Discussion Papers In Economics
And Business

Collusion in Repeated Procurement Auction: a Study ofPaving Market in Japan

Rieko Ishii

Discussion Paper 07-16

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANCollusion in Repeated Procurement Auction: a Study ofPaving Market in Japan

Rieko Ishii

Discussion Paper 07-16
May 2007

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANCollusion in Repeated Procurement Auction: a Study ofPaving Market in Japan∗

Rieko Ishii†
May, 2007

Abstract
We present an econometric approach to the problem of detecting bid rigging inprocurement auctions using bidding data for paving works in Ibaraki City, Osaka,
Japan. We ﬁrst show that sporadic price wars are caused by the participation ofpotential “outsiders.” Assuming that the ring is all-inclusive in the absence of theseoutsiders, we estimate the rule by which the ring selects the winner. It is found thatthe ring tends to select a bidder whose time elapsed from the last winning is long andwhose winning amount in the past is small relative to other bidders.
JEL Classiﬁcation D44, H57, L44
Keywords: Bid rigging, repeated auction.

∗

I am grateful to Masaki Aoyagi, Daiji Kawaguchi, Miki Kohara, Akihiko Matsui and Shinichi Sakata
for helpful suggestions and discussions. I also thank seminar participants in University of Tokyo, Nagoya
University, Japanese Fair Trade Commission, National Graduate Institute for Policy Studies, and Design
Science Young Seminar (Osaka University) for comments. All errors are mine.
†
Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka, Ibaraki-shi, Osaka,567-0047, JAPAN; E-mail: dg009ir@mail2.econ.osaka-u.ac.jp

1

Introduction

Bid rigging is pervasive in public procurement auctions. As bid rigging in public auctions
has recently become a major social problem and attracted more public attention, the innerworking of bidding rings has begun to be revealed by journalists, lawyers and industry
experts who were formally involved in ring activities themselves.1 Their reports uncover
the rules under which contracts are allocated among ring bidders. For example, Suzuki(2004) documents the allocation rules of 252 bid rigging cases between 1947 and 2000.
It is nortworthy that a number of rings use a class of schemes which allocates contracts
mainly based on the history of auctions.
This paper proposes an approach to detect bid rigging, which is eﬀective when the ringis all-inclusive in the market and its allocation rule belongs to a class, in which allocation
is based on public history of auctions.
We look at auctions for road-paving works in Ibaraki City, Osaka, Japan for the fouryear period between 2002 and 2005. Though there is no legal case of bid rigging ﬁled
against bidders in the market, collusion is suspected due to consistently high winning
prices with the exception of sporadic price wars.2
We ﬁrst analyze the cause of the price wars and ﬁnd that the price wars during thedata period mainly occurred when either of two speciﬁc ﬁrms were present. It is supposedthat the price wars were between the ring and a small number of competitive biddersin the market, and that all the ring bidders submitted low bids in order to prevent theoutsiders from winning.
We then assume that the high prices were maintained by an all-inclusive ring which
allocates contracts to its members by some prespeciﬁed rule, and examine the data to see
how the ring selects the winner among its members. We ﬁnd that the ring tends to assign
a win to its member whose time elapsed from his last win is long and whose winning
amount in the past is small relative to other ring bidders.
It has been pointed out that the pattern of bid rotation is not of itself evidence ofcollusion. When bidders’ cost functions exhibit decreasing returns to scale, bid rotation
can be an outcome of a competitive equilibrium. In competitive auctions, ﬁrms with idle
capacity are more likely to win a contract than those with ongoing contracts, and hence bid
rotation can be a natural outcome (Zona (1986), Porter and Zona (1993), Porter (2005)).
Our approach descriminates between collusive and non-collusive bid rotation by separating
the eﬀect of capacity utilization from the rotating bid aggreement. We construct variables
for ﬁrms’ used capacity and for the priority measure that determine the turn in the rotation
scheme, separately, and analyze their eﬀect on the events of winning or losing. We can1

Hironaka (1994), Kato (2005).
In this paper, we use the term, a “price war” to indicate an auction whose winning price is significantly
below the usual prices.
2

1

discriminate competition and collusion by testing the independence of the events from thepriority measure of the rotation scheme.
There are many empirical work on bid rigging aiming at detecting collusion in procurement auctions. Most of them compare the behavior of known or suspected colluding
bidders with that of competitive bidders. Porter and Zona (1993) studies auctions forpaving works on Long Island, New York. They ﬁnd that a colluding winner’s response inbidding to a change of the cost factor is diﬀerent from that of colluding losers even when
there should be no statistical diﬀerence between them in the absence of collusion. Porterand Zona (1999) analyzes the ring members’ bidding behavior in school milk procurement
auctions in Ohio State. They focus on the relationship between the bids and the distance
between schools and bidders. Their results suggest that the bidders form territories. Bajari and Ye (2003) observes the violation of exchangeability and conditional independence,
the two conditions that a competitive bidding strategy must satisfy, using the auction datafor highway construction works in Midwest. These approaches make full use of observable
cost asymmetry among bidders by measuring ﬁrms’ used capacity or the distance between
their oﬃces and the work site.
The previous works and ours are complementary in detecting collusion. The advantagesof our empirical approach over previous methods are, ﬁrst, it works even when the existing
methods require a large number of competitive bidders for speciﬁcation and comparison
purposes, and hence are not applicable because the ring is nearly all inclusive. Second,
unlike the previous methods, we do not require a large degree of asymmetry across bidders
in observable features such as distance from the work site and capacity utilization.
Theories of collusion in auctions highlights the role of pre-auction meeting of bidders.
The seminal paper by McAfee and McMillan (1992) shows that the most eﬃcient bidder
collusion in a ﬁrst price auctions is that the ring member with the minimum cost bids at
the reserve price while the other members bid 0 along with the monetary transfers fromthe winner to the losers. They also characterize an eﬃcient collusion when no side transfer
is possible. It is a static scheme in which the choice of the designed winner is independentof the history.
The analysis is extended to a repeated framework by Aoyagi (2003) and Skrzypacz andHopenhayn (2004), who analyze collusion without a side transfer in repeated auctions. In
contrast to McAfee and McMillan’s static bid rotation, Aoyagi constructs a dynamic bid
rotation scheme in which bidders coordination is based on past history. In the scheme, playrotates among diﬀerent phases that treat the bidders diﬀerently and collusion is sustained
because these phases enable intertemporal transfer of bidders’ payoﬀ.
Among the existing works, Skrzypacz and Hopenhayn (2004) and Pesendorfer (2000)
are most closely related to ours. Skrzypacz and Hopenhayn (2004) proposes a collusion
scheme named a “chips mechanism”, in which the winner gives one chip to each loser,2and when a bidder runs out of chips he is supposed to allow other bidders to win for a
speciﬁc number of periods. An important factor in the scheme is the number of winningand losing in the past. Surprisingly, it is known that an alike mechanism has been used
by Japanese bidding rings (we name it the “contribution rewarding scheme”), and our
method is aimed at detecting this type of scheme.
Pesendorfer (2000) illustrates the diﬀerence of two forms of cartel, in which one cartel
in Florida uses side payments and the other in Texas does not. He ﬁnds that the cartel
without side payments maintains relatively constant market shares, despite some eﬃciency
losses from not allocating a contract to the low cost ﬁrm, in order to maintain internal
discipline. Our method is also aimed at detecting the scheme which keeps the balance ofthe members’ total revenues in the past, which is the very scheme used by the cartel in
Texas.
The paper is organized as follows. Section 2 describes the market, the auction procedure, and the data we analyze. Section 3 documents the observation on the price wars,
and describes the possible ring’s behavior in the market. Section 4 shows the empiricalresult of the analyses on collusion scheme. Section 5 concludes.

2

The Market Description

This study looks at auctions for paving contract awarded by Ibaraki City, Osaka, Japan,
during four years between April 2002 and March 2005. During the data period, Ibaraki
City awards 139 contracts through auction ( 30-40 contracts every year). Typically, thecontracted work involves the resurfacing of local roads for hundreds of meters. The winning
price varies from 1 to 40 million yen, with an average of about 7 million yen. Figure 1
shows the distribution of the contract value. Annual total of 2-3 hundred million yen iscontracted out.
Thirteen ﬁrms participated in the auctions during the data period with one ﬁrm exiting
early. Most ﬁrms do paving work as their primary business, and other civil engineering
works as secondary. Nine ﬁrms are local in the sense that their headquarters are locatedwithin Ibaraki City, and the rest only have a branch in the city.

2.1

Auction procedure

The auction is the ﬁrst price sealed bid format with a maximum acceptable (reserve) priceand a minimum acceptable price (henceforth a minimum price). The minimum price is
set aiming at preventing ﬁrms from doing works with a low quality. A bidder with thelowest bid wins the contract, if and only if the bid is between the minimum price and thereserve price. Auction proceeds as follows: Prior to each auction, the city oﬃcials estimate
how much the work will cost an average ﬁrm to complete the work, taking into account3

material prices and the budget of the city. The estimated price is then used as the reserve
price in the auction. The minimum price is set at about 80% of the reserve price. The
city announces the reserve price and the minimum price one week before the auction.
Actual participants of the auction are chosen by the city. A limited number of ﬁrms
are nominated from a list of candidates a week before each auction. Technical documents,
which are needed to estimate the cost, are distributed to eligible bidders at the city oﬃce
at the announced date and time prior to the auction. It gives the bidders a chance to
see each other in advance and to know whether there is an outsider. On the date of theauction, bidders gather and submit sealed bids. If there are more than two bidders who
submit the lowest bid, then the winner is determined by a public lottery.
The cost of each contract is private information of each bidder, and hence, each auction
is a private value auction. When a bidder wins an auction, he would earn proﬁt equal to
the winning price minus his private cost.
The number of nominated bidders depends on the reserve price of the auction. Whenthe reserve price is high, the number of bidders tends to be large. Table 1 summarizes the
distribution of the number of bids per auction.

2.2

The Data Source

We have two data sources, bid data and corporate data. The bid data were provided
by Ibaraki City Oﬃce. The bid data contain the following information on every projectawarded: date of auctions, submitted bids, names of bidders, the reserve price and theminimum price, the starting and ending dates of projects, and location of projects.
The corporate data of each ﬁrm were provided by Construction Industry Information
Center’s database. The corporate data contain the number of years of running, numberof technical workers, annual sales, and proﬁt per sales.
In the analyses, we used a variable which represents bidder’s used capacity. It is not
suﬃcient in capturing the ﬁrm’s used capacity as long as we see only the contracts boughtby Ibaraki City, since the ﬁrms do the works bought by private ﬁrms and other local
governments neighboring Ibaraki City. In calculating each bidder’s used capacity, we usedthe data of contracts which were awarded by Osaka Prefectural Government, as well as
by Ibaraki City. Osaka Prefectural Government is one of the major clients of ﬁrms, andprovides contract data through its website. The deﬁnition of variables are shown in Table
4.

4

3

Possible collusion scheme

3.1

Agreement to fight against outsiders

We describe distinctive price wars observed during the data period and argue the reason.
The observation in this section shows that most bidders bid at the minimum price inthe price wars, and that such a price war take place mainly when either of two ﬁrms
participates in the auction. It is natural to think that an agreement in bidding at theminimum price is in place when a speciﬁc bidder participates.
Figure 2 shows the variance of “normalized bids” of each auction, and Figure 3 showsthe “normalized winning bids” of each auction. “Normalized” means that the bids are
divided by the reserve price. As Figure 3 shows, in 123 out of 139 auctions, winning prices
are in the neighborhood of 93% of the reserve price. On the other hand, remaining 16
contracts were won at the minimum price which was set at 80-85% of the reserve price,that is, the auctions were price wars. There is no contract won between 85% and 90% of
the reserve price, and therefore, the distribution of winning bids has a gap as shown in
Figure 3. Furthermore, in 13 price wars, the variance of the normalized bids is zero as
shown in Figure 2, indicating that all of the bidds were submitted at the minimum priceand hence, the winner was determined by the public lottery.
It is likely that the ring bidders have an agreement on submitting a bid at the minimum
price when they face an outsider in an auction. As described, the bidders have an oﬃcial
chance to meet each other prior to the auction. Once the existence of an outsider is
conﬁrmed, all of the ring bidders must be instructed to bid at the minimum price in theauction.3
We further show that price wars are mainly caused by the pariticipation of either of
two speciﬁc ﬁrms. Figure 4 shows the participation of every ﬁrm in every auction. The
X axis shows auction ID, t = 1, 2, ..., 139, and the Y axis shows ﬁrm ID, i = 1, 2, ..., 13. A
white dot in the ﬁgure indicates that the auction was a price war, and a black dot indicatesthat it was not. When a dot at coodinate (x, y) is framed, it indicates bidder y wins in
auction x. For example, the black dot without a frame at coordinate (15, 2) implies thatﬁrm 2 submitted a bid and lost in auction 15, and that the auction was not a price war.
In Figure 4, there exists a sequence of 4 white dots from coordinate (2, 13) to coordinate(10, 13), which are in square A. The dots indicate the price wars which may have beencaused by the participation of ﬁrm 13. These auctions took place during 3 months fromMay 2002 to July 2002. No auction is price war if ﬁrm 13 was absent during this period.
It can be inferred that ﬁrm 13 is a possible outsiders. In addition, ﬁrm 13 did not submit
3

Bajari and Ye (2003) models a cartel behavior when it faces outsiders in auctions. In their model, themember with the minimum cost in the cartel submits a serious bid, and the other member submit phonyhigh bids. In contrast to their model, all the ring members must be supposed to submit the lowest possible
bid when they face an outsider in the market we analyze.

5

a bid in any auctions after auction 11. It suggests that ﬁrm 13 went out of the market
after the auction, perhaps due to the price war against the ring continued from before thedata period.
There exists another sequence of 8 white dots from coordinate (68, 8) to coordinate(81, 8) in square B. The dots indicate the price wars which were probably caused by theparticipation of ﬁrm 8. These 8 auctions were held during 5 months from May 2004 to
October 2004. The other 53 auctions that ﬁrm 8 submitted a bid were not price wars. This
may suggest that ﬁrm 8 stayed out of the ring only during the 5 months, and reconciledwith the ring after that.
It is conﬁrmed that the price wars took place in all auctions where ﬁrm 13 submitted
bids and in a series of auctions during 5 months where ﬁrm 8 submitted bids. This suggeststhat there may have been an agreement that the ring bidders bid at the minimum pricewhen one of the two ﬁrms participated in the auction. We further infer that the ring musthave been all-inclusive after ﬁrm 13’s exit, except the ﬁve months in which ﬁrm 8 stayedout of the ring. The causes of 12 price wars out of 16 are explained: 4 of them were caused
by ﬁrm 13 and 8 were caused by ﬁrm 8. However, 4 price wars in Auction 28, 78, 131 and139 are left unexplained.
The exit of ﬁrm 13 and the possible reconciliation of ﬁrm 8 suggest that the pricewars worked as a predation. It is likely that winning a contract at the minimum price isunproﬁtable for most of the ﬁrms, since the ratio of proﬁt to sales is 0.27% on averagein this market (Table 3). If it is unproﬁtable in fact, the above observations ﬁt to thecontext of the “deep pocket predation” in which the ring aims at deriving the outsiders
out of the market by causing price wars that give losses to both. While the ring’s losses
can be shared among the members, the outsiders will therefore be unable to survive suchlosses for a long time. Sooner or later, they have to give up and leave the market or join
the ring, allowing the ring to be all inclusive and recoup losses. The ring might have been
doing this at the sacriﬁce of short term proﬁt, aiming at the all inclusive environment
which enables the ring to enjoy the beneﬁt of collusion fully in the long run.
Note that the price wars we ﬁnd cannot be an evidence of collusion by itself. There still
remains a possibility that there is no agreement among bidders.4 However, the ﬁnding
gives a signiﬁcant support for the assumption we use in the main analysis that all thebidders belong to the ring if the auction is not a price war.

4

Suppose a situation where winning a contract is profitable for all firms even when the price is equal tothe minimum price, and firm 8 and firm 13 are so aggressive bidders that they always bid at the minimum
price. If it is common knowledge, a series of price wars we observe can be a natural outcome without any
agreement, since it is best for other bidders to respond by bidding at the minimum price.

6

3.2

Operation of a collusion scheme as a comparison of bidders’ priority

We next hypothesize the rules under which the winner is selected when the ring is allinclusive in the auction. Many of those schemes are based on comparing its members’
priority to win the contract. We pick following four classes of hisotry dependent schemes
typically used in the past cases.
1) Simple rotation scheme
In a simple rotation scheme, the ring members rotate the chance of winning. Note thatthe ring cannot use a mechanical rotation, due to the exogenous choice of bidders by
the city before each auction. Instead, a bidder is chosen as the winner if his time oflosing streak is longer than that of any other members. The ring compares the numberof days from the last win, and the bidder with the greatest number wins the contract.
2) Revenue equalizing scheme
A revenue equalizing scheme maintains equity of the revenue of its members by assigning a contract to the bidder whose total revenue in the past is the smallest among themembers.
3) Contribution rewarding scheme
A contribution of the ring member is to submit a phony bid allowing the other bidder
to win. A contribution rewarding scheme gives more priority to bidders who made more
contribution in the past auctions. Once his contribution is rewarded with a winning, theamount of his contribution is decreased. The ring compares each member’s contribution
to the ring, which is measured by the number of losing and the number of winning in
the past.
4) Combination
There can be a scheme in which some of above schemes are combined. There can bevarious combinations of above schemes in which more than two factors of the above
schemes are considered in the selection of the winner. For example, a bidding ring inOkayama prefecture used a combination of the symple rotation scheme and the revenue
equalization scheme, that is, the ring basically uses revenue equalizing scheme, and incase of a tie, they compared the number of days elapsed from one’s last win.
Each scheme depends only on the public history (the date, the participants, the winner,and bids of every previous auction), and not on the private information. A merit of theseschemes is the simplicity of the operation. They do not require any report from bidders
even when the cost of doing the work is private information. They maintains collusion by
giving each member an expectation to win in a near future. The schemes are eﬃcient in
the sense that a bidder who recently won a contract tends to lose in the next auction.
7

When either of above schemes is in operation, it is possible for us to detect the collusion.
There must be a link between the outcome of each auction and history when bidders collude
using the scheme, whereas, there must be no such link between each auction result andthe history under competition. Therefore, we can see if they are collusive by testing if thehistory has a supposed impacts on the auction result. In Section 4, we examine the data
to see if these schemes were in operation.

4

Detection of collusion scheme

In the following, we analyze the data to detect the collusion by testing if there is a collusion
scheme that explains the data. We examine if there is a factor that has nothing to do withthe cost, but has an impact on the auction result. The existence of bid rigging is supportedby the existence of such a factor. In the analysis, we use the data of 123 auctions thatwere not the price war.
An important assumption here is that the ring was all-inclusive in these auctions.
When the ring is all-inclusive in an auction, the designated winner wins the contract forsure. Therefore, the winner’s characteristic in all-inclusive ring must reﬂect characteristicsof the collusion scheme.
Porter and Zona (1993) models bidder’s probability of winning in competition, imposing an assumption that the ﬁrms respond similarly to changes in the observable cost
factors. Each bidder’s probability of winning in an auction is represented as a functionof cost factors, since bidder i’s bidding function in auction t is approximated as a linear
function of cost factors. We extend their model allowing the ring to choose the designatedwinner according to the collusion schemes described in Section 3.2.

4.1

The model of the ring’s choice on the winnerPorter and Zona (1993) models a bidder’s bidding function in an auction as a linear
function of cost factors, and then, analyzes winning probability of the bidder given thecost factors as a conditional logit model.
The model is modiﬁed into the ring’s choice model. We suppose that the ring chooses∗ is the highest among the set ofa bidder i as the winner if his measure of priority wit

bidders Mt in auction t, where∗= β xit + γ  zit + uit , i ∈ Mt .
wit

(1)

xit denotes the vector of factors that determine bidder i’s priority in the collusion schemes.
zit is a vector of observable variables aﬀecting bidder i’s cost on project t. uit is thedisturbance that arises in bidder’s priority.

8

The probability that bidder i is chosen as the winner in auction t conditional on Mt
and xt is written as:
∗
∗
≥ wjt
∀j ∈ Mt , j = i | Mt , xt , zt ),Pr(w t = i | Mt , xt , zt ) = Pr(w itwhere wt indicates the identity of the winner in auction t, and xt and zt are vectors thatconsist of xit and zit for all i ∈ Mt , respectively. McFadden (1973) showed that when
we assume that the uit ’s are independent and identically distributed with Type I extreme
distribution, the probability can be written as:
exp(β xit + γ  zit ).
j∈M t exp(β xjt + γ zjt )Pr(w t = i| Mt , xt , zt ) = (2)

We obtain the estimator of parameters by maximizing the following log likelihood function:ln L(β, γ|wt, Mt , xt , zt ) =

eit ln Pr(w t = i| Mt , xt , zt ),t∈S i∈M t

where eit is an index variable which is 1 if i won in auction t and 0 otherwise and S is theset of auctions that were not the price wars.
Recall that the factors that determine bidder i’s priority in each collusion scheme is1) the number of days elapsed from one’s last winning in the simple rotation scheme, 2)
the total revenue in the past in the revenue equalizing scheme, 3) the number of winning and the number of losing in the past in contribution rewarding scheme. Therefore,
xit = (NUMDAYSit , WINVALUEit , WINNUMit , LOSENUMit ). We construct two variables which capture the revenue in the past, WINVALUE1it and WINVALUE2it . Since
WINVALUEit and WINNUMit are highly correlated, we estimate some speciﬁcations dropping either of them.
The variables which represent observable cost factors in our model are zit = (CAPit ,CAPSQit , YEARSi , WORKERi , PROFRATEi , DISTit , BRANCHi ).5 We allow bidders∗.
to have diﬀerent intercepts in wit

Since we are interested in whether xit has an impact on the winning probability in
auctions, we test the null hypothesis H0 : β = 0 against H1 : β = 0.
We also try the following extension in which the impact of xit on the priority is diﬀerent
across bidders:∗= eδi β  xit + γ zit + uit .
wit

(3)

The extension allows us to estimate the schemes which treat the ring members diﬀerently:
bidders may not be treated equally in the schemes even though their xit are the same.
5
In Porter and Zona (1993), zit includes the capacity utilization rate (CAPit ), squared utilization rate
(CAPSQ it), a firm’s maximum capacity, squared maximum capacity, and CAPit and CAPSQit are theonly statistically significant variables in their model.

9Some ﬁrms may be treated better than the others, for example, because they are thefounding members of the ring, or outside ﬁrms may be handicapped due to local ﬁrms’
territorial imperative. We set δ1 = 0 for bidder 1 as a standard. The greater value of δi
implies the better treatment for bidder i.

4.2

ResultTable 5 shows the empirical results.
Columns (1) and (2) of Table 5 show the results using WINVALUE1 as the proxy of thetotal revenue in the past, and (3) and (4) correspond to the results using WINVALUE2.
(5) and (6) show the result using the number of winning in the past, instead of the total
revenue. Column (7) shows the result of the extended model which allows the heterogeneityof bargaining power.
Throughout the speciﬁcations, it can be seen that a bidder’s probability of winningtends to be high if the number of days elapsed from his last win is large, and in somespeciﬁcations, it can be seen that the total revenue in the past decreases the winningprobability.
The estimate for branch dummy is negative. This may suggest that an outside ﬁrm
is less powerful in the bargaining for the allocation. As shown in Table 3, the number ofwinning tends to be small if a ﬁrm’s headquarter is not located within Ibaraki City. Firm
1,2,6 and 11 are outside ﬁrms, and their frequencies of winning are less than half of thoseof the local ﬁrms.
It can be said that either the simple rotation scheme or the combination of the simple
rotation scheme and the revenue equalizing scheme is most likely to be used. That is,
the ring selected a bidder as the winner if he is on a losing streak for a long time and its
winning value until the auction was small relative to the other bidders.
The above ﬁnding can be the evidence of collusion if we can say competitive bidding
behavior is never aﬀected by the number of days elapsed from one’s last win. However,there remains a possibility that the number of days from the last win may be related to theﬁnancial pressure which makes a competitive bidder aggressive, and therefore may induce
the bidder to decrease his bids. If so, it is natural if the winner has the larger number ofdays elapsed from the last win.
In order to see if the number of days from the last win increases competitive bids, weanalyze the normalized “losing” bids. Table 5 shows the results of linear regression models
which explains the normalized losing bids by the independent variables of the conditional
logit model. The number of days from the last win increases the losing bids in somespeciﬁcations, however, there is no evidence that the number of days from the last win
reduces the bids.
In total, there is little support that the positive impact of the length of one’s loosing

10

streak found in the conditional logit analyses is due to the ﬁnancial pressures. It can beconcluded that the impact is the evidence of collusion.
We should note that the models do not ﬁt the data well. This may be because there
remain some other factors which are not considered in our model. Figure 5 shows who
won in each auction. A small dot, a middle-size dot, and a big dot show that the contract
value is small (less than 5 million yen), middle (5-10 million yen) and big (greater than 10
million yen), respectively. The ﬁgure shows that ﬁrm 3 tends to win big contracts withlong intervals, while ﬁrm 9 and 10 tend to win small or middle-size contracts with shortintervals. This may suggests that some factors such as bargaining power or preference ofﬁrms may also aﬀect the decision signiﬁcantly.

5

Conclusion

We analyze auction data to ﬁnd an empirical evidence of collusion in procurement auctions
for paving works. We ﬁrst observe the happening of the price wars and ﬁnd that mostprice wars occured when either of speciﬁc two ﬁrms submitted bids. It is inferred that thetwo ﬁrms are possible outsiders and that all the ring bidders submit bids at the minimum
price only when outsiders were in the auction.
We next analyze if some possible collusion schemes are used when the winner was
selected assuming that the ring is all-inclusive if the auction is not a price war. We model
some possible schemes as a comparison of each member’s priority to win, and the ring
selects the member whose priority is the greatest among other bidders. We focus on
schemes in which a bidder’s priority is measured based on events in the past.
It is found that, a bidder tends to win when the time elapsed from his last win is long,and his amount of win in the past was low relative to other bidders.
Since the number of days from the last win may be related to the ﬁnancial pressure
which makes a competitive bidder aggressive, it may induce a competitive bidder to decrease his bids. We ﬁnd that there is no relation between the number of days from thelast win and the losing bids, and conﬁrm that the impact of the number of days from thelast win on the winning probability is the evidence of collusion.
Our ﬁnding ﬁgures out the behavior of the ring. The ring allocates contracts to thering bidders, balancing the frequency of winning and the revenue among its members, andwhen an outsider is in an auction, all the ring bidders bid at the minimum price.

References[1] Aoyagi, M. (2003), “Bid Rotation and Collusion in Repeated Auctions,” Journal of
Economic Theory, 112, pages 79-105.

11

[2] Bajari, P. and Ye, L. (2003), “Deciding Between Competition and Collusion,” Review
of Economics and Statistics, 85.4, pages 971-989.
[3] Hironaka, K. (1994), “Dango survives after all (Soredemo dango ha nakunaranai),”
Tokei Publishing (in Japanese).
[4] Kato, M. (2005), “We did Dango (Dango shimashita)”, Saizusha (in Japanese).
[5] McAfee, R. P. and McMillan, J. (1992), “Bidding Rings,” American Economic Review, 82.3, pages 579-599.
[6] McFadden, D. (1973) “Conditional Logit Analysis of Qualitative Choice Behavior,”
in Frontier in Econometrics, edited by Paul Zarembka. Academic Press.
[7] McMillan, J. (1991) “Dango: Japans Price Fixing Conspiracies”, Economics andPolitics, 3, pages 201-218.
[8] Motta, M. (2004), “Competition Policy,” Cambridge University Press.
[9] Pesendorfer, M. (2000), “A Study of Collusion in First-Price Auctions,” Review of
Economic Studies, 67, pages 381-411.
[10] Porter, R. H. and Zona, J. D. (1993), “Detecting of Bid Rigging in Procurement
Auctions,” Journal of Political Economy, 101.3, pages 518-538.
[11] Porter, R. H. and Zona, J. D. (1999), “Ohio school milk markets: an analysis of
bidding,” RAND Journal of Economics, 30.2, pages 263-288.
[12] Skrzypacz, A. and Hopenhayn, H. (2004), “Tacit collusion in repeated auctions,”
Journal of Economic Theory.
[13] Suzuki, M. (2004), “A study of bid rigging (Nyusatsu dango no kenkyu),” Shinzansha(in Japanese).
[14] Zona, J. D. (1986), “Bid-rigging and the Competitive Bidding Process: Theory andEvidence.” Ph.D. dissertation, State University of New York at Stony Brook.

12

Table 1: Bid concentration
Number of bidders
Number of auctions

5
52

6
52

7
28

8
5

9
2

Total
139

10-20
16

20-30
4

Table 2: Winning priceWinning price (in million yen)
Num of auctions

1-3
24

3-5
36

5-10
58

301

total
139

Table 3: Information of ﬁrms
Firm ID
1
2
3
4
5
6
7
8
9
10
11
12
13
Average

Headquarter/ Num. ofBlanchworkers
B
158
B
22
H
16
H
12
H
19
B
9
H
3
H
9
H
6
H
4
B
16
H
7
H
23.4

Years ofoperating
55
15
15
31
36
34
30
24
22
6
26
21
26.3

13

Ratio of operating proﬁt to sales
5.79%-0.33%
1.21%
1.27%
1.14%
-0.86%
2.58%
0.41%
0.60%
1.04%
-9.50%-0.17%
0.27%

Num.
of bids
29
40
93
95
97
37
95
61
72
83
39
81
4
63.5

Num. ofwinning
4
5
14
17
13
3
14
13
20
13
6
17
0
10.7

Table 4: Deﬁnition of variables 2
Variables
CAPit

Deﬁnition
The measure of capacity utilization rate. This is deﬁned as the value of backlog contracts devided by theﬁrm’s annual sales, which is observed in 2004. A backlog contract is a contract which Firm i already won in
public auctions in Ibaraki City and Osaka Prefecture,
and whose time overlaps the contract of Auction t.

CAPSQ it

Square of CAP.

YEARSiThe number of years of Firm i’s operation, observed in
2004.

WORKERi

The number of technical workers, observed in 2004.

PROFRATE i

The rate of proﬁt on sales, observed in 2004.

DISTitDistance between the work site and Firm i’s oﬃce.

BRANCHi

A dummy variable that takes 0 if bidder i is the headquarter of a ﬁrm located within Ibaraki City, and 1 if
bidder i is a branch oﬃce of an outside ﬁrm.

NUMDAYS it

The number of days between Firm i’s last winning andthe date of Auction t.

WINVALUE1 it

The total value of contract that Firm i has won since
the start of the data period until the date of Auction t.

WINVALUE2 it

The total value of contract that Firm i has won within
half a year of Auction t.

WINVALUE3 it

The total value of contract that Firm i has won within
a year of Auction t.

WINNUM it

The number of times that Firm i won in auctions fromthe start of the data period until the date of Auction t.

LOSENUM it

The number of times that Firm i lost in auctions fromthe start of the data period until the date of Auction t.

14

15

Winning price (in million yen)

0

5

10

15

20

25

30

35

40

45

0

5

10

15

20

25

30

35

40

45

50

55

60

70

75

Auction ID

65

Figure 1: Winning price

80

85

90

95 100 105 110 115 120 125 130 135 1401600.00010.00020.00030.00040.00050.00060.00070.00080.0009

0.001

0

5

Auction No.

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Figure 2: Variance of normalized bids

Note: The ﬁgure does not include three exceptionally large values 0.0023, 0.0011, and 0.0076 for Auction No. 2, 74, and 139, respectively.

Variance of normalized bids

17

Winning pirce / Reserve price

75%

80%

85%

90%

95%

100%

0

5

Auction No.

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Figure 3: Normalized winning bids

18

Firm ID

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0

5

10

15

A

20

25

30

35

40

45

50

55

60

70

75

Auction ID

65

80

85

B

Figure 4: Participation and price wars

90

No price war
Price war
Winner95 100 105 110 115 120 125 130 135 140

Table 5: Estimation results for conditional logit model

WINVALUE1(1)-0.010(0.006)(2)-0.027**(0.009)WINVALUE2

(3)

(4)

-0.033*(0.016)-0.038*(0.018)WINNUMLOSENUM
NUMDAYS
CAP
CAPSQ
YEARS
WORKERPROFRATEDIST
BRANCH
δ2

(5)

(6)

-0.139(0.077)0.008(0.021)0.006**(0.001)-5.100(4.106)
5.119(10.560)-0.042(0.027)-0.079(0.045)0.029(0.071)-0.116(0.064)-1.750*(0.790)Yes-190.52
0.122

0.006
(0.015)0.006**(0.001)-3.810(3.985)5.024(10.120)-0.004(0.012)-0.013(0.026)-0.052(0.056)-0.146**(0.062)-2.287**(0.560)0.031(0.023)0.006**(0.001)-5.978(4.116)
7.278(10.690)-0.042(0.027)0.011(0.057)0.032(0.071)-0.114(0.064)-1.722*(0.732)-0.005(0.014)0.006**(0.001)-2.126(4.186)2.500(11.235)-0.002(0.012)-0.021(0.024)-0.053(0.055)-0.152*(0.062)-2.300**(0.552)-0.006(0.021)0.006**(0.001)-3.401(4.291)
3.310(11.785)-0.047(0.027)-0.069(0.046)0.033(0.070)-0.125(0.064)-1.728*(0.734)-0.065(0.060)-0.004(0.014)0.006**(0.001)-3.793(4.022)
4.587(10.032)
0.002(0.012)-0.034(0.022)-0.065(0.056)-0.139*(0.062)-2.561**(0.659)No-194.23
0.105

Yes-187.700.135

No-193.39
0.108

Yes-189.650.126

No-195.15
0.100

δ3
δ4
δ5
δ6
δ7
δ8
δ9
δ10
δ11
δ12
Bidder ﬁxed eﬀect
Log likelihood
Pseudo R2

Notes:(i) **: 1% signiﬁcance level, *: 5% signiﬁcance level.
(ii) The number of observations of each column is 725.

19

(7)-0.007(0.010)0.021(0.020)0.012**(0.004)-3.587(4.809)3.603(12.354)-0.018(0.027)0.089(0.053)-0.367*(0.149)-0.107(0.065)-3.349*(1.477)0.108(0.263)-1.179(0.797)-0.005(0.384)-1.191(1.017)-0.092(0.244)0.620(0.384)-0.240(0.502)0.201(0.456)-0.034(0.552)-1.791(1.256)0.273(0.461)
No-181.30
0.164

Table 6: Estimation results for normalized bids 1

util
utilsq
years
staﬀ
proﬁt
distdir
blanchtotalwin1
dayfroml n
R-squared
Fixed eﬀect
Clustering(1)2.485**(0.277)-4.795**(0.768)0.013**(0.001)0.015**(0.002)-0.015**(0.004)0.053**(0.007)-0.078*(0.038)0.007**(0.001)0.001**(0.000)
0.940
No
A

(2)
-0.018(0.013)0.033(0.026)0.000**(0.000)0.051**(0.000)-0.017**(0.000)0.000(0.000)0.378**(0.002)0.000(0.000)-7.81E-06(4.52E-06)
1.000
B
A

(3)
0.380
(0.363)-0.791(0.773)0.002(0.002)0.001(0.001)-0.002(0.002)0.014(0.013)0.009(0.010)0.002(0.002)
2.88E-05(3.41E-05)
0.995
A
A

(4)
0.000**(0.000)0.000**(0.000)0.000**(0.000)0.050**(0.000)-0.017**(0.000)0.000**(0.000)0.371**(0.000)0.000**(0.000)1.06E-17**(2.60E-18)
1.000
A&B
A

(5)
2.485**(0.537)-4.795**(1.315)0.013**(0.004)0.015(0.008)-0.015(0.019)0.053**(0.014)-0.078(0.149)0.007*(0.002)0.001*(0.000)0.940
NoB

Notes:(i) **: 1% signiﬁcance level, *: 5% signiﬁcance level.
(ii) The number of observations of each column is 602.
(iii) “A” in the “Fixed eﬀect” row indicates that auction speciﬁc ﬁxed eﬀects are included in themodel, and “B” indicates bidder speciﬁc ﬁxed eﬀects.
(iv) “A” in the “Clustering” row indicates that the standard errors are clustered by auctions, and“B” indicates clustering by bidders.

20

21

Firm ID

0

1

2

3

4

5

6

7

8

9

10

11

12

13

0

5

Small (-5mln Yen)

Medium (5-10mln Yen)

Auction ID
Large (10-mln Yen)

Price war

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Figure 5: Winner of auctions