Market overviews
SessionRatio. (producers

Qualities of theWinning price Winner’s costproduced goods

without initial
cash balance win)

No. ofobs.

1

0.37 (0.02)

16.20 (0.49)

10.45 (0.45)

0.94

80

2

0.33 (0.02)

16.84 (0.47)

9.93 (0.52)

0.96

80

total

0.35 (0.01)

16.52 (0.34)

10.19 (0.34)

0.95

160

Table 2. Tobit regression of winners’ qualities on periods# Left-# Right-censoredcensored80

00–0.01*** (0.00) 0.09

80

0

0

–0.01*** (0.00) 0.15

160

0

0

Adjusted

Session Intercept

Period10.51*** (0.03)–0.02*** (0.00) 0.222

0.43*** (0.04)

total

0.47*** (0.03)

2R

No. of obs.

Note: Standard errors are in parentheses. Adjusted R2 is the result of the OLS regression. *, **, and*** denote significance at the 10%, 5%, and 1% levels, respectively.

Table 3. Tobit regression of winning prices on periods
Session Intercept

PeriodAdjusted
2

R

No. of obs.

# Left-# Right-censoredcensored1

20.77*** (0.84) –0.46*** (0.09) 0.41

80

0

0

2

20.77*** (0.84) –0.46*** (0.09) 0.25

80

0

0

total

21.06*** (0.57) –0.53*** (0.06) 0.33

160

0

0

Note: Standard errors are in parentheses. Adjusted R2 is the result of the OLS regression. *, **, and*** denote significance at the 10%, 5%, and 1% levels, respectively.

Table 4. Effect of proper cost
Intercept

PeriodPropercost

20.86*** –0.53***0.01(1.36)(0.06)(0.04)

Qualities of the

0.74***–0.01***-0.01***

produced goods(0.05)(0.00)(0.00)

Winning prices

Adjusted R2

No. of # Left-# Right-obs.

censored censored

0.33

160

0

0

0.28

160

0

0

Note: Standard errors are in parentheses. Adjusted R2 is the result of the OLS regression. *, **, and*** denote significance at the 10%, 5%, and 1% levels, respectively.

16

Table 5. Relation between costs and bids if b < b
Propercost

F-statistics
Intercept

Price(price=0.5,
Intercept=0)

Adjusted No. of # Left-# Right-

2

R

obs.

censored censored24–0.78 (1.19)

0.62*** (0.07) 8.69***

0.49

78

0

0

30

–1.61 (1.55)

0.72*** (0.08) 26.87***

0.51

80

0

1

36

–0.74 (1.19)

0.71** (0.05)

0.67

80

0

0

42

–4.27*** (1.30) 0.87*** (0.06) 58.00***

0.72

80

0

0

54.62***
2

Note: Standard errors are in parentheses. Adjusted R is the result of the OLS regression. *, **, and*** denote significance at the 10%, 5%, and 1% levels, respectively.

Table 6. Relation between costs and bids if b ≥ b
Propercost

F-statistics
Intercept

Price(price=0,Intercept=3d/4)

Adjusted No. of # Left-# Right-

2

R

obs.

censored censored24

13.18***(1.84) 0.23***(0.07) 10.09***

0.08

82

0

10

30

19.25***(2.51) 0.15*(0.07)

6.05***

0.01

80

0

8

36

24.58***(3.57) 0.14*(0.09)

8.69***

0

80

0

11

42

24.28***(5.93) 0.28**(0.13)

17.26***

0.04

80

0

19

2

Note: Standard errors are in parentheses. Adjusted R is the result of the OLS regression. *, **, and*** denote significance at the 10%, 5%, and 1% levels, respectively.

17

Figure 1. Qualities of the produced goods
Session 1

Session 2

Total

The quality of the produced goods

1
.9
.8
.7
.6
.5
.4
.3
.2
.1
0
0

5

10

15

0

5

10

15

0

5

10

15

PeriodProducers with zero initial cash balance

Producers with positive initial cash balance

OLS regression line

Figure 2. Winning prices

Session 1

60
58

Session 2

Total

50

Winning price

40

30

20

10

0
0

5

10

15

0

5

10

15

0

5

10

15

PeriodProducers with zero initial cash balance

Producers with positive initial cash balance

OLS regression line18