Discussion Paper No. 743

AN EXPERIMENTAL STUDYOF PROCUREMENT AUCTIONSWITH ENDOGENOUS MINIMUM PRICES
Kenju Akai
Tatsuyoshi Saijo
Shigehiro Serizawa

June 2009
Revised July 2010

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

An Experimental Study of Procurement Auctions with
Endogenous Minimum Prices‡
Kenju Akaia, *, Tatsuyoshi Saijoa,y , Shigehiro Serizawaa,ya Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaragi, Osaka
5670047, Japan
Abstract
Several European countries and many Japanese local governments began including endogenous minimum prices (EMPs) in rst-price auctions (FPAs) in their public procurements. The
EMP is calculated based on its relation to the average of all bids or to some lowest bids. Any
bid lower than the EMP is considered abnormally low and is excluded from the procurement
procedure. Producers who join this new auction institution have the incentive to raise their bids
and pull up the EMP in order to exclude others. A theoretical analysis reveals that the EMP
does not affect winning bids but changes the Nash equilibria of the standard FPA that does nothave any minimum prices. A laboratory analysis reveals that the winning bids of this new auction institution (i) are close to the production cost and coincide with those of the standard FPA
under the identical cost condition and (ii) are higher than the lowest production cost and thoseof the standard FPA under our different cost condition when subjects' identi cations and bids
are revealed.
JEL classi cation: C92; D44; L15
Key words: Public procurement; First-price auction; Experiment; Abnormally low tender;
Endogenous minimum price‡ This is revised version of "An Experimental Study of Japanese Procurement Auctions with

Endogenous Minimum Prices" published in ISER Discussion Paper No. 743.
*Corresponding author: k-akai@iser.osaka-u.ac.jp, Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaragi, Osaka 5670047, Japan. Tel.: +81-6-68798552; Fax: +81-6-6879-8584.
y E-mail: saijo@iser.osaka-u.ac.jp (T. Saijo), serizawa@iser.osaka-u.ac.jp (S. Serizawa)1. I NTRODUCTION
In recent public procurements, several European countries and many Japanese local governments have introduced minimum prices that have been calculated based on their relation to theaverage of all bids or some lowest bids in rst-price auctions (FPAs)1 . In this auction institution, any bid lower than the minimum price is excluded and the winning bid is the lowest amongbids higher than the minimum price. According to the European Commission's report (1999),
Belgium, Italy, Portugal, Spain, and Greece recognize (and/or suspect) a tender as being abnormally low "if the price offered is less by a certain percentage than the average of the tenders
submitted or discounts granted, with various differences in the percentage and/or calculationof the average".
Although there are several methods to calculate minimum prices, in this paper we referto minimum prices based on their relation to the average of all bids or some lowest bids as
endogenous minimum prices (EMPs); we investigate their performance using theory and laboratory experiment. Basically, the EMP excludes abnormally low bids that cannot satisfy thequality of public work that the auction authorities require. The EMP is, however, often criticized by legal and political sides as curbing fair competition. For instance, the European Courtof Justice said that "tenders may not automatically be excluded if they deviate more than a xed
percentage rate from the average of all other tenders submitted2 ".
Since the EMP is determined by its relation to the average bids, producers who join thisauction institution have an incentive to raise their bids and pull up the minimum price to exclude
others and become a winner. In this case, the winning bid is likely to be higher than its costwhich is the best outcome for the government and taxpayers to minimize their expenditure.
For example, let EMP = 0.8 average of the three lowest bids. This kind of method of
calculation is popular among Japanese local governments. The ranking of bids is presented inTable 1. In this case, the EMP is $103, the winner is Bidder 2, and the winning bid is $105.
However, if Bidder 3 whose bid is $130 raises his/her bid to $149, the EMP becomes $ 106 andhe/she can be the winner.
——————————————————————————
Table 1 is around here——————————————————————————
Although this is a rough example, it indicates the risk of taxpayers wasting their money.
Especially in Japan, the total contract price of public procurement for all local governmentsfrom 2005 to 2007 is approximately 24 trillion yen (229 billion US dollars)3 , whereas that forthe central government is about 7 trillion yen (67 billion US dollars)4 . Therefore, the EMP is
likely to result in huge social losses in Japan. This situation would be more serious in the EU
because the EU has a wider economy than Japan does. To con rm this, we theoretically analyze
the Nash equilibria in the FPA with EMP. We nd that the EMP does not affect the winning bidsof the standard FPA that does not have any minimum prices but expands its Nash equilibria as
including the Nash equilibria such that bi < c; for some i:
1 Ohno and Harada (2006) compare public procurement systems in Japan with systems in the US and the EU.

2 Refer to Judgement of 18 June 1991 in case C-295/89 “Alonso”; judgement of 26 October 1995 in case C-

143/94 “Furlanis”; and judgement of 16 October 1997 in case C-304/96 “Genova”.
3 1 US dollar = 105 Japanese yen.
4 Original data are obtained from the websites of East Japan Construction Surety Co., Ltd; Hokkaido Construction Surety Co., Ltd; and West Japan Construction Surety Co., Ltd.

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To verify the above theoretical results, we use experimental methods that feature three treatment variables—minimum prices (the EMP vs. no-minimum price), production costs (identicalvs. different), and the information of subjects' identi cations and bids (disclosure vs. nondisclosure). In the identical cost condition, the winning bids in both the FPA with EMP and thestandard FPA are consistent with the cost regardless of disclosing the information of subjects'
identi cations and bids. In the different cost condition, when the information of subjects' identi cations and bids is disclosed, the winning bids of the FPA with EMP diverge from the lowest
cost and are signi cantly higher than those of the standard FPA. In the latter condition, sincemost producers bid higher than their costs and the EMP becomes higher than the lowest cost,producers with the lowest cost bid higher prices than their costs not to be excluded by the EMP.
Thus, winning bids become higher than the lowest cost.
We are only aware of two literatures that analyze the EMP. The rst is Calveras et al. (2004),
who theoretically show that even in the second-price auction, producers with a small amountof initial cash can make a pro t by bidding low and declaring bankruptcy if the cost is foundto be high. Under this assumption, they brie y suggest that the EMP employed in European
countries does not work well. Second, Decarolis (2009) theoretically shows that the auction
authorities prefer average bid auctions employed in European countries than the FPA when
their monitoring cost is high, and empirically analyzes the monitoring cost in Italy. Therefore,
our study is, to the best of our knowledge, the rst experiment evaluating the performance of
the EMP.
In the procurement auction experiments, when costs are independent private values, Cox
et al. (1996) observe that too-low bids in the FPA lead to cost overruns when post-acution
cost is uncertainty, and Brosig and Reiß (2007) show that bids are lower than the theoreticalpredictions. On the other hand, when the cost is common knowledge, Saijo et al. (1996),
Dufwenberg and Gneezy (2002), Kawagoe (2003), and Dufwenberg and Gneezy (2004) ndthat the FPA mostly works well, except for the case in which they allow collusion or disclose
losing bids. In Japan, since only local governments employ the EMP and their procurement
auctions are held in a restricted area, the wages and rental costs of producing homogenous
goods do not vary and the production cost is common knowledge among producers. Therefore,
in this paper, we assume that goods are homogenous and those costs are common knowledge
among producers; we then analyze the Nash equilibria5 .
Nevertheless, in the procurement auction, the quality of public construction is a non-negligible
issue. Optimal auction schemes considering quality have been studied by Sinclair-Desgagne(1990), Dasgupta and Spulber (1990), Che (1993), Von Ungern-Sternberg (1994), Manelli andVincent (1995), and Naegelen (2002)6 . They reveal that private information on producers'
quality leads to the distortion of social welfare. This paper is, however, the rst step towards
evaluating the performance of the EMP. Therefore, we simplify our model setting to focus on
price competition, and release our attention from quality7 .
Apart from the procurement auction, from the viewpoint of price controls, price oors andceilings have been studied by Isaac and Plott (1981) and Smith and Williams (1981). Theynd that non-binding price controls affect the competitive equilibrium in the double auction
5 We restrict our attention to the winner's curse in Vesteg et al.

(2009), who nd that the EMP prevents thewinner's curse and that the effect is magni ed as the number of bidders increases.
6 Although Dasgupta and Spulber (1990) consider exible quantity instead of quality in their context, their
quality context can be read as quality in our context.
7 We explicitly introduce the quality of goods in the procurement auction model of Akai et al. (2009a). Theynd that an FPA without any regulation induces low-quality goods because of the producer's corner-cutting.

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experiment. Coursey and Smith (1983) observe the same result in the posted offer market, andGode and Sunder (2004) present a simple dynamic model with “zero-intelligence” traders to
explain this discrepancy.
The paper is organized as follows. Section 2 develops the theoretical model and hypotheses.
Section 3 details the experimental design and procedures. Section 4 analyzes the results, andSection 5 contains the conclusion and discussion.

2. T HEORETICAL MODEL AND HYPOTHESIS
2.1. T HEORETICAL MODEL
A rule of the FPA with EMP is simply described as follows. Consider that n producers whojoin this procurement auction. Let p be the reservation price determined by a government inadvance. Denote producer i's bid by bi 2 [0; p], and let this bid function be continuous. A bid
pro le is n-tuple b = (b1 ; : : : ; bn ) 2 [0; p]n . Given a bid pro le b = (b1 ; : : : ; bn ), denote the rst
lowest bid by b1 , the second lowest bid by b2 , and so on. Given a bid pro le b, 2 m < n,and k 2 (0; 1), denote the average bid am (b) = [b1 + + bm ]=m of the m lowest bids and theminimum price d(b) = k am (b)8 . When a bid pro le is b, the winner is a producer whose bid
is the lowest between d(b) and p inclusively, and the winning bid is his/her bid. In case of a tie,such producers win with equal probability.
Procurement auctions for Japanese local governments are held with the same sets of producers who work in the same cities or prefectures. Since wages and rental costs do not generally
vary in local areas and a reference book for estimating public constructions is freely available,
we assume that every producer has an identical cost c to produce a homogenous good, and thecost is common knowledge among producers9 . The winning bid in the Nash equilibrium is
described in Proposition 1 below, with the proof in Appendix.
P ROPOSITION 1. If a bid pro le b is a Nash equilibrium, the winning bid coincides with thecost:
In the following example, we divide the Nash equilibria of the FPA with EMP into twocases in order to compare it with the Nash equilibria of the standard FPA that does not have any
minimum prices. In Case I, we show the Nash equilibria such that all bids are not less than thecost, that is, bi c; for every i. This condition is satis ed if the bid pro le is a Nash equilibriumin the standard FPA because any producer bidding less than the cost obtains negative payoffs. In
Case II, we show the Nash equilibria such that some bids are less than the cost, that is, bi < c; forsome i: Although there is no Nash equilibrium that satis es this condition in the standard FPA,
there are many Nash equilibria that satisfy this condition in the FPA with EMP as described in
the example below.
E XAMPLE 1:Let n = 5; k = 0:8; m = 3; p = 243; and c = 97:
8 In Akai et al. (2009b), we classify the EMP into four types: (i) k = 1 and m < n, (ii) k = 1 and m = n, (iii)k < 1 and m < n, and (iv) k < 1 and m = n: If the cost is identical, Type (iii) of the EMP that we introduce in thispaper is the most ef cient for the governments and taxpayers to minimize their expenditures.
9 In this environment, auction is playing fair institution as authorities justify that they do not choose a contractor
arbitrarily.

3Case I: Nash equilibria such that bi c; for every i: Consider a bid pro le b = (97; 97;
130; 150; 160): The minimum price is d(b) = 0:8 (97 + 97 + 130)=3 = 86:4; and the winneris one of the producers bidding 97. If one of the producers bidding 97 raises his/her bid to 130,
then since the minimum price becomes d(b) = 0:8 (130 + 97 + 130)=3 = 95:2 and still remains
less than 97, he/she cannot exclude the other producer bidding 97. If a producer raises his/herbid to 150, then since the minimum price becomes d(b) = 0:8 (150 + 97 + 130)=3 = 100:5
and still remains less than 130, he/she cannot exclude the producers bidding less than 130.
A producer cannot affect the minimum price by raising his/her bid to a price more than 150.
If the producer bidding 130 raises his/her bid to 150, then since the minimum price becomesd(b) = 0:8 (97 + 97 + 150)=3 = 91:7 and still remains less than 97, he/she cannot exclude theproducers bidding 97. In this bid pro le, nobody has an incentive to raise the bid and exclude
others. Hence, this bid pro le is a Nash equilibrium, and the winning bid coincides with thecost of 97.
Next, consider a bid pro le b = (97; 97; 130; 220; 230). Since b4 = 220 is much higher thanb3 = 130, the producer bidding b3 = 130 can exclude the producers bidding 97 by raising his/herbid to b4 = 220. Thus, this bid pro le is not a Nash equilibrium. In this auction institution, sinceb4 is the same as the price ceiling for producers bidding less than b4 , b4 should not be so highthat the producers bidding prices less than b4 cannot exclude others if a bid pro le is a Nashequilibrium.
Case II: Nash equilibria such that bi < c; for some i: Consider a bid pro le b = (1; 97;
97; 150; 200): The minimum price is d(b) = 0:8 (1 + 97 + 97)=3 = 52; and the winner is oneof the producers bidding 97. If the producer bidding 1 raises his/her bid to 97, then since his/her
payoffs still remain 0, he/she does not have an incentive to deviate from this bid pro le. If a
producer raises his/her bid to 150, then since the minimum price becomes d(b) = 0:8 (150 +97 + 97)=3 = 91:7 and still remains less than 97, he/she cannot exclude the producers bidding
97. If the producer bidding 97 raises his/her bid to 150, then since the minimum price becomesd(b) = 0:8 (1 + 97 + 150)=3 = 66:1 and still remains less than 97, he/she cannot exclude theother producers bidding 97. Thus, nobody can affect the minimum price if the producer raises
his/her bid more than 150. Hence, this bid pro le is a Nash equilibrium. Similarly, there aremany Nash equilibria such that some bids are less than the cost.
Although the EMP expands the Nash equilibria of the standard FPA, winning bids coincide with the cost. That is, the governments and taxpayers can minimize their expenditures
throughout this auction institution. Based on the discussion above, we propose hypotheses inthe experimental parameter values.

2.2. H YPOTHESESIn the experiment, we set the minimum price as 0:8 average of the lowest 5 bids of 10 producers (k = 0:8, m = 5, and n = 10)10 . We allow the subjects playing the roles of producers
to bid only nonnegative integers. To evaluate the performance of the EMP, we compare thewinning bids with those of the standard FPA in the identical cost condition and the different
cost condition.
First, we propose hypotheses in the identical cost condition. In the identical cost condition,
we set every producer's cost as 97 (c = 97). By Proposition 1, the winning bid coincides with
10 This is the

rst rule employed by the Japanese local governments.

4the cost of 97. Notice that since bids are only integers, a bid pro le b1 =a Nash equilibrium. Therefore, we obtain the following hypothesis.

= b10 = 98 is also

H YPOTHESIS 1. In the identical cost condition, the winning bid is 97 or 98.
In the standard FPA, the winning bid also coincides with the cost of 97. Additionally, since
bids are only integers, a bid pro le b1 == b10 = 98 is also a Nash equilibrium. Therefore,
we obtain the following hypothesis.
H YPOTHESIS 2. In the identical cost condition, the winning bids in the FPA with EMP coincidewith the ones in the standard FPA.
Next, we consider the winning bids in the different cost condition. Here, we consider thesituation that some big nationwide companies newly join procurement auctions for local governments and they have the power to cut wages and rental costs much more than small localizedcompanies do. We introduce this situation into the laboratory and set producer i's cost as 97(ci = 97, i = 2; 5; 8) and producer j's cost as 150 (c j = 150, j 6= i)11 .
Since there are many Nash equilibria in the different cost condition, it is complicated todescribe all of them. First, we analyze the winning bid in the Nash equilibrium in Proposition
2 below, with proofs in Appendix. Next, we present an example of the Nash equilibrium.
P ROPOSITION 2. Let c1 c2
cn . If a bid pro le b is a Nash equilibrium, the winningbid coincides with the lowest cost c1 .
P ROPOSITION 3. In the different cost condition, there is no Case I pure Nash equilibrium suchthat bi ci ; for every i.
The proof of Proposition 3 is provided in supplementary materials. To explain the above
proposition intuitively, consider a bid pro le b such that every producer whose cost is 97 bids
97 and every producer whose cost is 150 bids 150. If the producer bidding 97 raises his/herbid to 149, he/she can pull the minimum price above 97 and be the winner. Therefore, theproducers whose costs are 97 have the incentives to raise their bids more than 97 not to be
excluded. However, they also keep incentives to reduce their bids to win because there are three
producers whose costs are 97. Hence, they trade off raising and reducing their bids. Thus, there
is no Case I pure Nash equilibrium such that every producer bids a price more than or equal tothe cost. There are only Case II pure Nash equilibria such that bi < ci ; for some i in the example
below.
E XAMPLE 2. Case II: Nash equilibria such that bi < c; for some i: Consider a bid pro le bsuch that producers 2, 5, and 8 whose costs are 97 bid 97, producer 1 whose cost is 150 bids 1,
and the remaining producers whose costs are 150 bid 150, that is, b = (1; 97; 150; 150; 97; 150;
150; 97; 150; 150). In this bid pro le, the minimum price is 0:8 (97 + 97 + 97 + 1 + 150)=5 =70:7; and the winner is one of the producers bidding 97. Since nobody can pull the minimum
price above 97, this bid pro le is a Nash equilibrium. Similarly, there are many Case II Nashequilibria such that some bids are extremely low.
Notice that since bids are only integers in the experiment, there are Nash equilibria such thatthe wining bid is 98. For example, a bid pro le b such that producers 2, 5, and 8 whose costs
11 Dufwenberg and Gneezy (2000)

nd that price competition works well when the number of competitors isthree. We follow their idea and allocate the lower cost to three producers.

5are 97 bid 98, producer 1 whose cost is 150 bids 1, and the remaining producers whose costs are
150 bid 150, that is, b = (1; 98; 150; 150; 98; 150; 150; 98; 150; 150) is a Nash equilibrium12 .
Therefore, we obtain the following hypothesis.
H YPOTHESIS 3. In the different cost condition, the winning bid is 97 or 98.
In the standard FPA, the winning bid also coincides with the lowest cost of 97. Additionally,
since bids are only integers, a bid pro le such that producers 2, 5, and 8 bid 98 (b2 = b5 = b8 =98) and the others bid prices more than 98 is also a Nash equilibrium. Therefore, we obtain thefollowing hypothesis.
H YPOTHESIS 4. In the different cost condition, the winning bids in the FPA with EMP coincidewith the ones in the standard FPA.
In the different cost condition, although the Nash equilibria in the FPA with EMP are different from those in the standard FPA, the winning bids are same. From the above hypotheses,
there is no difference in the winning bids between the FPA with EMP and the standard FPA in
the both cost conditions.

3. E XPERIMENTAL DESIGN AND PROCEDURES
3.1. D ESIGN
Each session proceeded through a sequence of 10 procurement periods and comprised 10 producers who had the same homogenous good13 . Each subject bid only one selling price perperiod, and the experimenter bought only one unit of good per period with the reservation priceof 243 points of experimental cash. The winner produced a good and earned pro ts equal toselling price minus cost; other producers did not produce a good and earned zero pro ts for that
period14 .
Our experiment features three treatment variables—minimum prices, production costs, andthe information of subjects' identi cations and bids. The minimum prices of our most interest
have two conditions—the no-minimum price condition and the EMP condition. In the nominimum price condition, we employed the standard FPA that does not have any minimum
prices. In this condition, the winner was the producer whose bid was the lowest among bids
12 Sincebids are only integers in the experiment, there are several nonessential Nash equilibria. For
example, consider a bid pro le b such that producer 2 bids 120, producer 5 bids 130, producer 8 bids
145, producer 1 bids 97, producer 3 bids 121, and the remaining producers bid 145, that is, b =(97; 120; 121; 145; 130; 145; 145; 145; 145; 145): The minimum price is d(b) = 0:8 (97 + 120 + 121 + 130 +145)=5 = 98: 0, and the winner is the producer bidding 121. If the producer bidding 97 raises his/her bid to 120
and wins, since his/her cost is 150, he/she obtains negative payoffs. If the producer bidding 121 reduces his/herbid to 120 and wins, since his/her cost is 150, he/she obtains negative payoffs. If the producer bidding 130 reduces
his/her bid to 120, since the minimum price d(b) = (97 + 120 + 121 + 120 + 145)=5 = 120: 6; he/she cannot be thewinner. Thus, nobody has an incentive to change the bid, such that this bid pro le is a Nash equilibrium. However,essentially, the winning bid coincides with the lowest cost of 97 in the Nash equilibrium.
13 In Japan, the EMP is often employed when the number of bidders is more than 10. Producers who join the
procurement auction with the EMP award a contract roughly once a year. To capture this situation, we conduct anexperiment such that a subject wins once with equal probability in the identical cost condition.
14 We used the term selling price instead of bid and avoided terms such as winners and winning bids in the
instructions.

6not more than the reservation price, and the winning bid was his/her bid. In case of a tie, suchproducers won with equal probability. This was the benchmark control condition.
In the EMP condition, we employed the FPA with EMP. The EMP was 80% of the averageof the ve lowest bids among ten producers. The winner was the producer whose bid was thelowest between the reservation price and EMP inclusively, and the winning bid was his/her bid.
In case of a tie, such producers won with equal probability.
The production costs have two conditions—the identical cost condition and the different
cost condition. In the identical cost condition, we announced that the production costs for all
producers were 97 points. In the different cost condition, we announced that the production
costs for three producers with identi cation numbers 2, 5, and 8 were 97 points and those of theremaining producers were 150 points. In each condition, subjects were randomly assigned oneof the identi cation numbers and they remained in the same role throughout the session.
The information of subjects' identi cations and bids has two conditions—the disclosure
condition and the nondisclosure condition. In the procurement auctions for Japanese local
governments, producers work in a limited area and are well acquainted with each other. We
designed our experiments to assess this environment in the disclosure condition. To this end, inthe disclosure condition, at the beginning of the session, we wrote the seating chart of all the
producers on a whiteboard in order for the subjects to know which producer had which seat15 .
After the winner was decided, we clearly announced each bid, in addition to writing it oneach seat of the seating chart16 . After writing all the bids, in the no-minimum price condition,
the winning bid, winner's identi cation number, and winner's pro ts were displayed on eachsubject's screen. In the EMP condition, the winning bid, winner's identi cation number, theaverage of the ve lowest bids, the minimum price, and winner's pro ts were displayed on eachsubject's screen.
Since we examined the effect of information of subjects' identi cations and bids, we did
not disclose the seating chart and all bids in the nondisclosure condition. After the winner was
decided, the same type of information provided in the disclosure condition was displayed oneach subject's screen.
We used a full factorial design with 2 minimum price conditions 2 production cost conditions 2 information conditions of subjects' identi cations and bids. Table 2 summarizes oureight cells. Each cell included two sessions. The N and E pre x in the session name indicate
the no-minimum price condition and the EMP condition, respectively. The -I- and -D- in the
middle of the session name indicate the identical cost condition and the different cost condition,
respectively. The -D- and -N- suf x indicate the disclosure condition and the nondisclosure
condition, respectively.
——————————————————————————
Table 2 is around here——————————————————————————
3.2. P ROCEDURES
The experiments were conducted in the PC laboratory of the Institute of Social and Economic
Research at Osaka University. A computerized interface was programmed with the software
z-Tree (Fischbacher 2007). Subjects included undergraduate and graduate students of Osaka
15 In our laboratory, the subjects sitting at the rear can see the backs of the subjects sitting ahead of them.

16 In Japan, some local governments that employ the EMP disclose all bids along with the companies' names.

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University17 . They were invited to sign up at designated websites by yers posted around thecampus and e-mail solicitations sent to students who had signed up for other experiments before.
No one participated in more than one session.
Upon arrival, the subjects sat at separate computer terminals, and no communication was
permitted throughout the session. The instructions and PC operation manuals are provided in
the supplementary materials. Subjects listened to prerecorded instructions, while they followed
along on their own copies. Next, they privately read questions and answers about the instructions in 10 minutes to con rm the rules of the experiment18 . Next, they listened to prerecorded
PC operation manuals, while they followed along on their own copies.
After the above procedures were completed, the producers' identi cation numbers 1 to 10
were determined by a lottery, and each subject received a record sheet. We then provided 10
minutes for subjects to consider the strategy of subsequent auctions.
Then, period 1 began. All the subjects entered their selling price in the computer and theirrecord sheets within three minutes; this was done in each period. As soon as all the subjects
bid, the auction was automatically closed and the winner was decided even if three minutes had
not elapsed.
In the disclosure condition, we called each bid with an identi cation number and wrote
it on each seat of the seating chart on the whiteboard. In the nondisclosure condition, we
did not announce this information. In the no-minimum price condition, subjects entered thewinning bid, winner's identi cation number, and their own pro ts in their record sheets. In theendogenous minimum price condition, subjects entered the winning bid, winner's identi cation
number, the average of the ve lowest bids, the minimum price, and their own pro ts, in theirrecord sheets.
After period 10 was completed, the record sheets were collected, and their total pro ts were
calculated. Subjects were paid their experimental points in cash under the conversion rate of
1 point equal to 30 yen (29 cents)19 . All the sessions lasted for approximately 1.5 hours, andthe earnings of the subjects ranged from 900 yen ($8.57) to 5,070 yen ($48.29), with a mean ofapproximately 1,710 yen ($16.29).

4. R ESULTS
We divide the results into two subsections. Section 4.1 presents the results of the identical costcondition, and Section 4.2 presents the results of the different cost condition. We provide graphs
and raw data of the entire experiment in the supplementary materials.
17 Subjects were a mixture of economics majors and noneconomics majors.

18 Subjects sometimes ask about the detailed strategy of experiments, which might result in a bias in their de-cision making in the subsequent auction periods. Since we prohibited any questions and excluded any biases, weprepared questions and answers about instructions and distributed them to each subject.
19 In cells N-I-N and E-I-N, although the conversion rate of 1 point was 30 yen (29 cents), we did not informthe subjects about it. We announced that their initial experimental points were zero and that the higher theirexperimental points, the more will be their earnings from the experiments. We ensured minimum payments even if
the nal experimental points were less than or equal to zero in the questions and answers. The minimum payment
was 1500 yen ($14.28), which was equal to 50 points 30 yen (29 cents).

8

4.1. T HE IDENTICAL COST CONDITIONFirst, we test Hypothesis 1. Figure 1a presents the average winning bids in cell N-I-D and theaverage winning bids and the EMP in cell E-I-D. The horizontal axis represents the number of
periods and the vertical axis the price. The average winning bids in cells N-I-D and E-I-D arevery close to the theoretical prediction of 97 or 98. The median of the pooled winning bids
across the sessions is 98 in cells N-I-D and E-I-D20;21 . Wilcoxon signed-rank tests do not reject
the null hypothesis that the median of the pooled winning bids across the sessions coincides
with the theoretical prediction of 98 in cells N-I-D and E-I-D (two-tailed p-values are 1.00 and
0.453, respectively)22 .
——————————————————————————
Figure 1 is around here——————————————————————————
Figure 1b presents the average winning bids in cell N-I-N and the average winning bids andthe EMP in cell E-I-N. The average winning bids in cells N-I-N and E-I-N are very close to
the theoretical prediction of 97 or 98, except in the last period in cell N-I-N. The median of thepooled winning bids across the sessions is 97 in cells N-I-N and E-I-N23 . Wilcoxon signed-rank
tests do not reject the null hypothesis that the median of the pooled winning bids across thesessions coincides with the theoretical prediction of 97 in cells N-I-N and E-I-N (two-tailed pvalues are 1.00 and 0.146, respectively). These results support Hypothesis 1. Hence, we obtainthe following result.
R ESULT 1. In the identical cost condition, the winning bids in the FPA with EMP and those in
the standard FPA coincide with the theoretical prediction in both the information conditions.
Next, we test Hypothesis 2. The distributions of the average winning bid in cell N-I-N (N-ID) appear to be similar to those in cell E-I-N (E-I-D). Wilcoxon rank sum tests do not reject thenull hypothesis of no difference in the medians of the pooled winning bids across the sessions
between cells N-I-D and E-I-D (two-tailed p-value = 0.264) and do not reject the null hypothesisof no difference in the medians of the pooled winning bids across the sessions between cells
N-I-N and E-I-N (two-tailed p-value = 0.209). These results support Hypothesis 2. Hence, we
obtain the following result.
R ESULT 2. In the identical cost condition, the winning bids of the FPA with EMP coincide withthose of the standard FPA in both the information conditions.
Next, we focus on the information effect of subjects' identi cations and bids within the sameauction institution. Wilcoxon rank sum tests do not reject the null hypothesis of no difference
20 Throughout this section, we pool data across two sessions to increase the sample size to 20, which is suf

cient
to conduct nonparametric tests. We also report the statistical results, comparing the distribution between two
sessions in each cell in each footnote.
21 The Wilcoxon rank sum tests do not reject the null hypothesis of no differences in the distributions between
sessions in the cells N-I-D and E-I-D (two-tailed p-values are 0.69 and 0.15, respectively).
22 Although the observations are not independent across the periods within a session, we use Wilcoxon signedrank tests to aid the reader's interpretation of comparing with the theoretical prediction throughout this section.
23 The Wilcoxon rank sum tests do not reject the null hypothesis of no difference in the distribution between
sessions in cell N-I-N (two-tailed p-value is 0.69) but reject it in cell E-I-N (two-tailed p-value is 0.04).

9

in the medians of the pooled winning bids across the sessions between cells E-I-N and E-I-D(two-tailed p-value = 0.128) but reject the null hypothesis of no difference in the medians of thepooled winning bids across the sessions between cells N-I-N and N-I-D (two-tailed p-value =0.002). Hence, we obtain the following result.
R ESULT 3. In the identical cost condition, the winning bids of the FPA with EMP in the disclosure condition coincide with those in the nondisclosure condition. However, the winning bids ofthe standard FPA in the disclosure condition are slightly higher than those in the nondisclosure
condition.
Dufwenberg and Gneezy (2002) nd, in their FPA experiment, that although winning bids
converge towards the theoretical prediction when they disclose only winning bids, winning bids
diverge from the theoretical prediction when they disclose losing bids. In contrast, the winningbids of our standard FPA coincide with the theoretical prediction, and the differences of winningbids between the two information conditions are very small.
The slight difference in the nondisclosure condition seems to be due to the different information of payment schemes. In cells N-I-N and E-I-N, we did not provide a formula to calculate
cash rewards from experimental points. Some subjects tended to misunderstand their rewards
would be higher when they sold a good than when they did not sell it if their pro ts were negative. This misunderstanding motivates some subjects to bid prices lower than or equal to thecost of 97 to win.
To avoid the aforementioned misunderstanding, we provide a formula to calculate theirrewards in cells N-I-D and E-I-D. It was easier for subjects to understand that negative payoffs
would reduce their rewards, so they tried to bid prices higher than the cost of 97 to earn positive
pro ts.
Since the number of bids less than or equal to 97 in cell N-I-N is more than that in cell N-ID, the different information about payment schemes seems to induce the difference of winningbids between these cells. However, we do not observe these differences between cells E-I-N and
E-I-D. Although more experimental work is needed to obtain precise results, the information ofsubjects' identi cations and bids does not have a critical impact on the winning bids in either
auction institution.
The above results show that both auction institutions achieve the same winning bids. Next,
we shift our focus from price competition to evaluating the performance of EMP in relation tothe other reason why Japanese local governments employ the EMP, as described below.
Japanese local governments traditionally set the minimum price at 80–90% of the reservation price, which is generally estimated as the standard cost set by the governments. They
believe that the minimum price should be a benchmark of the quality of public works24 . ManyJapanese local governments announce the reservation price and/or the minimum price in orderto achieve transparency and fairness25 . This pre-announcement, however, creates the problemof all producers who join this auction bidding the minimum price; the winner is selected bylottery regardless of the real costs and qualities26 . Even when they pre-announce only the reser24 In Japan, the law of local government procurement requires reservation prices in order to avoid a situation inwhich contract prices exceed the budget.
25 According to the Ministry of Land, Infrastructure, Transport and Tourism's survey (2007) of 1,874 local
governments, 64% of all local governments announced the reservation price in advance, and 65% of all local
governments employed the minimum price. Of these governments, 20% announced the minimum price in advance.
26 According to the Ministry of Land, Infrastructure, Transport and Tourism's survey (2006) of 1,826 local
governments that employed the minimum price from April 2003 to July 2004 (this frequency is about 56% of the10vation price, the same problem occurs because producers can easily estimate the minimum pricefrom the traditional reservation price. Thus, not only in order to exclude abnormally low bids
but also to avoid selecting the winner by lottery, they have started to employ the EMP.
To test this performance, we compare the frequency of deciding winners by lottery between
the FPA with EMP and the standard FPA. The numbers pertaining to deciding the winner by
lottery are 13 and 10 in cells E-I-D and N-I-D, respectively. The proportion test does not
reject the null hypothesis of no difference in the frequencies of deciding the winner by lottery
between cells E-I-D and N-I-D (two-tailed p-value = 0.337). On the other hand, the numbers
pertaining to deciding the winner by lottery are 12 and 8 in cells E-I-N and N-I-N, respectively.
The proportion test does not reject the null hypothesis of no difference in the frequencies ofdeciding the winner by lottery between cells E-I-N and N-I-N (two-tailed p-value = 0.205).
Hence, we obtain the following result.
R ESULT 4. In the identical cost condition, there is no difference in the frequency of deciding winners by lottery between the FPA with EMP and the standard FPA in both information
conditions.
As a result, the winners were decided by lottery in roughly half the periods in both auctions.
In the identical cost condition, the EMP does not affect the winning bids or the frequency
of deciding the winner by lottery. Next, we evaluate the effect of EMP in the different costcondition.

4.2. T HE DIFFERENT COST CONDITIONFirst, we test Hypothesis 3. Figure 2a presents the average winning bids in cell N-D-D and theaverage winning bids and the EMP in cell E-D-D. The winning bids in cell E-D-D depart fromthe theoretical predictions of 97 and 98. The medians of the pooled winning bids across thesessions in cells N-D-D and E-D-D are 100 and 119.5, respectively27 . Wilcoxon signed-rank
tests reject the null hypothesis that the medians of the pooled winning bids across the sessions
coincides with 97 or 98 at the 1% signi cance level in both the cells.
Figure 2b presents the average winning bids in cell N-D-N and the average winning bids andthe EMP in cell E-D-N. Both the winning bids tend to decrease toward the theoretical prediction
as the periods proceed. The medians of the pooled winning bids across the sessions in cells ND-N and E-D-N are 106 and 102, respectively28 . Wilcoxon signed-rank tests reject the null
hypothesis that the median of the pooled winning bids across the sessions coincides with 97 or
98 at the 1% signi cance level in each cell.
——————————————————————————
Figure 2 is around here——————————————————————————
3,228 local governments existing at the time), 145 local governments decided the winner by lottery during that
period. This frequency is 61% of the 236 local governments that announced the minimum price in advance.
27 The Wilcoxon rank sum tests reject the null hypothesis of no difference in the distribution between sessions incell N-D-N (two-tailed p-value is 0.01), but do not reject it in cell E-D-N (two-tailed p-value is 0.61).
28 The Wilcoxon rank sum tests reject the null hypothesis of no difference in the distribution between sessions incell N-D-D (two-tailed p-value is 0.01), but do not reject it in cell E-D-N (two-tailed p-value is 0.79).

11

The winning bids in cells N-D-N and E-D-N, however, appear to converge towards thetheoretical prediction of 98; those in cells N-D-D and E-D-D do not. We test whether thewinning bids converge towards the theoretical prediction. We de ne that the winning bids
converge towards the theoretical prediction if the slopes of the OLS regression of winning bidson the number of periods are signi cantly negative and the winning bids in the last ve periods
coincide with the theoretical prediction.
——————————
Table 3 is around here——————————
Table 3 presents the results of the OLS regression of the pooled winning bids across two
sessions on the number of periods in cells N-D-D, E-D-D, N-D-N, and E-D-N:
Winning bids = a + b Period + ε
In cells N-D-D and E-D-D, however, the slopes are not signi cant at the 5% level, and thejoint F-statistic tests of slopes and constants are not signi cant at the 5% level. The mediansof the pooled winning bids in the last ve periods across the sessions are 100 and 116 in cells
N-D-D and E-D-D, respectively. Wilcoxon signed-rank tests reject the null hypothesis that themedians of the pooled winning bids in the last ve periods across the sessions coincides with98 in cells N-D-D and E-D-D (two-tailed p-values are 0.015 and 0.002, respectively). These
results do not support Hypothesis 3, that is, winning bids do not converge towards 98.
In cells N-D-N and E-D-N, the slopes are negative and the constants are positive. They are
signi cant at the 1% level. The joint F-statistic tests of slopes and constants are also signi cantat the 1% level. The medians of the pooled winning bids in the last ve periods across thesessions are 100.5 and 98 in cells N-D-N and E-D-N, respectively. Wilcoxon signed-rank tests
do not reject the null hypothesis that the medians of the pooled winning bids in the last ve
periods across the sessions coincide with 98 in cells N-D-N and E-D-N (two-tailed p-values
are 0.062 and 1.000, respectively). These results support that winning bids converge towards
98. Therefore, Hypothesis 3 is supported in the nondisclosure condition. Hence, we obtain thefollowing result.
R ESULT 5. In the different cost condition, the winning bids in the FPA with EMP and thestandard FPA do not converge towards the theoretical prediction in the disclosure condition, butconverge towards the theoretical prediction in the nondisclosure condition.
Next, we test Hypothesis 4. The average winning bids in cell E-D-N are higher than thosein cell N-D-N, except in Period 9. Wilcoxon rank sum tests reject the null hypothesis of nodifference in the medians of the winning bids between cells N-D-D and E-D-D (two-tailed pvalue = 0.000). On the other hand, the distribution of the average winning bids in cell E-D-D
appears to be similar to that in cell N-D-D. Wilcoxon rank sum tests do not reject the null
hypothesis of no difference in the medians of the winning bids between cells N-D-N and ED-N (two-tailed p-value = 0.463). Therefore, Hypothesis 4 is supported in the nondisclosure
condition but not in the disclosure condition. Hence, we obtain the following result.

12

R ESULT 6. In the different cost condition, the winning bids of the FPA with EMP are higher
than those of the standard FPA in the disclosure condition. However, the winning bids of the
FPA with EMP coincide with those of the standard FPA in the nondisclosure condition.
The above result implies that the information of subjects' identi cations and bids affects
the winning bids. Next, we focus on the effect of this information within the same auction
institutions. Wilcoxon rank sum tests reject the null hypothesis of no difference in the mediansof the pooled winning bids between cells E-D-N and E-D-D (z-value = 3.88, two-tailed p-value= 0.000), but do not reject the null hypothesis of no difference in the medians of the pooled
winning bids between cells N-D-N and N-D-D (z-value = –1.28, two-tailed p-value = 0.199).
Thus, we obtain the following result.
R ESULT 7. In the different cost condition, the winning bids of the FPA with EMP in thedisclosure condition are higher than those in the nondisclosure condition. However, the winningbids of the standard FPA in the nondisclosure condition coincide with those in the disclosure
condition.
Next, we compare E-D-N and E-D-D and consider why winning bids in cell E-D-N diverge
from the theoretical prediction. As we described in Section 2.2, in the different cost condition,
the FPA with EMP has many Case II Nash equilibria such that bi < ci ; for some i; but it does
not have any Case I pure Nash equilibrium such that bi ci ; for any i: The FPA with EMP
approximately achieves Case II Nash equilibria in the nondisclosure condition in the last ve
periods but not in the disclosure condition in all the periods.
There are many 1 point bids in cell E-D-N, whereas there are three 1 point bids in cell E-DD. Speci cally, in cell E-D-N, Producers 7, 9, and 10 in Session 1, and Producer 4 in Session 2
repeatedly bid 1. The EMPs fell below 80 from Period 5, except in Period 10 in Session 1. In
cell E-D-D, however, nobody repeated a bidding of 1 from Period 5, and the EMPs were higher
than 105, except in Periods 6, 9, and 10 in Session 1.
According to the questionnaire sheets that we distributed after the experiment, Producers 4
and 10 who repeated a bidding of 1 in cell E-D-N changed their strategies during the course of
the experiment to reduce the payoffs of the producers whose costs are 97 by bidding extremely
low prices. Their motivation seems to be similar to the spiteful strategies de ned by Cason etal. (2004) in the non-excludable public goods experiments. They de ne a strategy as beinga spiteful strategy “if he/she selects a strategy reducing both his/her own payoff and the othersubject's payoff in comparison to the payoffs when he/she takes an own payoff-maximizing
strategy, given an expected strategy of the other subject”29 :We expand this de nition to include the meaning of expected payoffs and apply it to the
incentive of repeated bidding of 1 for the producer whose cost is 150. Since bidding a pricelower than the cost has the risk of negative payoffs, the expected payoffs of the producer whose
cost is 150 are smaller when he/she bids 1 than when he/she bids 151, given any bid pro les.
The producer's strategy of bidding 1, however, reduces not only his/her own expected payoffs
but also those of the producer whose cost is 97.
Given bidding prices of more than 150 from producers whose costs are 150, if producers
whose costs are 97 bid prices between 97 and 150, they can win, and the winner's payoff ranges
from 1/3 to 5230 . On the other hand, given a bidding price of 1 from producers whose costs
29 Cason et al. (2004), p. 89, l.4–6.

30 The minimum expected payoff is 1/3 if three producers, whose costs are 97, bid 98; the maximum expected

payoff is 52 if only one producer, whose cost is 97, bids 149 and wins.

13are 150, the expected payoff-maximizing strategy of producers whose costs are 97 is bidding
98, and their expected payoffs are 1/3 at the most. Thus, a bidding price of 1 from producers
whose costs are 150 is a spiteful strategy in view of expected payoffs. Thus, the nondisclosure
condition leads to a spiteful strategy, which motivates producers whose costs are 97 to bid prices
close to their costs so that the winning bids are close to their costs.
The disclosure condition, however, reduces the spiteful strategy of bidding 1 which leads
to Case II Nash equilibria. If producers whose costs are 97 do not assume extremely low bids
and assume that all producers bid prices higher than their costs, they have the incentive to bid
prices more than their cost not to be excluded by the EMP. Speci cally, consider a situation inwhich a producer whose cost is 97 bids 150 and producers whose costs are 150 bid 151. In thissituation, if the remaining producers whose costs are 97 bid 98, they are excluded by the EMPof 103. Thus, since producers whose costs are 97 bid prices more than their costs not to be
excluded, the winning bids in cell E-D-N diverge from their costs.
Next, we consider the market ef ciency de ned by the total surplus of the government andproducers. In view of the market ef ciency, the most ef cient case is that the producer whose
cost is 97 produces the goods and sells them to the government. In cell E-D-D, Producer 10
whose cost is 150 won with her bid of 151 in Period 10 of Session 1, and Producer 7 whose costis 150 won at her bid of 155 in Period 8 of Session 2. These observations imply that the FPA with
EMP has a risk of losing market ef ciency when production costs are different if governments
disclose producers' identi cations and bids. We compare the frequency of achieving the mostef cient case between cells N-D-D and E-D-D. The proportion test does not reject the null
hypothesis of no difference in the frequencies of achieving the most ef cient case between cells
N-D-D and E-D-D (two-tailed p-value = 0.146). Hence, we obtain the following result.
R ESULT 8. In the different cost condition, there is no difference in the market ef ciencies
between the FPA with EMP and the standard FPA.
In both the auction institutions, producers whose costs are 97 mostly win. Next, we compare
the frequencies of deciding winners by lottery between the FPA with EMP and the standard
FPA. The numbers pertaining to deciding the winners by lottery are 1 and 2 in cells E-I-D and
N-I-D, respectively. The proportion test does not reject the null hypothesis of no differencein the frequencies of deciding the winners by lottery between cells E-D-D and N-D-D (twotailed p-value = 0.548). On the other hand, the numbers pertaining to deciding the winners by
lottery are 10 and 2 in cells E-D-N and N-D-N, respectively. The proportion test rejects the null
hypothesis of no difference in the frequencies of deciding the winners by lottery between cells
E-I-N and N-I-N (two-tailed p-value = 0.005). Hence, we obtain the following result.
R ESULT 9. In the different cost condition, there is no difference in the frequencies of deciding
the winners by lottery between the FPA with EMP and the standard FPA in the disclosure
condition. However, the frequency of the FPA with EMP is higher than that of the standard FPA
in the nondisclosure condition.
The frequencies of deciding the winners by lottery in cell E-D-N is high and is the same as
those in cells in the identical cost condition. One possible reason why cell E-D-N induces highfrequencies is that the bidding price of 1 from producers whose costs are 150 lowers the EMP,
which allows producers whose costs are 97 to easily stay close to their costs of 97 relative to thestandard FPA. In the standard FPA, since there are only three producers whose costs are 97 andthe competition power is weak, they try to bid higher prices than their costs in order to increase
14

their pro ts instead of bidding close to their costs to become the winner. If this interpretation iscorrect, the existence of the EMP leads to having to decide the winners by lottery. This situationis unexpected for Japanese local governments that wish to prevent deciding winners by lottery.

5. C ONCLUSION AND DISCUSSION
In this paper, we evaluate the performance of the FPA with EMP relative to the standard FPA
which does not have any minimum prices. Theoretically, in the identical cost condition, the
EMP expands the Nash equilibria of the FPA, and the FPA comes to include the Nash equilibria
such that bi < c; for some i: In the different cost condition, the EMP changes the Nash equilibriaof the FPA, and the FPA comes to hold only the Nash equilibria such that bi < c; for some i:
However, in both production cost conditions, since the EMP does not affect the winning bids ofthe FPA in the Nash equilibria, the winning bids consistent with their costs which are the mostef cient outcomes for the government and taxpayers to minimize their expenditures.
In the experiment, in the identical cost condition, the winning bids in both the FPA with EMP
and the standard FPA are consistent with the cost; these values are not signi cantly different
regardless of the information of subjects' identi cations and bids. Further, the EMP does notaffect the frequency of deciding the winners by lottery.
In the different cost condition, when the information of subjects' identi cations and bids
is disclosed, the winning bids of the FPA with EMP diverge from the lowest cost and are signi cantly higher than those of the standard FPA. However, when the information of subjects'
identi cations and bids are not disclosed, the winning bids of the FPA with EMP and the standard FPA converge towards the theoretical predictions, and these values are not signi cantly
different. In latter case, the EMP increases the frequency of deciding the winners by lottery.
The EMP, however, does not affect market ef ciency de ned by the total surplus of the government and producers.
In the different cost condition, the nondisclosure of subjects' identi cations and bids leads
to bidding 1 point to reduce the payoffs of producers with the lowest cost, using the spitefulstrategy. This behavior lowers the EMP to below the lowest cost. Thus, producers with thelowest cost bid prices close to their costs to win and winning bids converge toward the lowest
cost.
The disclosure condition, however, does not lead to bidding 1 point as the spiteful strategy,
and the EMP becomes higher than the lowest cost. Thus, producers with the lowest costs
raise their bids not to be excluded by the EMP; the winning bids diverge from the lowest cost.
Since the disclosure of subjects' identi cations and bids reduces the bidding of 1 as the spitefulstrategy, it seems to be easier for subjects to adopt the spiteful strategy when their identi cations
and actions are hidden. In socio-psychology, Yamagishi (1988a; 1988b) nd that the mutual
monitoring and sanctioning remove the free riding in Japan. In our different cost condition, themutual monitoring removes spiteful strategy, which makes the winning bids diverge from thelowest cost.
These results suggest that auctioneers need to pay attention to the information control ofproducers' identi cations and bids when they employ the EMP. Isaac and Walker (1985) andDufwenberg and Gneezy (2002) also caution about the disclosure of information concerning
losing bids because this information reduces (increases) the auctioneer's revenues (losses). Additionally, our results are similar to those of Isaac and Plott (1981), Smith and Williams (1981),
Coursey and Smith (1983), and Gode and Sunder (2004), who reveal that non-binding price15

controls affect trading prices in the competitive market. Although the EMP does not affectthe winning bids of the FPA in theory, it affects them under the speci c information control
experiment.
Although more experimental work is needed to obtain precise results, if we can say thatconcealing the identi cations and actions of subjects induces a spiteful strategy, which in turninduces the ef cient outcome for the government and taxpayers, auction authorities have to takesteps to protect companies' identi cations in the procurement procedures. To this end, sealed
bids by postal mail or via the Internet, recently employed by some Japanese local governments,
are useful in concealing who the bidder is. The EMP, however, does not have a critical impact
on the prevention of deciding winners by lottery, as expected by Japanese local governments.
Although our result calls the government's attention to the EMP's risk of inducing higher
winning bids and a higher frequency of deciding winners by lottery, our study cannot deny theneed of the EMP in procurement procedures because we restrict our attention to homogenous
goods. As we mentioned in the introduction, auctioneers began using the EMP to prevent buying abnormally low-quality goods. Next, we expand on Akai et al. (2009a), who explicitly
introduce quality into the procurement auction model, and evaluate whether the EMP prevents
the purchase of low quality goods and whether it increases social welfare in various environments.
Additionally, bid-rigging is a substantive problem, as Isaac and Walker (1985), Saijo et al.
(1996), and Kawagoe (2003) study. Since bidders can manipulate the EMP, this method is often
criticized for its tendency to collude in manipulating the EMP and excluding their rivals. A
simple way to manipulate the EMP is to create a dummy company. In fact, these problems areconcerned when Japanese local governments began employing the EMP. If auction authorities
follow our suggestions and do not disclose information about bidder's identi cations and bids,
they can promote collusion or the creation of dummy companies and make it dif cult to statethat the auction institution is transparent and fair for public procurement. Our nal goal is toassess whether the EMP prevents the purchase of abnormally low-quality goods at a fair priceeven if we allow bidders to conspire.
ACKNOWLEDGEMENTS
This research was partially 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 Scienti c Research on Priority Areas). We wish toacknowledge the helpful comments of Toshiji Kawagoe, Akihiko Matsui, Charles Noussaire,
Vesteg Robert, Junyi Shen, and Thakehiko Yamato and participants at meetings of the Asia
Paci c Economic Science Association and Japanese Economic Association and conferences of
the Experimental Social Sciences in Japan. We also thank Keiko Aoki, Atsushi Hirata, andTsuyoshi Nihonsugi for assistance conducting the experiment.

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18Appendix
P ROOF OF PROPOSITION 1.
Step 1: More than one producers bid b . Suppose that only one producer bids b . Thiswinner can raise her bid to the price slightly less than the second lowest bid, b + ε < b2 , andincrease her payoffs. This is a contradiction.
Step 2: b = c: Suppose b > c: Case 1: d(b) < b : The producer bidding b has an incentive
to reduce her bid to b ε and increase her payoffs. This is a contradiction. Case2: d(b) = b :If the producer bidding b raises her bid to the price slightly less than the second highest bid,b2 ε; then since she can pull the minimum price above b and exclude other producers biddingb , she can increase her payoffs. This is a contradiction.
P ROOF OF PROPOSITION 2.
Step 1: More than one producers bid b . Suppose that only one producer bids b . Thiswinner can raise her bid to the price slightly less than the second lowest bid, b + ε < b2 , andincrease her payoffs. This is a contradiction.
Step 2: The winner is a producer whose cost is c1 . Suppose that the winner is a producer
whose cost is more than or equal to c3 . Since b > c3 ; the producer whose cost is c1 can raise
her bid to b and increase her payoffs. This is a contradiction.
Step 3: c1 b < c3 : Suppose b < c1 : Since the winner is the producer whose cost is c1 andher payoffs are less than zero, she has an incentive to raise her bid to c1 and increase her payoffs.
This is a contradiction. Suppose bc3 : Case 1: d(b) < b : The producer whose cost is c1
has an incentive to reduce her bid to bε; and increase her payoffs. This is a contradiction.
Case2: d(b) = b : If the producer whose cost is c1 raises her bid to the price slightly less than
the second highest bid, b2 ε; then since she can pull the minimum price above b and exclude
other producers bidding b , she can increase her payoffs. This is a contradiction.
Step 4: b = c1 : Suppose b > c1 : Case 1: d(b) < b : The producer whose cost is c1 has anincentive to reduce her bid to b ε and increase her payoffs. This is a contradiction. Case2:
d(b) = b : If the producer whose cost is c1 raises her bid to the price slightly less than thesecond highest bid, b2 ε; then since she can pull the minimum price above b and exclude
other producers bidding b , she can increase her payoffs. This is a contradiction.

19

Table 1. An example of the EMP
Ranking of bids

1

2

3

4

5

6

7

The EMP The winning bid

bids (before)$100 $105 $130 $150 $160 $180 $200

$103

$105

bids (after)$100 $105 $149 $150 $160 $180 $200

$106

$149

Table 2. The environment of each cell
Cell

Number of

Minimum pricesessions

conditions

Production

Information conditions ofcost conditions subjects’ identifications and bids

N-I-D

2

No

Identical

Disclosure

E-I-D

2

Endogenous

Identical

Disclosure

N-I-N

2

No

Identical

Nondisclosure

E-I-N

2

Endogenous

Identical

Nondisclosure

N-D-D

2

No

Different

Disclosure

E-D-D

2

Endogenous

Different

Disclosure

N-D-N

2

No

Different

Nondisclosure

E-D-N

2

Endogenous

Different

Nondisclosure

Table 3. OLS regressions of winning bids on periods
Cell

N-D-D

a

102.60*** (5.60) 131.77*** (5.49)

127.83*** (3.81) 131.20*** (4.66)

b0.40 (0.90)－1.54* (0.88)－3.23*** (0.61) －4.05*** (0.75)

F-statistic

0.20

3.03*

27.67***

29.18***

adjusted R

－0.04

0.10

0.58

0.60

No. of Obs.

20

20

20

20

2

E-D-D

N-D-N

E-D-N

Note: Standard errors are in parentheses. *, **, and *** denote significance at the 10%, 5%, and 1%
levels, respectively.

20

Figure 1. Average winning bids and EMPs in the identical cost condition
Figure 1a
Figure 1b
150

price

97

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

9

10

periodAverage winning bids in E-I-D(left) or E-I-N(right)
Average winning bids in N-I-D(left) or N-I-N(right)
Average EMP

Figure 2. Average winning bids and EMPs in the different cost condition
Figure 2a
Figure 2b
150

price

97

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

periodAverage winning bids in E-D-D(left) or E-D-N(right)
Average winning bids in N-D-D(left) or N-D-N(right)
Average EMP

21

8Supplementary Material for"An Experimental Study of Procurement Auctions
with Endogenous Minimum Prices"
This supplementary material has four sections. Section 1 provides the proof of Proposition 3. Section 2 contains instructions and PC operation manuals. Sections 3 and 4
provide graphs and raw data of the entire experiments, respectively.
1. Proof of Proposition 3
Here, we show that there are no Case I pure Nash equilibrium in our setting. First we
describe four lemmas and use them for the proof of Proposition 3.
In the following model, when a bid pro…le is b, producer i’s probability Xi (b) of selling
the good is : Xi (b) = 0 if bi > minfbj : bj d(b)g, and Xi (b) = 1=n0 if bi = minfbj : bj
d(b)g, where n0 is the number of bids of arg minfbj : bj
d(b)g. When a bid pro…le isb, producer i’s (expected) payo¤ is ui (b) = (bi ci ) Xi (b), where ci is producer i’s costfor the good considered. Following the experiment, we assume that bids are nonnegative
integers and that producer 1 has the lowest cost, producer 2 has the second lowest cost,and so on, that is, c1 c2
cn . Given a bid pro…le b; let b (b) be the winning bid
of b, that is, b (b) = minfbi : i 2 N and bi d(b)g.
Lemma 1: In a Nash equilibrium b such that bi
ci for every i, no bid is excludedby d(b), that is, b1 (b) d(b).
Proof. Suppose that there is a bid bi excluded by d(b); that is, bi < d(b). Notethat ui (b) = 0: Let bbi = b (b). If producer i can be a winner by bidding bbi , that is,bbi = minfbj : j 2 N and bj
d(bbi ; b i )g, then since bbi = b (b)d(b) > bi > ci , andbbbbXi (bi ; b i ) > 0; it follows that ui (bi ; b i ) = (bi ci ) Xi (bi ; b i ) > 0 = ui (b): This isa contradiction to Nash equilibrium. Let ebi = bm (b), that is, ebi is equal to the m thlowest bid among fb1 ; : : : ; bn g. Note that ebi > d(ebi ; b i )d(bbi ; b i )d(b): Thus, if
producer i cannot be a winner by bidding bbi , then producer i can be a winner by bidding
some bi 2 [b (b); bm (b)], and similarly he can obtain a positive ui (bi ; b i ): This is also acontradiction to Nash equilibrium.
QED
Remark: In the Nash equilibrium b such that bi ci for all i, b (b) = minfbi : i 2 N g.
Lemma 2: Let bi ci for all i: In the Nash equilibrium b, for all i 2 N; if b (b) > ci ,bi = b (b).
Proof. Suppose that b (b) > ci , and bi 6= b (b) for some i 2 N: By Lemma 1, for all
i 2 N; bib (b) d(b): Thus, bi > b (b) > ci : By bi > b (b); ui (b) = 0: Let bbi = b (b).
Note that d(bbi ; b i ) d(b) b (b) = bbi : By Lemma 1, for all j 2 N; bj b (b) = bbi : Thus,
producer i can be a winner by bidding bbi , that is, bbi = minfbj : j 2 N and bj d(bbj ; b 1 )g.
Since bbi = b (b) > ci , and Xi (bbi ; b i ) > 0; it follows that ui (bbi ; b i ) = (bbi ci ) Xi (bbi ; b i ) >0 = ui (b): This is a contradiction to Nash equilibrium. Thus, for all i 2 N; if b (b) > ci ,bi = b (b).
QED
Lemma 3: In the Nash equilibrium b such that bi ci for all i, if b (b) > maxfc1 +2; c2 g; then d(b) 2 (b (b) 1; b (b)]:1

Proof. Suppose b (b) > maxfc1 + 2; c2 g and d(b) b (b) 1: Since Lemma 2 implies
b1 = b2 = b (b), X1 (b) 1=2. Thus, u1 (b) = (b1 c1 ) X1 (b) (b1 c1 )=2: Noteb (b) > c1 + 2 ) 2 fb (b) c1 g 2 > b (b) c1) fb (b) 1 c1 g > (b1 c1 )=2.
By bidding b (b) 1; producer 1 can be a single winner and can obtain the payo¤ (b (b)1 c1 ) > (b1 c1 )=2 = u1 (b): This is a contradiction to Nash equilibrium. Thus, d(b) 2(b (b) 1; b (b)]:QED
12
Lemma 4: In the Nash equilibrium b such that bi ci for all i, b (b) = b (b) b (b)b (b) + 1:
Proof. By Lemma 1, b1 (b) = b (b)d(b): By de…nition, b1 (b)b2 (b): Thus, weshow b2 (b) b (b) + 1. Suppose b2 (b) > b (b) + 1. Let i 2 N be such that bi = b1 (b). Let
bbi = b (b) + 1. Then, ui (bbi ; u i ) = b (b) + 1 ci > b (b) ci = ui (b): This is a contradiction
to Nash equilibrium.
QED
Proposition 3: Let n = 10; m = 5; k = 4=5; c1 = c2 = c3 = 97; c4 == c10 = 150.
There is no Case I pure Nash equilibrium bi ci , for every i.
Proof. Suppose there is a Nash equilibrium b such that bi ci for all i. Since bi ci
for all i, it follows that for all i 2 N; ci < bi and ci < bi (b). Note that b (b)b1 (b)
c1 = 98. We derive a contradiction in each of the following cases.
Case 1. b (b) 151: (b (b) c5 + 1:)
By Lemma 2 and b (b) > c5 , b1 == b5 = b (b). Thus, by Lemma 1, b1 (b) ==5b (b) = b (b), and so d(b) = (4=5) b (b). By Lemma 3, (4=5) b (b) > b (b) 1. Thisinequality implies b (b) < 5. This is a contradiction to b (b) 151.
Case 2. 98 b (b) 150: (c3 + 1 b (b) c4 :)By Lemma 2 and b (b) > c3 , b1 = b2 = b3 = b (b). Thus, by Lemma 1, b1 (b) = b2 (b) =3b (b) = b (b), and so d(b) = (4=5) [3 b (b) + b4 (b) + b5 (b)]=5. Since bi ci , b4 (b) 151
and b5 (b) 151: Note that u3 (b) = [b (b) 97]=3 [150 97]=3.
By Lemma 3, b (b) 1 < (4=5) [3 b (b) + b4 (b) + b5 (b)]=5. Thus, [13 b (b) 25]=4 <b4 (b) + b5 (b). Let bb3 = b4 (b).
We show d(bb3 ; b 3 ) > b (b) = b1 = b2 . Suppose d(bb3 ; b 3 ) b (b). Since [13 b (b)25]=4 < b4 (b) + b5 (b); [13 b (b) 25]=4 b5 (b) < b4 (b). Thus,b (b)d(bb3 ; b 3 )4 2 b (b) + b4 (b) + b4 (b) + b5 (b)
=
5
5
4
=
2 b (b) + 2 b4 (b) + b5 (b)25
413 b (b) 25>
2 b (b) + 2
2 b5 (b) + b5 (b)25
41=
8 b (b) + 2 f13 b (b) 25g 4 b5 (b)251=34 b (b) 50 4 b5 (b) .
25
2

by b4 (b) >13 b (b)425

b5 (b)

Therefore,1
34 b (b) 50 4 b5 (b)2525 b (b) > 34 b (b) 50 4 b5 (b)4 b5 (b) > 9 b (b) 50
b5 (b) > [9 b (b) 50]=4.
b (b) >

Let bb4 = b5: Then,

4 3 b (b) + 2 b5 (b)d(bb4 ; b 4 ) =55
9 b (b)4
3 b (b) + 2
>
25
4
1
=
[30 b (b) 100] .
25

50

by b5 (b) >9 b (b)4

50

1Thus, if d(bb4 ; b 4 )b (b); then 25[30 b (b) 100] < b (b). This inequality implies
b (b) < 20: This is a contradiction to b (b) 98: Thus, d(bb4 ; b 4 ) > b (b) = b1 = b2 = b3 :Since d(bb4 ; b 4 ) b5 (b) = bb4 ; X4 (bb4 ; b 4 ) 1=2, and sou4 (bb4 ; b 4 )[b5 (b)c4 ]=2[151150]=2 > 0 = u3 (b):Since b is a Nash equilibrium, this is a contradiction. Therefore, d(bb3 ; b 3 ) > b (b) = b1 =
b2 .
Note
4 2 b (b) + b4 (b) + b4 (b) + b5 (b)d(bb3 ; b 3 ) =554=
3 b (b) + fb4 (b) b (b)g + b4 (b) + b5 (b)25
44=
3 b (b) + b4 (b) + b5 (b) +fb4 (b) b (b)g25
25
4
= d(b) +fb4 (b) b (b)g25
4b (b) +
fb4 (b) b (b)g25
< b (b) + fb4 (b) b (b)g = b4 (b).
Therefore, d(bb3 ; b 3 )u3 (bb3 ; b 3 )b4 (b) = bb3 . Thus, X3 (bb3 ; b 3 )[b4 (b)c3 ]=2[151

97]=2 > [150

Since b is a Nash equilibrium, this is a contradiction..

3

1=2, and so97]=3u3 (b).
QED

2. Instructions and PC operation manuals
Instructions (for cell E-I-D)
In this experiment, every subject makes a decision on selling the goods to theexperimenter. Please understand the rules of the experiment well, make an appropriate
decision, and earn as much rewards as possible.
Outline of the experiment
In this experiment, you will be assigned a role of a producer, and sell a “good”
to the experimenter. The number of subjects participating in this experiment is 10
people in total. Each subject acts the role of the producer. The computer acts as theexperimenter. The experiment will be repeated 10 periods. In each period, theexperimenter purchases a good from a producer according to pre-determined certain
rules. Following explains the rules of purchasing a good for the experimenter acted by
the computer and the role of a producer every subject acts.
The purchasing rules of the experimenterFirst, we explain the purchasing rules of the experimenter acted by thecomputer. The experimenter purchases one unit of “good” from one of 10 producers
according to the rules below. The purchasing rules of the experimenter are as follows.
First of all, the experimenter asks all 10 producers to submit the selling prices
for the good through computer display. Money used in this experiment is measured by“point” of a fictitious monetary unit. The experimenter purchases a good at the selling
price less than or equal to 243 points. Therefore, the maximum selling price of you as
the producer can submit to the experimenter is 243 pt. Note that selling prices you can
submit are only integers. You have three minutes to input your selling price on yourcomputer screen. Note that you cannot cancel the selling price once you havesubmitted it to the experimenter.
Next, the experimenter selects five producers in the order of the lowest selling
prices. The experimenter calculates the average selling price of these five producers.
Then, this average is multiplied by 0.8. The experimenter selects one producer whose
selling price is the lowest among all the producers who have submitted the selling
prices higher than or equal to “0.8 × (average selling price of lowest five producers)”.
The experimenter purchases the good from that producer at the selling price he/she
has submitted.

4

If there are two or more producers who have submitted that price, then theexperimenter randomly selects one of them and purchases the goods from that
producer.
Roles of producers
We explain the role of the producer you act. Before the beginning of theexperiment, every subject will be assigned to a producer’s identification number from
1 to 10 by a lottery. Once you receive a producer’s number, that number will notchange throughout the experiment.
Each producer can produce one unit of good at “production costs”. The
production cost of a good are common among all producers and it is 97 pt. The qualityof the good any producers produce is same.
When a producer is selected by the experimenter, he/she is to produce a goodand sell it to the experimenter to get “sales revenues”. Since the unit of goods you cansell is one unit, the sales revenue is equal to the selling price to the experimenter, i.e.
equal to the purchase price of the experimenter. The difference between the sales
revenue and the production cost of the good is a “profit” the producer earns from theproduction and sales. That is, “profit = purchase price of the experimenter – production
cost of the good.”
However, producers who do not sell the good to the experimenter do not
produce a good. In this case, these producers do not earn sales revenues but have no
production cost incurred either, so his/her profit is 0 pt.
Purchasing rules of the experimenter and an example of the way to calculate
producers’ profits
This section explains the purchasing rules of the experimenter and the exampleof way to calculate producers’ profits by using actual numbers. Although theexperimenter do not purchase any goods with the selling price higher than 243 points
in the experiment, here we assume that the experimenter can purchase a good at theprice higher than 243 points, and explain the example.
For example, producers number 1 to 10 submit the following selling prices
respectively as their selling prices: 3000 pt, 4000 pt, 5000 pt, 6000 pt, 7000 pt, 8000 pt,
5000 pt, 3000 pt, 4000 pt and 9000 pt. Five lowest prices are 3000 pt = 3000 pt < 4000
pt = 4000 pt < 5000 pt. The average of these prices is (3000 + 3000 + 4000 + 4000 +5000) / 5 = 3800 pt. Multiplying this with 0.8, we get 3800 × 0.8 = 3040 pt. All theselling prices equal to or higher than this number are 4000 pt = 4000 pt < 5000 pt =5

5000 pt < 6000 pt < 7000 pt < 8000 pt < 9000 pt. The lowest price is 4000 pt among
them. However, there are two producers who have submitted 4000 pt of selling price.
Therefore, one of them will be selected with the probability of 1/2, and that producer
sells the good to the experimenter.
At this point, the producer selected by the experimenter is to produce a goodat the production cost of 97 pt so that this producer’s profit is 4000 – 97 = 3903 pt. Allother producers’ profits are 0 pt.
Let us repeat that, in the actual experiment, the experimenter purchases thegood at the price lower than or equal to 243 pt. Every subject decide what selling priceyou are to submit to the experimenter, while taking account of what selling prices otherproducers submit, and try to earn as much rewards as possible.
Completion of the experiment and the calculation of rewards
Once all the producers submit their selling prices, the experimenter notify all
producers from whom the experimenter purchases a good according to the rules as we
explained earlier.
The experimenter discloses the following 4 types of information to all
producers: “producer’s identification number from whom the experimenter purchase agood”, “the purchasing price of the experimenter”, “average of five lowest selling
prices”, and “0.8 × (average of lowest five selling prices)”. At this point, the first period
finishes. Once the first period finishes, the second period will start with sameprocedures. At the time 10th period finishes this experiment is completed.
After the end of the experiment, the rewards each subject receives is calculated
from total profits of the producer each subject acts. Specifically, the rewards to eachsubject after the end of the experiment are calculated as the following formula.
Rewards after the end of the experiment = (50 pt + Gross profit) × 30 Yen
We explain about this formula in detail. At the beginning of the experiment, eachsubject is given 50 pt only once. Total profits as the sum of the profits of producer you
act for 10 periods are added to the 50 pts. However, profits can be minus in theexperiment. If you submit the selling price below the production cost and theexperimenter purchases the goods at that selling price, your profit will be minus. If thetotal profits as the sum of profits for 10 periods are minus, it will be subtracted from 50
pts given to you at the beginning of the experiment. Each subject receives the rewards incash under the conversion rate of 1 pt = 30 yen. Please try to earn as much rewards as

6

possible.
Above is the content of today’s experiment. During the experiment, do nottalk to others, and follow orders of the experimenter. You make a decision in theexperiment by the software that operates on the personal computer assigned to eachsubject. The attached “PC Operation Manual” describes how to operate the PC. We
will explain about this manual after the next reading period of “questions and answers
on instructions”.

This part is for the different production cost condition.
Roles of producers
We explain roles of producers you act. Before the beginning of the experiment,
every subject will be assigned to a producer identification number from 1 to 10 by alottery. Once you receive a producer number, that number will not change throughout
the experiment.
Each producer can produce one unit of good at “production cost”. Production
costs of a good are in the table below.
Producer No.

1

2

3

4

5

6

7

8

9

10

Cost

150 pt

97 pt

150 pt

150 pt

97 pt

150 pt

150 pt

97 pt

150 pt

150 ptProducer number 1 has the production cost of 150 pt, No. 2 has 97 pt, No. 3
150 pt, No. 4 150 pt, No. 5 97 pt, No. 6 150 pt, No. 7 150 pt, No. 8 97 pt, No. 9 150 pt,
and No. 10 150 pt. The quality of goods any producers produce is the same.
When a producer is selected by the experimenter, he/she is to produce a goodand sell it to the experimenter to get “sales revenue”. Since the unit of goods sold is one
unit, the sales revenue is equal to the selling price to the experimenter, i.e. equal to thepurchase price of the experimenter. The difference between the sales revenue and the
production cost of the good is the “profit” the producer earns from the production andsales. In other words, “profit = purchase price of the experimenter – production cost of
the good.”
However, producers who do not sell the good to the experimenter do not
produce a good. In this case, these producers do not earn sales revenue but have no
production cost incurred either, so his/her profit is 0 pt.

7

Purchasing rules of the experimenter and an example of the way to calculate
producers’ profits
This section explains the purchasing rules of the experimenter and the exampleof way to calculate producers’ profits by using actual numbers. Although theexperimenter do not purchase any goods with the selling price higher than 243 points
in the experiment, here we allow the experimenter to purchase a good at the price higher
than 243 points and explain the example.
For example, producers number 1 to 10 submit the following selling prices
respectively as their selling prices: 3000 pt, 4000 pt, 5000 pt, 6000 pt, 7000 pt, 8000 pt,
5000 pt, 3000 pt, 4000 pt and 9000 pt. Five lowest prices are 3000 pt = 3000 pt < 4000
pt = 4000 pt < 5000 pt. The average of these prices is (3000 + 3000 + 4000 + 4000 +5000) / 5 = 3800 pt. Multiplying this with 0.8, we get: 3800 × 0.8 = 3040 pt. All theselling prices equal to or higher than this number are 4000 pt = 4000 pt < 5000 pt =5000 pt < 6000 pt < 7000 pt < 8000 pt < 9000 pt. The lowest price is 4000 pt among
them. However, there are two producers who have submitted 4000 pt of selling price.
Therefore, one of them will be selected with the probability of 1/2, and that producer
sells the good to the experimenter.
At this point, if the producer with production cost of 97 pt is selected, thenhe/she produces a good at 97pt, so his/her profit is 4000 – 97 = 3903 pt. If the selected
producer has the production cost of 150 pt, then he/she manufactures goods at the costof 150 pt, and his/her profit is 4000 – 150 = 3850 pt. All other producers’ profits are 0pt.
Let us repeat that, in the actual experiment, the experimenter purchases thegood at the price lower than or equal to 243 pt. Every subject decide what selling priceyou are to submit to the experimenter, while taking account of what selling prices otherproducers submit, and try to earn as much rewards as possible.

This part is for the nondisclosure condition.
Completion of the experiment and the calculation of rewards
Once all the producers submit their selling prices, the experimenter notify all
producers from whom the experimenter purchases a good according to the rules as we
explained earlier.
The experimenter discloses the following 4 types of information to all
producers: “producer’s identification number from whom the experimenter purchase agood”, “the purchasing price of the experimenter”, “average of five lowest selling8

prices”, and “0.8 × (average of lowest five selling prices)”. At this point, the first period
finishes. Once the first period finishes, the second period will start with sameprocedures. At the time 10th period finishes this experiment is completed.
After the end of the experiment, the rewards each subject receives arecalculated from total profits of the producer each subject acts. Specifically, the rewards
to each subject after the end of the experiment are calculated as the following formula.
Rewards after the end of the experiment = (50 pt + Gross profit) × 30 Yen
We explain about this formula in detail. At the beginning of the experiment, eachsubject is given 50 pt only once. Total profits as the sum of the profits of producer you
act for 10 periods are added to the 50 pt. However, profits can be minus in theexperiment. If you submit the selling price below the production cost and theexperimenter purchases the goods at that selling price, your profit will be minus. If thetotal profits as the sum of profits for 10 periods are minus, it will be subtracted from 50
pts given to you at the beginning of the experiment. Each subject receives the rewards incash under the conversion rate of 1 pt = 30 yen.
The experimenter will not disclose to other subjects whom is assigned to which
producer number during and after the experiment. Therefore, try to earn as muchrewards as possible without concern for others. Please try to earn as much rewards as
possible.

This part is for cells E-I-N and N-I-N.
Completion of the experiment and the calculation of rewards
After the end of the experiment, the rewards for each subject are calculated
from total profits of the producer each subject acts. Although every subject cannot
know the formula to calculate the rewards, that formula is common among all subjects
and have a feature that greater the total profit of the producer you act the greater the
rewards.
At the beginning of the experiment, the profit of each producer is 0 pt. If you
submit the selling price below the production cost and the experimenter purchases the
goods at that selling price, your profit will be minus. Even if the total profits are 0 pt orminus, each subject is guaranteed to receive the minimum rewards. We cannot tell you
how much the minimum rewards are. The rewards paid to the subject with the negative
total profits are the same regardless of how big the negative profits are. Moreover, the9subject with the negative total profits and the subject with 0 pt will receive the same
minimum rewards.
The experimenter will not disclose to other subjects whom is assigned to which
producer number during and after the experiment. Therefore, try to earn as muchrewards as possible without concern for others.

10PC operation manuals (for the endogenous minimum price condition)
In the experiment, each subject sells a good to the experimenter by using the PC
assigned to each of them. We explain screens of the software we use in the experiment and how
to manipulate it as follows.

PeriodRemaining time (sec.)

your producer’s number
your production costthe selling priceScreen 1
As soon as period 1 starts, the experimenter asks each producer to submit aselling price. Screen 1 is shown in the screen of the PC in front of every subject.
Please see screen 1. In the center of this screen, “your producer’s number”, “yourproduction cost”, and a cell you submit a “selling price” are displayed. In this example, the cellof “your producer’s number” displays producer 1. Producer 1’s production cost is 150 pt so thatthe cell of “your production cost” displays 150 pt. Any subjects submit integers between 1 pt
and 243 pt (limits included). Every subject inputs the selling price and then writes thatselling price in the cell in the record sheet. After you complete writing, click OK button in
the upper-right corner of the screen. Note you can neither cancel nor correct once you

11click OK button. Please pay attention about it carefully.
Additionally, “period” in the upper-left corner of the screen displays what period is in
the experiment. In screen 1, it displays “1/10” as shown period 1. “Remaining period” in theupper-right corner of the screen displays how long you have left for submitting a selling price tothe experimenter. Any subjects input the selling prices within 3 minutes (180 seconds). You
necessarily input the selling price. The experimenter encourages subjects who do not input yet
after the remaining time elapse 0 to input the selling price. Notice once all subjects click OK
button, the experimenter start purchasing procedures even though 3 minutes do not elapse.

periodRemaining time (sec.)

your producer’s number
the experimenter buys a good from you
purchasing price of the experimenter
your production costyour profits

Screen 2
If the experimenter purchases the good from you, screen 2 is displayed. From the
top of the display, “your producer’s number”, “the experimenter buys a good from you”,“purchasing price of the experimenter”, “production cost”, and “your profits” are displayed. In
this example, the cell of “your producer’s number” displays producer 1. Producer 1’s production
cost is 150 pt so that the cell of “your production cost” displays 150 pt. Numerical numbers are
displayed in the white box cells of the right side of the “purchasing price of the experimenter”
and “your profit”.

12Every subject, in the actual experiment, transcribes the numerical number
displayed at the right side of “your profit” on the record sheet. After the transcription,please click OK button in the lower-left corner of the screen.

periodyour producer’s number
the experimenter buys a good from you
your profits

Screen 3
If the experimenter does not purchase the good from you, screen 3 is displayed. From
the top of the display, “your producer’s number”, “the experimenter does not buy a good fromyou”, “purchasing price of the experimenter”, “production cost”, and “your profits” aredisplayed. “Your profit” will be 0 pt.
Every subject, in the actual experiment, transcribes the numerical number
displayed at the right side of “your profit” on the record sheet. After the transcription,please click OK button in the lower-left corner of the screen.

13

period

your producer’s number
the experimenter buys a good from producer
the purchasing price of the experimenter
The average of five lowest selling price
0.8 × (average of lowest five selling prices)

Screen 4
After the experimenter decides from whom he buy the good, he disclose “producer’s
identification number from whom the experimenter purchase a good”, how much “thepurchasing price of the experimenter” is, how much “average of five lowest selling prices” is,and how much “0.8 × (average of lowest five selling prices)” is. These information aredisplayed from the top of screen 4. Here we show the case where we purchase the good fromproducer 1 as an example. Numerical numbers are displayed in the white box cells of the rightside of the “purchasing price of the experimenter”, “average of five lowest selling prices”, and“0.8 × (average of lowest five selling prices)”.
Every subject transcribes these information from the top on the cells of“producer’s number from whom the experimenter purchased the good”, “the purchasing
price of the experimenter”, “average of five lowest selling prices”, and “0.8 × (average oflowest five selling prices)” in the record sheet. After the transcription, please click OK
button in the lower-left corner of the screen. Once everybody click OK button, period 1 iscompleted and period 2 will start. The operation after period 2 is the same as one in period
1. The experiment is completed at the time when period 10 is completed.

14

This is the end of explain the PC operation manuals.

15

3. All graphs in each cell
In all graphs, the horizontal axis represents the number of periods, and vertical axis
represents the price of bids. Winning bids are connected by a straight line, and thesevalues are presented right next to the winning prices. Squares connected by a straightline represent the EMPs. In each graph of the identical condition, diamonds withnumbers 1 to 10 represent bids of producers 1 to 10, respectively. In each graph of thedifferent cost condition, diamonds with 2 (97), 5 (97), and 8 (97) represent bids ofproducers 2, 5 and 8 whose costs are 97, respectively. Triangles with identification
numbers 1, 3, 4, 6, 7, 9, and 10 represent bids of each producer whose cost is 150.

16

Figure S1. N-I-D
Session 1

Session 2

243
200

price

150

106

97

101 99

98

99

98

98

98

100 98

97

98

98

97

98

98

98

97

98

76

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

period
1
7

2
8

3
9

4
10

5
Winning bids

6

Figure S2. E-I-D
Session 1

Session 2

243
200

price

150

100 99

97

98

98

98

98

97

98

98

98

98

95

90

98

90

98

98

98

98

78

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

period
1
7

2
8

3
9

4
10

5
Winning bids

17

6
EMP

9

10

Figure S3. N-I-N
Session 1

Session 2

243
200

price

150

97

98

98

97

97

97

96

97

97

98

97

97

97

97

97

97

96

98

97

97

50

0

1

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

period
1
7

2
8

3
9

4
10

5
Winning bids

6

Figure S4. E-I-N
Session 1

Session 2

243
200

price

150

97

98

98

97

95

98

90

98

98

98

98

98

98

97

97

96

97

97

97

97

97

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

period
1
7

2
8

3
9

4
10

5
Winning bids

18

6
EMP

9

10

Figure S5. N-D-D
Session 1

Session 2

243
200

150

price

147
119
107

97

106

100

111

106 107

105

100

99

99

98

100 100 100 98

98

98

98

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

period1
72(97pt)8(97pt)3
94
105(97pt)Winning bids

6

Figure S6. E-D-D
Session 1

Session 2

243
200

150

155

price

151
121 119 119

128

135 132
120

115

126

121 117 117 120

119 115
111

115

110

97

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

period1
72(97pt)8(97pt)3
94
105(97pt)Winning bids

19

6
EMP

10

Figure S7. N-D-N
Session 1

Session 2

243
200

150

price

136

125 127 124

97

129
118

114 110106 107 105 103

106 102
99

98

98

98

98

98

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

period1
72(97pt)8(97pt)3
94
105(97pt)Winning bids

6

Figure S8. E-D-N
Session 1

Session 2

243
200

150

price

148

141
130

120
108

97

118
98

98

98

98

98

109 110 108
104 100
98

98

98

98

50

0
1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

period1
72(97pt)8(97pt)3
94
105(97pt)Winning bids

20

6
EMP

10

4. Row date in each cell
Producer's ID (cost)
N-I-D: session 1
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)
N-I-D: session 2
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)
N-I-N: session 1
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)
N-I-N: session 2
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)* shows the winning bids.

Period
5
6

1

2

3

4

109
143
125
125
178
140
117
110
106*
118

103
101*
115
125
135
106
108
104
112
102

99*
104
100
125
240
115
106
107
114
101

100
98*
100
123
100
107
105
100
121
100

98*
103
100
105
243
112
105
99
122
98

145
147
106
117
104
194
200
146
104
100*

119
99
104
117
98*
121
110
145
100
100

121
147
99
117
98
120
98
145
100
98*

163
147
97*
117
98
120
98
145
100
98

98*
115
130
120
124
99
127
117
177
143

98
98*
98
120
98
98
98
117
243
105

97
98
98
120
98
98
98
98
97*
98

199
222
199
147
119
98*
190
199
120
110

97*
190
169
98
100
99
120
199
98
98

97*
150
98
98
100
98
100
243
98
98

21

7

8

9

10

99*
99
100
126
200
102
105
100
121
100

99
99
100
156
98
99
98*
100
101
100

98
98
123
99
98
99
98
100
100
98*

98
98
123
98
98
97*
98
100
98
98

97
98
123
100
98
112
76*
100
98
98

109
117
99
117
98
197
98
145
100
98*

243
107
98
117
98*
197
98
117
100
98

98
107
98*
117
98
98
98
117
200
98

99
107
97*
117
98
98
98
200
210
98

121
107
98
117
98
98
98
200
220
98*

106
107
98
117
98
98
98
105
242
98*

97*
98
98
120
98
98
98
98
100
98

97
98
98
120
98
98
96*
98
200
98

97*
98
98
120
98
98
97
98
98
98

98
98
98
120
98
98
97*
98
98
98

97*
98
98
120
98
98
97
98
98
98

98
98
98
120
98
98
97*
98
120
98

98
98
98
120
98
1*
96
98
97
98

98
97*
100
97
100
98
100
200
98
98

98
120
98
97
98
98
98
200
97*
98

200
120
98
96*
100
98
98
200
97
200

98
100
98
98
98
98
98
200
97*
98

97
100
98
97*
98
98
98
197
97
98

200
100
98
98
98
98
98*
197
98
98

97*
98
98
98
98
98
98
197
98
98

Producer's ID (cost)
1
N-D-D: session 1
1 (150)152
2 (97)
127
3 (150)200
4 (150)160
5 (97)
198
6 (150)152
7 (150)160
8 (97)
119*
9 (150)243
10 (150)151
N-D-D: session 2
1 (150)163
2 (97)
142
3 (150)150
4 (150)160
5 (97)
99*
6 (150)200
7 (150)169
8 (97)
106
9 (150)160
10 (150)
155
N-D-N: session 1
1 (150)151
2 (97)
136*
3 (150)155
4 (150)170
5 (97)
137
6 (150)180
7 (150)197
8 (97)
160
9 (150)200
10 (150)
185
N-D-N: session 2
1 (150)243
2 (97)
135
3 (150)151
4 (150)158
5 (97)
138
6 (150)187
7 (150)200
8 (97)
129*
9 (150)151
10 (150)200* shows the winning bids.

Period
5
6

2

3

4

7

8

9

10

155
107*
160
155
168
152
151
107
243
151

151
100*
160
151
168
152
158
126
243
200

153
106*
160
151
168
152
155
135
243
155

151
117
160
243
168
152
160
111*
243
155

152
106*
160
151
155
152
151
111
243
155

152
107
160
151
107*
152
243
128
243
155

151
100*
160
151
128
152
161
108
243
155

151
105*
160
151
106
152
151
111
243
200

243
99*
160
151
243
152
155
109
151
200

243
120
150
155
99
160
168
98*
243
155

243
141
150
200
98*
160
242
114
243
154

237
150
150
240
100*
243
243
111
243
160

238
109
150
180
109
243
243
100*
243
154

226
109
150
230
105
243
243
100*
243
153

199
151
150
243
99
242
243
98*
243
153

239
151
150
240
98*
240
243
105
243
151

237
149
150
155
151
239
243
147*
243
153

155
125
149
184
120
160
243
98*
243
160

150
149
155
155
125*
151
151
150
170
160

152
127*
151
155
135
151
151
130
151
170

151
150
151
151
124*
151
151
125
150
155

151
114*
151
155
130
151
151
117
230
151

150
140
151
155
120
151
151
110*
240
243

151
119
151
160
106*
151
151
125
199
170

143
109
200
160
117
151
151
107*
240
243

151
109
151
152
105*
151
151
117
240
155

141
103*
151
151
106
151
151
104
240
160

243
119
150
158
118*
152
180
122
151
200

151
106*
151
158
107
150
230
112
151
200

151
108
151
158
102*
180
170
104
151
200

151
100
151
158
102
160
190
99*
151
200

151
98*
151
158
101
160
210
106
151
200

151
98*
151
158
100
160
220
99
151
200

151
99
151
158
99
160
160
98*
151
200

151
98*
151
158
98
160
215
107
151
200

151
98
151
158
98*
160
200
102
151
200

22

Producer's ID (cost)
E-I-D: session 1
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)EMP
E-I-D: session 2
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)EMP
E-I-N: session 1
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)EMP
E-I-N: session 2
1 (97)
2 (97)
3 (97)
4 (97)
5 (97)
6 (97)
7 (97)
8 (97)
9 (97)
10 (97)EMP* shows the winning bids.

Period
5
6

1

2

3

4

7

8

9

10

160
196
130
126
100*
200
105
158
160
117
92.5

99*
150
115
126
99
127
105
104
160
115
83.5

98
243
130
243
98
110
105
102
243
98*
80.2

98*
243
130
243
98
147
105
99
243
107
81.1

98*
243
200
243
98
137
105
98
243
127
84.2

243
243
243
243
98
98
105
98
150
97*
79.4

98
147
130
243
98
137
105
98
150
98*
79.5

98*
147
243
222
98
147
105
98
1
118
64

194
127
243
111
98
140
105
98
222
98*
81.6

100
127
104
7
98
101
105
98*
109
102
64.6

150
194
49
153
98*
153
147
160
130
127
88.2

105
143
130
78*
105
120
122
138
98
101
77.9

100
106
90*
100
110
100
107
104
102
104
78.7

101
125
95*
98
99
99
98
99
98
120
78.1

160
90*
95
98
98
98
98
98
98
115
76.6

115
127
99
110
98
98
130
98*
98
115
78.6

101
120
100
98
98*
98
100
103
150
114
79

145
120
98
98*
98
98
243
100
140
98
78.4

98
145
98*
98
98
98
243
150
176
98
78.4

98
175
98
98
98
98
98*
98
111
98
78.4

98*
110
159
1
120
140
150
163
169
104
69.3

98
98
125
1
105
98
100
100
1
98*
47.4

98
98
98
98
100
97*
99
70
98
98
73.8

98
98
98
98
99
99
99
95*
100
98
77.9

98
98
90*
98
98
98
97
98
100
98
77

98
98
98*
1
98
243
98
98
100
98
62.9

98
98
101
98
98*
1
98
98
1
98
47.4

98
98
98
98*
98
98
98
98
98
98
78.4

98
98
98*
98
100
243
98
98
100
98
78.4

98
98
98
98
98
98
99
98*
100
98
78.4

120
116
168
150
104
125
140
133
98*
136
90.1

110
100
98
98
98*
115
98
98
98
109
78.4

100
98
98
98
97*
98
98
98
98
98
78.2

99
98
98
98
97
98
98
98
98
96*
77.9

98
98
98
98
97*
98
98
98
98
97
78.1

97
98
97*
98
97
98
98
98
98
97
77.8

97
98
98
98
98
98
98
98
98
97*
78.1

97*
98
98
98
98
98
98
98
98
2
62.9

97*
98
98
98
98
98
97
98
98
97
77.9

97
98
98
98
98
97*
97
98
98
98
77.9

23

Producer's ID (cost)
E-D-D: session 1
1 (150)2 (97)
3 (150)4 (150)5 (97)
6 (150)7 (150)8 (97)
9 (150)10 (150)
EMP
E-D-D: session 2
1 (150)2 (97)
3 (150)4 (150)5 (97)
6 (150)7 (150)8 (97)
9 (150)10 (150)
EMP
E-D-N: session 1
1 (150)2 (97)
3 (150)4 (150)5 (97)
6 (150)7 (150)8 (97)
9 (150)10 (150)
EMP
E-D-N: session 2
1 (150)2 (97)
3 (150)4 (150)5 (97)
6 (150)7 (150)8 (97)
9 (150)10 (150)
EMP* shows the winning bids.

Period
5
6

1

2

3

4

159
180
153
160
165
165
152
110
155
151*
115

151
147
155
151
121*
155
151
150
155
152
115

243
119*
160
151
124
180
151
120
154
151
106

243
119*
220
151
149
200
151
108
210
151
108

243
128*
243
151
110
220
243
112
210
242
114

180
175
158
159
120*
163
163
135
170
160
117

155
138
155
167
200
195
160
135*
200
160
119

160
142
243
230
200
160
161
132*
200
243
121

170
126*
243
243
140
243
155
127
225
243
115

157
148*
193
152
112
156
159
150
155
151
114

153
141*
243
151
107
153
151
150
160
151
112

200
150
243
151
130*
155
155
138
155
243
116

180
120
157
158
118*
151
243
180
181
175
113

151
120
170
158
109*
151
243
130
155
155
106

151
110*
184
243
103
151
151
130
170
190
103

24

7

8

9

10

152
135
243
151
131
225
243
120*
230
243
110

243
119
243
151
118
190
243
115*
222
243
111

243
121*
243
151
115
243
230
113
222
243
116

151
125
243
151
150
240
220
117*
222
225
111

151
117*
180
151
120
230
219
118
222
200
105

160
119*
243
180
130
243
156
137
243
243
112

200
125
1
180
115*
243
156
180
243
243
92.3

200
113
243
243
130
160
156
111*
243
243
107

200
105
243
243
115
190
155*
199
243
243
122

198
122
243
1
121
243
159
115*
243
243
82.9

195
146
155
1
110
154
163
110*
180
200
83.4

152
128
243
243
129
155
150
120*
175
243
109

165
108*
243
243
119
155
1
111
243
243
79

151
104
243
243
98*
155
1
103
3
1
33

170
102
243
151
98
155
153
98*
1
1
48

151
98*
243
243
102
155
155
98
155
1
72

240
98
243
243
98*
155
200
98
240
1
72

160
98*
243
160
103
155
151
98
1
1
48.2

151
108
198
243
108*
200
243
125
151
151
103

151
104*
190
1
104
200
151
106
155
149
74.2

151
102
185
1
100
160
151
100*
161
140
70.9

151
99
188
1
98*
160
151
102
240
135
69.6

151
98
180
1
98
160
151
98*
155
130
68

151
98*
178
1
243
160
243
98
153
125
75.7

151
98*
181
158
98
160
243
98
241
120
90.4