Discussion Papers In Economics
And Business

Detecting Collusion through Exchange of Favors in
Repeated Procurement Auctions
Rieko Ishii

Discussion Paper 07-15

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANDetecting Collusion through Exchange of Favors in
Repeated Procurement Auctions
Rieko Ishii

Discussion Paper 07-15
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Detecting Collusion through Exchange of Favors in
Repeated Procurement Auctions∗Rieko Ishii†
May, 2007

Abstract
It is known that bid rigging in public-work auctions in Japan often takes the formof exchanging favors. In such a scheme, the winner is designated based on the amountof favor he has given to other members of the ring. By explicitly modeling “favor”
as an explanatory variable, this paper analyzes data from the public-works auctions
for consulting works in Naha, Japan, to conﬁrm that such a collusion scheme is inoperation.
JEL Classiﬁcation D44, H57, L44
Keywords: Bid rigging, repeated auction.

∗
I am truly indebted to Masaki Aoyagi. I am also grateful to Fumio Ohtake for extremely helpful
discussions at the start of this research. I thank Koki Arai, Andreas Blume, Shigemi Izumida, Masaki
Nakabayashi, Kazuo Ogawa, Martin Pesendorfer, Tatsuyoshi Saijo, Yasuo Takatsuki, Junmun Wan andseminar participants in Hitotsubashi University, Kyoto University and Micro Mini Conference at Hakone
for valuable comments on earlier versions. Any 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 a pervasive problem in procurement auctions. According to Suzuki (2004),
all antitrust cases of bid rigging between 1947 and 2000 in Japan involve a pre-auction
meeting of ring members that determines the winner in their own way. As reported by
Suzuki, former industry experts, and media, it is widely observed that the exchange offavors plays an important role in collusive negotiations in Japan. According to Hironaka(1994), a written confession by a former industry expert, it is common for a ring member
to insist on his right to win the contract because he has given a favor to the others. In
cases of Okinawa Prefecture and Takaraduka City, for example, each ring member kept
precise record of auction results named the “balance sheet”, which includes the date ofauctions, the winning price, and the name of the winner, so that they can see the balanceof favors among the ring (Okinawa Times June 9, 2005, Kobe District Court Decision
WA810, November 7, 2001).
The objective of this paper is to hypothesize a speciﬁc collusion scheme based on
the exchange of favors and show that actual bid data are consistent with the scheme. Our
strategy is to test how the outcome of auctions is aﬀected by a factor that is potentiallyused in the scheme, but is irrelevant when bidding is competitive. If the outcome isaﬀected by such a factor, then it can be concluded that collusion is present. For example,
if bidders choose the winner according to the well-known “phase of the moon” scheme,
then we should observe a correlation between the identity of the winner and the phase of
the moon.
In this paper, we propose a method to detect whether bidders collude by exchanging favors. Speciﬁcally, we deﬁne a favor to be the action of letting some other bidder win
by making a phony bid. If bidder A lets bidder B win, then we say A gives B a favor.
When B subsequently does the same thing for bidder A, we say B returns the favor. We
say that exchange of favors takes place if B returns the favor after A gives B a favor. It
should be noted that favors can be exchanged between a pair of bidders.
Favor can be measured by the value of contracts a bidder has given up by making1a phony bid. We construct a measure for the exchange of favors that has taken place
between every pair of bidders, and call it a score. The main objective of this paper is toanalyze its eﬀect on the winning probability of each bidder in auctions. The score at any
point in time represents the net amount of favor a bidder has given to another bidder tothat date: it is positive if he has given favors to her, and negative if he owes. Our resultshows that the winning probability is positively related to the score. This ﬁnding suggests
the presence of collusion which uses the bilateral relationship in determining the winner.
Our data show infrequent but signiﬁcant drops in prices. We suppose that the ringis nearly all-inclusive in the market, and that those drops are caused by participations of asmall number of non-collusive bidders. The ring bidders submit extremely high bids when
the auction is all inclusive, whereas some of them lower their bid down to competitive level
when they face an outsider in an auction. Therefore it is supposed that a collusive bidder’sbid is higher than that of a competitive bidder on average. We classify the bidders into twogroups by the average bid level. We ﬁnd a tendency that a pair of bidders exchange favors
when both of them submitted high bids on average, whereas bidders do not exchange
favors when either of them submitted low bids on average. Our ﬁnding is consistent withthe prediction that favors are exchanged only when both bidders are collusive.
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 eﬃcientbidder collusion in a ﬁrst price auctions is that the ring member with the minimum costbids at the reserve price while the other members bid 0 along with the monetary transfersfrom the winner to the losers. They also characterize an eﬃcient collusion when no sidetransfer is possible. It is a static scheme in which the choice of the designed winner is
independent of the history. The analysis is extended to a repeated framework by Aoyagi (2003) and Skrzypacz and Hopenhayn(2004), who analyze collusion without a sidetransfer 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 basedon past history. In the scheme, play rotates among diﬀerent phases that treat the bidders
diﬀerently and collusion is sustained because these phases enable intertemporal transfer2

of bidders’ payoﬀ. Skrzypacz and Hopenhayn (2004) proposes a collusion scheme nameda ‘chips mechanism’, in which the winner gives one chip to the loser, and when a bidderruns out of chips he is supposed to allow other bidders to win for a speciﬁc number of
periods. A numerical analysis shows that this mechanism is asymptotically optimal when
the distribution of bidders’ values is assumed to be uniformly distributed.
It should be noted that our analysis adopts the empirical technique of Duggan
and Levvit(2002), to a repeated auction environment. They analyzed match rigging inJapanese sumo wrestling and found statistical evidence of collusion: a wrestler who ison the verge of ending a tournament with a losing record wins the last bout with an
unusually high frequency, but that he loses to the same opponent with an unusually highfrequency when they meet the next time. Their ﬁnding suggests that a wrestler colludes
with his opponent by exchanging favors: If his opponent gives him a favor today by losing
intentionally, then he will return a favor in the same way in the future. The situation
is more complex in bid rigging, because the value of a win varies considerably from one
auction to the next, and the number of bidders is usually more than two. For example,
in our data set, the largest contract is worth more than ten times than the smallest one(Figure 1). We adapt the approach of Duggan and Levvit(2002) to such a situation.
There are some empirical works on bid rigging in procurement auctions. Most ofthem analyze the presence of bid rigging by comparing the behavior of known or suspectedcolluding bidders with competitive bidders. Porter and Zona (1993) ﬁnd that a winner’s
bidding behavior is diﬀerent from that of losers even when there should be no statistical
diﬀerence between them in the absence of collusion. Pesendorfer (2000) illustrates the difference in estimated bidding strategy between collusive bidder and competitive one. Bajari
and Ye (2003) observe the violation of exchangeability and conditional independence, thetwo conditions that a competitive bidding strategy must satisfy. These approaches makefull use of observable cost asymmetry among bidders measured by the distance between
the oﬃce and the work site, or the amount of backlog contracts.
Our empirical approach has mainly three advantages over those mentioned above.
First, it works even when the existing methods are not applicable. They are not applicable3

when the ring is nearly all inclusive: they require suﬃcient number of competitive bidders
for speciﬁcation or comparison purposes. Our approach is useful since all inclusive rings
are common in Japan, where the regional business association is often the ring itself.
Second, unlike the previous methods, we do not require a large asymmetry acrossbidders in observable features such as distance from the work site and capacity utilization.
Bidder asymmetry is generally small in Japanese procurement auctions because of thediscretionary prescreening of potential bidders by local governments: In many cases, only
those ﬁrms in a close proximity to the work site are nominated in the name of promoting theregional economy, resulting in almost identical transportation costs. Asymmetry throughthe presence of a backlog is also absent since some local governments avoid nominatingbidders who already have a local public project in order to equalize the opportunity.
Finally, our approach discriminates the eﬀect of backlog contracts from bid rotation. The pattern where a bidder with high capacity utilization loses and one with low
capacity utilization wins under competition resembles collusive bid rotation. In competitive auctions, ﬁrms with idle capacity are more likely to win a contract than those withongoing contracts, if bidder’s cost functions exhibit decreasing returns to scale, as pointed
out by Porter and Zona (1993). Meanwhile, bid rotation allocates the winning in turn andhence, the bidder with idle capacity tends to be selected. As capacity utilization is one ofmain factors of the cost asymmetry in their methods, it does not work in discriminatingcompetition and collusion.
Our method deals with this diﬃculty by constructing proxy variables for both thefavor and the backlog, separately. Both factors are obtained from the history of auctions,but irrelevant each other. A competitive result may depend on history only through thebacklog, not through the favor, whereas a collusive rotation may depend on it throughboth of them. Therefore we can discriminate them by looking at the independence of theauction result from the score.
The paper is organized as follows. Section 2 describes the market and the data.
We deﬁne the idea of favor in bid rigging and discuss how the collusion scheme whichuses favors works. We also describe how variables are constructed. Section 3 presents our
4empirical model, and Section 4 shows the results. Section 5 concludes.

2

The Market and the Data

We ﬁrst describe the bidding system of Japanese public auctions. Most local governments
use a pre-screening system, in which they select the bidders themselves. In this system,
the government nominates a limited number of bidders out of a list of qualiﬁed ﬁrms
before each auction, and only the nominated ﬁrms can submit a bid. Basically, local
governments have their own nomination policies, and some of them are made public.
However, government oﬃcials can use discretion in the nomination process which is notclear to the outside observers.
The auction is the ﬁrst price sealed bid procurement auction with a highest acceptable (reserve) price. Prior to the auction, governments estimate how much it will
cost an average ﬁrm to complete the work, taking into account material prices and thegovernmental budget. The estimated price is then used as the reserve price in the auction.
The bidder who submits the lowest bid wins the contract, as long as his bid is lower than
the reserve price. Some local governments announce the reserve price before the auction,and others do not. However, according to the former industry experts, bidders can guess
the reserve price by analogy with previous contracts, even when the reserve price is notannounced (Hironaka (1994)).
We investigate the public contract auction data from a market for compensation
consulting works in Naha City of Okinawa, Japan. The city planner needs to hire compensation consultants when the city relocate private buildings for its public project suchas constructing a new road. The compensation consultants estimate the value of lands,
buildings and plants that the city needs to purchase from their owners. The bidders aremainly real estate appraisers, architects and construction companies. Naha city uses the
pre-screening system. The city chooses about 10 bidders out of 136 qualiﬁed ﬁrms for eachauction. In April 2003, the middle of our data period, it started to announce the reserve
price before each auction. Once the reserve price is announced, bids are valid as long as
they are lower than the reserve price. Figure 2 shows the distribution of bids relative to5the reserve price for 175 auctions during the data period. Bids above the reserve pricewere submitted until April 2003, whereas all the bids are within the reserve price after
that, due to the start of the announcement of the reserve price. The bids are 101% of thereserve price on average before the start of the announcement, and 97% after that. The
winning price is 93% of the reserve price on average with variance 0.72% before the startof the announcement, and 94% on average with variance 0.83% after that. We assume
that the start of the announcement did not change the scheme of the ring.
The auction data are made public by Naha City through its web site, which include
the results of auctions for four ﬁscal years (from April 2001 to March 2005). Among many
procurement markets, we choose the compensation consulting market because the numberof bidders relative to the frequency of auctions is small and it is appropriate to describe
the market as repeated auctions.
The data include the date of auctions, the winning price, the reserve price, identityand bid of each bidder, starting and ending dates of each contract, and each bidder’snumber of employers, the number of years of running, and the annual sales of consulting
works averaged over FY2003 and FY2004. The sales data include projects bought by Naha
City, the Okinawa prefectural government, as well as other cities and public institutions.
Basic statistics are given in Table 1 to Table 4. During the data period, 1748 bids
were made by 136 ﬁrms in 175 auctions. The number of contracts a ﬁrm won is 1.3 onaverage with the variance 2.9. 67 ﬁrms did not win a contract during the data period,
while 33 ﬁrms win more than three contracts. The number of auctions a ﬁrm participatedin varies from one to 43 with the average 12.9 and the variance 147.9.
Although we have no legal evidence of collusion, extreme closeness of the winning
price to the reserve price in many auctions suggests the existence of bid rigging. Figure 3
shows the distribution of the winning price relative to the reserve price. In 72% of the all
auctions, the winning price is within 95% of the reserve price. For a geographical reason,
it is hard for ﬁrms outside Okinawa to enter the market. It is hence natural for local
ﬁrms to foster a long run relationship among themselves creating an ideal environment forcollusion.
6

At the same time, some auctions appear to be competitive, because the winning
prices are considerably lower than the reserve prices. As Figure 3 shows, in 11 out of 175
auctions, the winning price is less than 80% of the reserve price. It is supposed that thering faced some competitive bidders in the market, and that the ring and the competitive
bidders were severely competing. However, since the frequency of the price wars is small,the number of competitive bidders would have been small.

2.1

The measure of favors

In this section, we give the deﬁnition of a favor, and present a measure of favor used in
the analysis. The underlying assumption is that the collusive bidders meet prior to eachauction to determine who wins the contract, and then coordinate their bids. We supposethat the likelihood that any bidder is selected as the winner depends on the history of his
reciprocal relationship with other bidders.
A favor in an auction indicates the action of making a phony bid in order to let
other bidder win. If bidder A makes a phony bid to let bidder B win, then we say A
gives B a favor. When B makes a phony bid to let A win after that, we say B returns thefavor. We say that exchange of favors takes place if B returns the favor after A gives B afavor. Therefore, if they are exchanging favors, A can expect B to help him in the future.
It should be noted that, as deﬁned in this paper, a favor between A and B is a bilateralrelationship and does not involve any other bidder. In other words, the favor which wasgiven by A to B can be returned only by B.
It is reasonable to think that the value of favors varies by contracts. A favor given
by A to B in an expensive contract auction can not be fully redeemed in a single amountof a small contract, because bidder A sacriﬁced much for bidder B. Therefore, we suppose
for simplicity that the favor given from one bidder to another in any auction is equal to the
expected payoﬀ forgone by participating in that auction. Since we consider that a favor
cannot be returned completely until the same amount of sacriﬁce is made, we measure
the balance of favors. The balance of favors is the value of the favor which was given bya bidder to another bidder, but has not been returned yet. We create a variable named7

“score”, which represents the balance of favors between every two bidders in the ring.
Bidder A’s score against bidder B in period t is the net balance of favors which were given
by bidder A to bidder B in all previous periods.
In the following, we illustrate how to construct the score from auction data. To
see the history between every pair of bidders, we consider an ordered pair (i, j) for every
i, j = 1, 2, ..., M, i = j, where M is the number of the ring members. Suppose, forexample, there are 3 ﬁrms A,B and C in the ring. In this case we have 6 pairs, (A,B),(A,C), (B,C), (B,A), (C,A) and (C,B). Denote by xijt ﬁrm i’s score against ﬁrm j at thetime of auction t. It is natural to deﬁne ﬁrm j’s score against i by xjit = −xijt , for everyt = 1, 2, ..., T , and assume all the scores equal zero at the beginning. xijt is updated after
every auction which both i and j participate in. If ﬁrm i is selected by the ring and wins
the contract in auction t, it implies that j gives a favor to i. Suppose vt denotes the valueof the favor that j gives i. Then xij t+1 = xijt − vt and xji t+1 = xjit + vt. If neither i nor
j wins, their scores against each other remain the same: xij t+1 = xijt and xji t+1 = xjit .
As discussed above, it is reasonable to measure the value of favors by the expected
payoﬀ that is foregone. For simplicity, we assume the value of the contract is common to
all the bidders in the auction, and is equal to the price. Therefore, vt = pt /Nt , where pt
is the winning price and Nt is the number of ring bidders in auction t. The underlying
assumption is that each ring bidder has an equal chance of winning and an equal valuationon the contract.
An important assumption is that all bidders in the market belong to the ring.
Therefore, Nt is assumed to be the number of bidders in the auction. The true Nt is
unknown. However, as shown in Figure 3, the frequency of price wars is small. It seems
that the ring was majority in the market and faced only a small number of competitive
bidder.
We suppose that a bidder is likely to be selected as a winner if he has positivescore against other bidders.

8

2.2

An inference on collusion scheme

In this section, we make an inference on how the idea of favor exchange works in bid rigging
when there are more than two bidders. We present an example of possible collusion scheme
which chooses the winner based on the balance of favors, and show that the scheme canbe equilibrium.
We suppose that N symmetric bidders participate in inﬁnitely repeated ﬁrst priceprocurement auctions. I is the set of players of the game. The highest acceptable (reserve)
price of each auction is r < 1, and the bidder’s cost of delivering the work is 0. The setof possible bids in stage auction is Ai = [0, 1], i ∈ I. The game begins at period 1.
Action proﬁle in period t is denoted by bt = (bt1 , bt2 , ..., btN ), bti ∈ Ai . y t represents the
public randomization device in period t. ht is history of the game, which is deﬁned ash1 ≡ ∅, ht ≡ ((b1 , y 1 ), ..., (bt−1 , y t−1 )), t = 2, 3, ..., and H t is the set of possible ht .
The stage payoﬀ πi (bi , b−i ) is bi if bi is strictly lower than any other bid, and 0 if
bi is not the lowest bid, and bi /m if m bidders including bi are tie for the ﬁrst.
xij (ht ) represents the score between i and j in history ht . To make it easy toﬁnd an equilibrium, we set a ceiling on the score. It is deﬁned that xij (h1 ) = 0, andfor t > 1, if j won in period t − 1, then xij (ht ) = min{xij (ht−1 ) + 1, 1} and if i won inperiod t − 1, xij (ht ) = max{xij (ht−1 ) − 1, −1}. If neither i nor j won in period t − 1, thenxij (ht ) = xij (ht−1 ). Denote xi (ht ) = j=i xij (ht ).
Consider the following scheme σit : H t → Ai . The scheme instructs bidder i tobid r if he is a designated winner of the auction, and 1 otherwise. The selection of thedesignated winner is as follows: If player i has the greatest value of xi (ht ) among I, theni is the designated winner. In the case where more than one players have the greatestxi (ht ), the designated winner is selected by public randomization. If someone deviatesfrom the above instruction at least once during ht , then i bids 0. This scheme assigns acontract to the bidder i whose xi (ht ), the number of bidders who were given a favor fromi is the greatest.
To show that the strategy proﬁle σ is a subgame perfect equilibrium of the game,9

we will say that the payoﬀ obtained on the equilibrium path is greater than that ofdeviation at any information set of the game. We consider an upper bound on the numberof successive periods, in which a player goes without being chosen as the winner on thepath. Let LN denote the maximum number of periods until every player wins at least
once when the number of players is N. By listing all possible patterns, it can be seenthat L2 = 3, L3 = 5. and L4 = 7. All players except i win once within at most LN −1
periods, and win twice within at most 2LN −1 periods if i doesn’t win at all. Note thatin the subgame from ht , whatever xij (ht ) is, player i will win with probability 1 until
after every other player wins twice, because every other player’s twice wins assure thatxi (ht ) = N − 1. Therefore, LN ≤ 2LN −1 + 1, and then, LN ≤ 2N −2 (L2 + 1) − 1 = 2N − 1.
It is said that when the number of player is ﬁnite, LN is ﬁnite. Since from every on-path
information set, each player will win within LN + 1 periods, there exists a lower bound of
payoﬀ from t on, which is written as:
u = δLN +1 r + δ2(LN +1) r + ... =δLN +1 r.
1 − δLN +1

The payoﬀ of deviation is at most r − ε for a small ε > 0, and u exceeds this when δ is
suﬃciently large.

2.3

Dependent variable

The dependent variable in our analysis is an index variable which represents whether
bidders won or lost in auctions. Suppose there are Nt bidders in auction t. We create
Nt − 1 pairs of bidders, which consist of a winner i and every loser j. Henceforth, wecall the pair of the winner and the loser, a “match”. We then create two observations
wijt = 1 and wjit = 0 for a match, which mean i wins over j, and j loses to i, respectively.
Therefore, 2(Nt − 1) observations are made for each auction t. The average of wijt is 0.5.
Consider an example where three bidders A,B, and C participated in auction t,
and A won. There are two matches, (A,B) and (A,C). Then four observations are created
for auction t such that wABt = 1, wBAt = 0, wACt = 1, and wCAt = 0.
There are two observations for a match. Since they are constrained each other, thetwo observations are perfectly correlated and standard errors are not correctly estimated.
10

Following Duggan and Levvit (2002), we correct standard errors by clustering.

3

Empirical Model

We analyze the dependence of the event that a bidder won or lost an auction, on his score
between each of the other bidders and other factors that might aﬀect win. We estimate
the following binary response model by probit:
wijt =
where

1 if yijt > 0,
0 if yijt ≤ 0

yijt ≡ ai + b xijt + c1 ∆backlogijt + c2 ∆salesij+c3 ∆num joinij + c4 ∆workerij + c5 ∆yearsij + εijt

(1)

= zijt β + εijt ,i, j = 1, 2, ..., M, i = j, t = 1, 2, ..., T.
We assume Pr(w ijt = 1|zijt ) = Φ(zijt β), where Φ(·) is the standard normal distribution function and zijt is the vector of explanatory variables. The log likelihood for eachobservation can be written as:
ln Lijt = wijt ln Pr(yijt > 0 | zijt ) + (1 − wijt ) ln Pr(yijt ≤ 0 | zijt )= wijt ln Φ(zijt β) + (1 − wijt ) ln(1 − Φ(zijt β)).
M is the number of ﬁrms and T is the number of auctions during the data period. wijt is
an index variable that takes 1 if bidder i won over j in auction t and 0 otherwise.
xijt is i’s score against j at t. The following variables: ∆backlogijt , ∆salesij ,∆num joinij , ∆workerij , and ∆yearsij are included in order to capture the diﬀerence
between bidder i and j, which might aﬀect the result. ∆backlogijt ≡ backlogit − backlogjt ,where backlogit is the value of backlog projects that i has at auction t, divided by its annual
sales. A backlog project is a project that bidder i has already contracted and its project
period overlaps project t. backlogit proxies the ﬁrm’s capacity utilization.1 ∆salesij ≡salesi − salesj , where salesi is the annual sales of compensation consulting works of each1
In the present analysis, the backlog data is constructed using contract data bought by Naha City only.
Though true backlog status must be aﬀected by unobservable works such as private works, we assume it
identical among bidders.

11bidder averaged over FY2003 and FY2004. ∆num joinij ≡ num joini − num joinj ,where num joini is the number which represents how many times bidder i participatedin the auction. ∆workerij ≡ workeri − workerj , where workeri is the number of workers
bidder i has. ∆yearsij ≡ yearsi − yearsj , where yearsi represents the number of years
that bidder i has been operating. Dummy variables for ﬁrms are also included in order tocapture the ﬁxed eﬀect ai for ﬁrm i.
εijt is the error term which is assumed to follow a standard normal distribution
given zijt . εijt is assumed to be independent across matches, that is, the ﬁght between iand j in auction t is independent of that between i and other bidders. Note that εijt andεjit are negatively correlated within the match because wijt and wjit are generated by thesame match where wijt = 1 implies wjit = 0. However, the pooled probit estimator has anice feature that estimated parameters will be consistent and asymptotically normal evenif error terms are arbitrarily correlated within groups of observations (Wooldridge (2002)).
Following Duggan and Levvit (2002) who adjusted standard errors by clustering after OLS
estimation of the linear probability model, we clustered standard errors by matches.2
The parameter which interests us is b. If the auction is competitive, then xijt has
no eﬀect on the event, that is, b is zero. If the bidders are exchanging favors, xijt has
a positive eﬀect on the probability. We test the null hypothesis H0 : b = 0, against thealternative hypothesis H1 : b > 0.

4

Empirical result

Our analysis consists of two parts. In the ﬁrst analysis, we estimate equation (2) andanalyze the dependence of the winning probability on the score. Our result shows that2

Clustering robust
standard errorinprobit model G
−1is the square root of the diagonal elements of matrix−1  GG
g=1 Ag (β̂)

g=1 sg (β̂)sg (β̂)

Ag (β̂) =sg (β̂) =g=1 Ag (β̂), where g = 1, 2, ..., G are the matches and{φ(zijt β̂)}2 zijt zijt
Φ(zijt β̂){1 − Φ(zijt β̂)}φ(zijt β̂)zijt {wijt − Φ(zijt β̂)}Φ(zijt β̂){1 − Φ(zijt β̂)}++

See Wooldridge (2002) Ch.13 for details.

12{φ(zjit β̂)}2 zjit zjit
Φ(zjit β̂){1 − Φ(zjit β̂)},φ(zjit β̂)zjit {wjit − Φ(zjit β̂)}Φ(zjit β̂){1 − Φ(zjit β̂)}.

the winning probability is positively dependent on the score.
Favors would be exchanged between pairs of collusive bidders, and not between apair of a collusive bidder and a competitive bidder. In the second analysis, we analyze
whether the data conﬁrm this prediction. Bidders who are colluding by favor exchange willsubmit passive high bids on average, whereas competitive bidders will submit aggressive
low bids on average. Therefore, favors must be exchanged among a pair of passive bidders,
not among a pair where either of the bidders is aggressive.
In the analysis, bidders are classiﬁed by their average bid level into two groups:“aggressive” bidders and “passive” bidders. An “aggressive” bidder is a bidder who makes
low bids on average throughout the data period. A “passive” bidder is a bidder who makes
high bids on average. If a bidder’s average bid is lower than 95% of the reserve price, thenhe is “aggressive”.3 If a bidder’s average bid is higher than 95%, then he is “passive”. We
test the dependence of winning probability on the score, when both i and j are passive,
and when one of them is aggressive.
At the beginning of the data period, xijt = 0 for all i, j by deﬁnition. In bothanalyses we omitted observations such that xijt = 0 because these observations lower the
sample variance of xijt , and standard error of its parameter may be underestimated. We
also omit ﬁrms which haven’t won a contract during the data period, because obviously
they didn’t exchange favors. Finally, we have 60 ﬁrms in which 4 are aggressive bidders
and 56 are passive bidders. All ﬁrms are located within Naha City.
The analysis using early period data may be still aﬀected by the assumption thatxijt = 0. To see the robustness of the results, we estimate the model with several data sets
sequentially eliminating early period observations. We use three data sets: (a) observationsof all ﬁscal years, (b) observations after the second ﬁscal year, and (c) observations after
the third ﬁscal year. Therefore, (a) consists of observations during FY2001-2004, and (b),(c) consist of observations during FY2002-2004, FY2003-2004, respectively. The number
3

We used 95% of the reserve price to divide a passive bidder and an aggressive bidder. The reason
is that Japan Citizen’s Ombudsman Association claims that bid rigging is strongly suspected in markets
where the winning price is within 95% of the reserve price on average. The association mainly consistsof lawyers, and their claims are based on their nationwide research and antitrust accusations cases in the
past.

13

of observations in each data set is 812, 736 and 518, respectively. The analysis using thelatter data set is freer from the assumption, but the number of observations is smaller.

4.1

Analysis 1: Evidence of exchanging favors

We estimate model (2) to test whether the score aﬀects the winning probability. Table 5shows the result. The estimation results using data set (a) are in the ﬁrst two columns.
Next two columns shows the results using data set (b). The ﬁnal two columns show theresults using data set (c). For each data set we ran a couple of speciﬁcations: with andwithout bidder’s ﬁxed eﬀect. The ﬁrst column of every two columns corresponds to theestimation result of the model without ﬁxed eﬀect, and the second column corresponds tothe ﬁxed eﬀect model. The number of observations are diﬀerent between with and without
ﬁxed eﬀect models. Since we have dummy variables for bidders in the ﬁxed eﬀect model,
observations were lost due to perfect prediction. In data set (c), the parameter of backlog
is not identiﬁed since no bidder has backlog project.
We are primarily interested in the parameter of the score shown in the ﬁrst row
of the table. It is positive and signiﬁcant in all columns in the table. The null hypothesisthat b = 0 is rejected in all data sets in models with and without ﬁxed eﬀect. This implies
that the winners tend to have positive score against losers, that is, the winners have given
favors to the other bidders. This supports the possibility that bidders are exchanging
favors: a bidder who has given a favor tends to win.
The bidders’ diﬀerence in the number of participation in the auction is signiﬁcantand negative. This implies that the winners tend to submit bids less frequently than thelosers. The negative sign is unexpected and remains unexplained. The diﬀerence in thenumber of operating years is also signiﬁcant and has positive sign. This implies that thewinners tend to be operating longer than the losers. It is supposed that members are notequally treated, but a ﬁrm who is operating long has relatively strong negotiation powerin the pre-auction communication.

14

4.2

Analysis 2: Favor exchange and average bid level

We analyzed whether the score aﬀects the winning probability when the bidder and theopponent are aggressive or passive. A modiﬁed form of model (2) is estimated, in which
the term b xijt is replaced into the sum of the following 3 terms, b1 Pi Pj xijt , b2 Pi Aj xijt ,and b3 Ai Pj xijt . Ai and Pi are dummy variables which indicate whether i is aggressive or
passive. Pi takes 1 if bidder i is passive and 0 otherwise. Ai takes 1 if bidder i is aggressive
and 0 otherwise. Ai Aj xijt is not included because there is only a match where both i andj are aggressive.
Table 6 shows the estimation result. As shown in the ﬁrst row of the table, theparameter of Pi Pj xijt is positive and signiﬁcant in data sets (a), (b) and (c) in both
speciﬁcations. Therefore the score raises the winning probability when both bidder i andbidder j are passive. On the other hand, the parameter of Pi Aj xijt and Ai Pj xijt is not
signiﬁcant with 5% signiﬁcance level in any data set as shown in the second and the thirdrows of the table.
It can be said that when either i or j are aggressive and the other is passive, thescore has no impact on winning probability. This suggests that the impact of the scoreon the winning probability is eﬀective only when both i and j are passive, and invalid
when one of them is aggressive. The result is consistent to the expectation that favors areexchanged only between passive bidders.

5

Conclusion

This paper provides an empirical analysis to see if bidders are colluding by exchanging
favors in repeated procurement auctions. Bidding data of consulting works bought by Naha
City are studied to assess if collusion by favor exchange is in operation. We constructed avirtual variable named “score”, which represents the balance of favors between every pairof bidders assuming that all bidders are collusive. We then analyzed the dependence ofbidders’ winning probability on the score.
The result shows that the winning probability in auctions tends to be positively
dependent on the score. That is, if bidder A has given a favor to another bidder B, A
15

tends to win against B. This conﬁrms the prediction that collusion by exchanging favors
is in operation.
We next classiﬁed the bidders into two groups, supposing that the ring was not all
inclusive in the market and there were some competitive ﬁrms. A bidder who submitted
high bids on average was classiﬁed as a “passive” bidder and a bidder who submitted
low bids on average was classiﬁed as an “aggressive” bidder. We then found that favors
were exchanged within a pair of passive bidders, but not within a pair in which one wasaggressive. The result is consistent with a prediction that a collusive bidder tends to bid
higher than a competitive bidder.
Our analysis would be useful in detecting bidder collusion by favor exchange. However, there remains a possibility that the result is untrue. A history of auction generated
through other collusion schemes can show the same characteristics as the collusion byfavor exchange. For example, a simple bid rotation scheme can be seen as if they areexchanging favors when bidders are ﬁxed throughout auctions. Further analyses using
artiﬁcially generated data would be useful to know how to discriminate various collusion
schemes.

16

References[1] Aoyagi, M. (2003), “Bid Rotation and Collusion in Repeated Auctions,” Journal of
Economic Theory, 112, pages 79-105.
[2] Bajari, P. and Ye, L. (2003), “Deciding Between Competition and Collusion,” Review
of Economics and Statistics, 85.4, pages 971-989.
[3] Duggan, M. and Levitt, S. D. (2002) “Winning Isn’t Everything: Corruption in Sumo
Wrestling,” American Economic Review, 92(5), pages 1594-1605.
[4] Hironaka, K. (1994), “Dango does exist after all (Soredemo dango ha nakunaranai),”
Tokei Publishing (in Japanese).
[5] McAfee, R. P. and McMillan, J. (1992), “Bidding Rings,” American Economic Review, 82.3, pages 579-599.
[6] Pesendorfer, M. (2000), “A Study of Collusion in First-Price Auctions,” Review of
Economic Studies, 67, pages 381-411.
[7] Porter, R. H. and Zona, J. D. (1993), “Detecting of Bid Rigging in Procurement
Auctions,” Journal of Political Economy, 101.3, pages 518-538.
[8] Skrzypacz, A. and Hopenhayn, H. (2004), “Tacit collusion in repeated auctions,”
Journal of Economic Theory.
[9] Suzuki, M. (2004), “A study of bid rigging (Nyusatsu dango no kenkyu),” Shinzansha(in Japanese).
[10] Wooldridge, J. M. (2002), “Econometric Analysis of Cross Section and Panel Data”,
MIT press.
[11] Zona, J. D. (1986), “Bid-rigging and the Competitive Bidding Process: Theory andEvidence.” Ph.D. dissertation, State University of New York at Stony Brook.

17

Figure 1: Compensation consulting works in Naha City

18

150%
140%
130%

Bid / Reserve price

120%
110%
100%
90%
80%
70%
60%
50%
40%

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

100

110

120

130

140

150

160

170

Auction No.

Figure 2: Distribution of bids
110%

Winning price / Reserve price

100%

90%

80%

70%

60%

50%

40%
0

10

20

30

40

50

60

70

80

90

Auction No.

Figure 3: Distribution of winning price19

Table 1: Number of land evaluation project auctions in Naha City
Fiscal year
Number of auction

2001
50

2002
43

2003
38

2004
44

Total
175

Table 2: Number of bids
Fiscal year
Number of bids

2001
498

2002
430

2003
380

2004
440

Total
1748

Table 3: Distribution of ﬁrms: frequency of participation
Number of Participation
1-10
11-20
21-30
31-40
41Total

Firms
79
27
11
16
3
136

Table 4: Distribution of ﬁrms: frequency of winning
Number of winning
0
1
2
3
4
5Total

20

Firms
67
22
15
14
11
7
136

Table 5: Analysis 1
Dependent Variables
Score∆Numjoin∆Sales∆Backlog∆Worker∆YearsConstant
Firm dummies
Number of obs
Pseudo R2
Log-likelihood

Data set(a)0.0398 **(0.0127)-0.0258 **(0.0074)-0.0026(0.0018)-0.0019(0.0054)-0.0041(0.0052)
0.0212 **(0.0064)0.0000
(0)
No
812
0.071
-522.90(a)0.0572 **(0.0141)-0.0266 **(0.0081)-0.0028(0.0021)-0.0024(0.0046)-0.009(0.0055)
0.0291 **(0.0073)
Yes
736
0.151
-432.93(b)0.0357 *(0.0130)-0.0242 **(0.0076)-0.0014(0.002)0.0013(0.0052)-0.0042(0.0053)
0.0252 **(0.0067)0.0000
(0)
No
736
0.071
-473.72(b)0.0483 *(0.0142)-0.0265 **(0.0084)-0.0006(0.0023)0.0005(0.0042)-0.0101(0.0054)0.0347 **(0.0077)
Yes
658
0.159
-383.37(c)
0.0439 *(0.016)-0.0206 *(0.009)-0.0042(0.0024)-(c)
0.0557 *(0.0168)-0.0251 *(0.0104)-0.0059(0.0032)-0.0140(0.0082)
0.0230 **(0.0085)0.0000
(0)
No
516
0.104
-320.390.0123(0.0098)
0.0294 **(0.0110)
Yes
417
0.246
-226.47

Note: Robust standard errors are reported in parentheses. Estimation results reported
in even number columns are those of ﬁxed eﬀect models. Bidders’ dummy variables areabbreviated. **: 1% signiﬁcance, *: 5% signiﬁcance.

21

Table 6: Analysis 2
Dependent Variables
Score*P*P
Score*P*A
Score*A*P∆Numjoin∆Sales∆Backlog∆Worker∆YearsConstant
Firm dummies
Number of observations
Pseudo R2
Log likelihood

Data set(a)0.0401 **(0.0131)0.0159(0.0622)0.0159(0.0622)-0.0260 **(0.0075)-0.0027(0.0018)-0.002(0.0054)-0.0041(0.0052)
0.0213 **(0.0064)
0
(0)
No
812
0.071
-522.98(a)0.0578 **(0.0142)0.0808(0.0747)0.0096(0.0538)-0.0268 **(0.0081)-0.0029(0.0021)-0.0025(0.0046)-0.0096(0.0055)
0.0297 **(0.0072)
Yes
744
0.159
-433.66(b)0.036 **
(0.0133)
0.0185(0.062)0.0185(0.062)-0.0243 **(0.0077)-0.0014(0.0019)0.0013(0.0052)-0.0042(0.0053)
0.0252 **(0.0067)
0
(0)
No
736
0.071
-473.81(b)0.049 **
(0.0142)0.0729(0.073)0.0157(0.0534)-0.0267 **(0.0084)-0.0006(0.0023)0.0005(0.0041)-0.0103(0.0054)0.0353 **(0.0077)
Yes
666
0.167
-384.13(c)
0.0447 **(0.0158)-0.0104(0.0817)-0.0104(0.0817)-0.021 *(0.009)-0.0042(0.0024)-(c)
0.0566 **(0.017)0.0585(0.105)-0.0075(0.0577)-0.0253 *(0.0104)-0.0059(0.0032)-0.014(0.0083)
0.0230 **(0.0085)
0
(0)
No
516
0.105
-320.270.0119(0.0098)
0.0303 **(0.0109)-

Note: Robust standard errors are reported in parentheses. Estimation results reported
in even number columns are those of ﬁxed eﬀect models. Bidders’ dummy variables areabbreviated. **: 1% signiﬁcance, *: 5% signiﬁcance.

22

Yes
423
0.2141-226.95