Silviase/jgov_v1.4_full_ann huggingface dataset:
響を評価できた。国内では、河川・湖沼について、複数の指標にもとづいて全国評価を実施し、保護を優先すべき場所と、護岸や水質、外来魚などの主要なリスク要因を特定できた。

6)保護上重要な海域 EBSAに関する国際的に合意された7基準を定量的に評価する指標を考案し、これらの評価結果を相補性などを考慮して統合する手法を開発した。また、温暖化に伴う海水温の上昇と海洋酸性化の相互作用を考慮して、日本近海のサンゴ礁の将来予測を行い、サンゴ礁が消滅するリスクがあることを示した成果は、学術的にも社会的にも注目された。

7) 以上のような遺伝子・種・生態系レベルの多様性の評価において、一般化線形モデル・相補性解析などの共通の解析手法を採用するとともに、地図化手法の高度化・共有化を推進した。

## (2) 環境政策への貢献

本プロジェクトの重要な使命は、IPBES アセスメントに対して貢献することにあった。この課題については、概念枠組み策定から地域アセス実施にまで一貫して関与し、貢献してきた。

これらの IPBES への貢献に加え、環境省生物多様性センターと協力して APBON の強化をはかり、第 4 回（2011 年）第 5 回（2013 年）第 6 回（2014 年）第 7 回（2016 年 2 月）のワークショップを開催し、アジア・太平洋地域における生物多様性観測を推進するとともに、国際的な生物多様性観測ネットワーク（GECBON）の構築に貢献した。

## ＜行政が既に活用した成果＞

1)「生物多様性国家戦略 2012-2020」95 ページにおいて、「世界的に見ると農地の拡大や違法伐採などによる森林減少、砂漠化などが要因となり生物多様性の状況が悪化しています。わが国は、食料や木材などの資源の多くを海外から輸入しており、他国の生物多様性を利用しているという視点に立ち、地球規模での生物多様性保全に貢献する必要があります」という記述に活用された。

2）生物多様性条約第5回国別報告書において、以下の章・節で成果が活用された。

第1章 生物多様性の状況、傾向と脅威

1.1 生物多様性の重要性

（３）世界の生物多様性に影響を与える日本

1.5 生物多様性の将来シナリオ

（２）海洋酸性化のサンゴ礁への影響について

3) 種の保存法に基づく種指定作業において、日本の維管束植物の絶滅リスク評価と保全優先地域選定に関する S-9 の成果（Kadoya et al. 2014；査読付き論文 7）を基に候補植物種が選ばれた。

## <行政が活用することが見込まれる成果>

本プロジェクトを通じて日本、および東南アジア諸国において保護を優先すべき地域の選定に関する科学的な根拠にもとづく資料が得られた。これらの資料は、今後の保全施策の優先順位決定において活用されることが見込まれる。また、生物多様性保全の必要性について、農業生産に寄与するハナバチの減少、漁業資源の減少、サンゴ礁の消失リスク、日本での消費が東南アジア熱帯林減少に与える影響、などのデータをもとに、国民に対して説得力のある説明をすることが可能になった。これらのデータは今後の生物多様性に関する普及啓発事業において活用が見込まれる。
## 4 ．委員の指摘及び提言概要

アジア規模でのさまざまな生物多様性を対象に、ホットスポットの評価、相補性評価による保全生態学的アプローチ等で森林、陸水、海域等を横断するこれまでにない貴重な試みであり、指標分類群の選定や絶滅のシナリオ分析を行うなど戦略的な研究遂行により成果を挙げている。一方で土壌圏・根圏を巡る課題が対象外とされたことや、資源利用とそれ以外の評価視点が混在して生物多様性保全の姿勢が不明確となったことが悔やまれる。

### 5. 評点

総合評点：A
# CPRC Discussion Paper Series

# Competition Policy Research Center Japan Fair Trade Commission

Ratifiable Collusion and Bidding Systems in Procurement

丹野 忠晋

跡見学園女子大学准教授

CPDP-37-E February 2009

1-1-1, Kasumigaseki, Chiyoda-ku, TOKYO 100-8987 JAPAN

Phone:+81-3-3581-1848 Fax:+81-3-3581-1945

URL:www.jftc.go.jp/cprc.html

E-mail:cprcsec@jftc.go.jp
# Ratifiable Collusion and Bidding Systems in Procurement

Tadanobu Tanno $ ^{*} $

Toulouse School of Economics (I.D.E.I.), 21 allee de Brienne, 31000 Toulouse, France

Atomii University, 1-9-6 Nakano, Niiza, Saitama 352-8501, Japan

December 23, 2008

## Abstract

This study explores stability in efficient collusion in government procurement auctions. In first- and second-price auctions with independent private values, we look at the possibility of vetoing collusion mechanisms and the learning of the other bidders after vetoing. The collusions in first-price auctions in simple case and second-price auctions are stable against the competition after a potential veto to take part in bid-rigging.

Keywords: auctions, bid rigging, collusion, procurement, ratifiability.

JEL Classifications: C72, D44, D82, L44, H57.
## 1 Introduction

Bid-rigging in procurement auctions is serious problem in many countries with regard to maintaining competition. In Japan, cases of collusion in procurement auctions represent the majority of violations in the Antimonopoly Act. While many authors study collusion in auctions, we need undertake further investigation to gain useful insights into methods for detecting and preventing bid-rigging. This study considers the effects of two auction formats on collusive behavior. We show that collusions in both these auctions are robust even if bidders have an option to deviate from bid-rigging and compete in auctions after vetoing. In the terms of auction theory, our result also adds knowledge of the similarity between these auctions.

Graham and Marshall (1987) extensively analyze collusion in second-price auctions for selling an item, and Mailath and Zemsky (1991) extend their model to asymmetric bidders. McAfee and McMillan (1992) analyze an efficient collusion in first-price auctions. Robinson (1985) compares possibilities to collude in first-price and second-price auctions. Holt (1980) shows that the choice between first- and second-price auctions gives significant impact on the expected cost of procurement when bidders are risk averse. There are a lot of empirical literature about collusion in procurement auctions. For example, Bajari and Ye (2003) study a method to identify bid rigging and find asymmetries in collusive behaviors as well as competitive bidder's costs due to location or capacity constraint.

In these theoretical models each bidder takes part in bid-rigging if incentive and individually rational conditions for collusion are satisfied. In reality, we observe breakdowns of collusion and thereafter competitive behavior. $ ^{1} $ A bidder has an opportunity to veto bid-rigging, and other riggers may be able to learn the cost information of the vetoer from his veto. $ ^{2} $ Cramton
and Palfrey (1995) present an elaborate concept of ratifiability in a mechanism design setting to analyze such situations. If a proposed mechanism is robust against some status quo mechanism after a veto, the mechanism is called ratifiable. They investigate the ratifiability of the monopoly outcome mechanism that is analyzed in Cramton and Palfrey (1990) against Cournot competition in two firms and linear demand. Since a low-cost firm prefers Cournot competition to collusion, collusion for the monopoly outcome is not ratifiable against the status quo. In terms of learning type after a veto, collusion in the quantity competition is not stable.

Tan and Yilankaya (2007) consider the ratifiability problem of bidder collusion in second-price auctions for selling an object with participation cost. The collusion in the auctions they consider is not ratified against the post second-price competitive auctions. However, we show that collusion in second-price auctions for buying an object with no participation cost is ratifiable against the post auctions.

In this study we investigate the possibilities of colluding in first-price and second-price procurement auctions. A government procurees an item from potential sellers in these auctions with no participation cost. The former auction corresponds to sealed low-bid auctions that governments commonly adopt. When values are private, the latter is strategically equivalent to open descending auctions. In our assumptions, the collusion in first-price auctions with uniform distribution and two bidders and general second-price auction are ratifiable. Bid-rigging in procurement auctions is relatively stable. When a cartel is strong, even if a procurer changes a sealed bid auction to an open auction, we expect that the cartel remains effective against the reform. Since the collusion in the Cournot competition is ratifiable (Cramton and Palfrey (1995)), auction environments are more vulnerable against collusion than the quantity competition. To detect and prevent bid-riggings, procurers in many countries reform bidding systems and competition authorities use some tools, e.g., leniency programs, ___

quently apply leniency to protect their profits. The defection and veto on collusion may bring some information about the exerciser.
etc. Our conclusion partially justifies these efforts to weaken incentives to commit bid-riggings. Since the participation cost restores competition (Tan and Yilankaya (2007)), their conclusion and our analysis imply that some kind of a burden for bidders before auctioning may be a key to preventing collusion.

Section 2 presents basic models and preliminary results compared with the standard auction literature. In Section 3 we provide an efficient collusion mechanism. Section 4 introduces ratifiability. We obtain ratifiability results in first-price auctions in Section 5 and second price-auctions in Section 6. Section 7 concludes.

## 2 Model and Noncooperative Auctions

A government seeks to buy an item from N potential sellers. Buyer’s reserve price is r. When the item is a public work, we may consider the reserve price to be an engineering cost estimate for the project. If the lowest bid is above r in each auction, the government does not buy it. In each auction, the lowest price bidder becomes a winner if the price is below or equal to the reserve price. When a tie occurs, to avoid the non-existence problem for an asymmetric case in the first price auction, we adopt status quo tie-breaking rule. $ ^{3} $ In this case the object is surely given to one of the bidders who quote the lowest price. In a first-price auction, a winner receives his quoted price, but, in a second-price auction he receives a price equal to the second lowest price if the price is below or equal to the reserve price. Otherwise, he receives the reserve price.

The sellers’ reservation utility is normalized to 0. They are risk neutral. Our model is a symmetric independent private value one. Each bidder i has cost $ c_{i} $ that is distributed according to a common distribution function F on $ [c, \bar{c}] $ with density function f, which is strictly positive on the domain. Each bidder’s cost is his private information. He infers the others costs from the
prior probability.

Here we consider a competitive first-price auction as a benchmark. We assume that all bidders use common nondecreasing strategy $ p(c) < r $ for a cost c. Let $ \pi^{1}(c|r) $ be a profit for a representative supplier with cost c in the first-price auction. The standard argument implies

$$ \pi^{1}(c|r)=\max_{p}(p-c)(1-F(p^{-1}(p)))^{N-1} $$

where $ p^{-1}(\cdot) $ is an inverse function for $ p(\cdot) $ . By the envelope theorem and $ p^{-1}(p) = c $ ,

$$ \frac{d\pi^{1}(c|r)}{d c}=-(1-F(c))^{N-1}. $$

By integrating the above profit, we obtain the bidder's equilibrium profit $ \pi^{1*}(c|r) $ :

$$ \pi^{1*}(c|r)=\left\{\begin{aligned}&0&(if c>r)\\ &\int_{c}^{r}(1-F(x))^{N-1}dx&(if c\leq r)\end{aligned}\right. $$

Substituting $ \pi^{1*}(c|r) $ in the objective function, the bidding function given the reserve price r is

$$ p^{1*}(c|r)=\left\{\begin{aligned}&No&(if c>r)\\ &c+\int_{c}^{r}(\frac{1-F(x)}{1-F(c)})^{N-1}dx&(if c\leq r)\end{aligned}\right. $$

where No means not participating.

Next, we consider a competitive second-price auction. By the standard argument, submitting true cost is a weakly dominant strategy for a bidder whose cost is not above the reserve price. Then, the equilibrium bid $ p^{2*}(c|r) $ is given by

$$ p^{2*}(c|r)=\left\{\begin{aligned}&No&(if c>r)\\ &c&(if c\leq r).\end{aligned}\right. $$

Let $ \pi^{2*}(c|r) $ be a profit for a representative supplier with cost c in the second-price auction. Since the density of the lowest order statistic among
N - 1 is $ (N - 1)(1 - F(x))^{N - 2}f(x) $ , a profit for a bidder with cost $ c \leq r $ is given by

$$ \pi^{2*}(c|r)=(r-c)(1-F(r))^{N-1}+\int_{c}^{r}(x-c)(N-1)(1-F(x))^{N-2}f(x)dx. $$

Note that the first term represents the profit in the case where all the rivals bid r or do not take part in the auction. Of course, the situation in this section satisfies the conditions under which the revenue equivalence theorem holds. A profit $ \pi^{1*}(c|r) $ for cost c supplier in the first-price auction is equal to (2).

We briefly study welfare analysis in the auctions. $ ^{4} $ The item that the government purchases has a social benefit S. However, the procurement entails some distortionary cost $ \lambda > 0 $ to raise a fund to buy it through taxation. When the payment made by the government to a bidder is p, the consumer surplus is $ S - (1 + \lambda)p $ . Adding expected profits for all firms, the welfare $ W^{*} $ can be easily computed:

$$ W^{*}=N\int_{\underline{c}}^{r}\left(S-(1+\lambda)c-\lambda\frac{F(c)}{f(c)}\right)(1-F(c))^{N-1}f(c)d c. $$

Note that by the revenue equivalence theorem the welfare is identical for the two auctions.

We can choose the optimal reserve price in the way that Myerson (1981) analyzes optimal auctions with a regularity condition. Let

$$ J(c)=(1+\lambda)c+\lambda\frac{F(c)}{f(c)} $$

be the virtual cost with shadow cost. We assume that the virtual cost is monotonically increasing in c and $ S > J(\underline{c}) $ . Just as Bulow and Roberts (1989) recognize a virtual valuation in auctions for a seller as an expected marginal revenue, we think $ J(c) $ as the expected marginal cost generated if a bidder of type c supplies the item. Since the government faces a zero-one problem about whether to procure one item or not under uncertainty, we
can also regard the social benefit S as a “marginal social benefit.” Actually, differentiating $ W^{*} $ leads to

$$ W^{*^{\prime}}=N(S-J(r))(1-F(r))^{N-1}f(r). $$

If $ S < J(\overline{c}) $ , to maximize the social welfare, the government attempts to set marginal benefit equal to marginal cost as the way to select reserve price $ r^{*} $ such that $ S = J(r^{*}) $ . Namely,

$$ S=(1+\lambda)r^{*}+\lambda\frac{F(r^{*})}{f(r^{*})}. $$

If the social benefit is sufficiently large such that $ S \geq J(\overline{c}) $ , the optimal reserve price is $ r = \overline{c} $ . In this case it is a corner solution and the government invites all types of firms.

## 3 Collusion

We consider an all-inclusive collusion with transfer. All bidders collude and coordinate their behavior through the direct mechanism as follows. Before an auction, the cartel members report their costs to the mechanism. If all bidders' reported costs are above or equal to the reserve price, the cartel does not bid in the auction. If at least one bidder's reported cost is lower than the reserve price, the bidder making the lowest report quotes the reserve price, the others bid a price higher than the reserve price, and the lowest report bidder sells the item by the price r and transfers his revenue equally to each losing bidder. If the collusion scheme is feasible, the outcome in the first-price auction is the same as that in the second-price auction.

McAfee and McMillan (1992) show that there exists such a mechanism that is incentive-compatible, ex post efficient, and ex post budget balanced. The collusive payoff $ \pi^{m} $ for a firm that has cost c and reports $ \hat{c} $ is given by

$$ \begin{aligned}\pi^{m}(\hat{c},c|r)=&(r-c-T(\hat{c}))(1-F(\hat{c}))^{N-1}+\\&\int_{c}^{\hat{c}}\frac{T(x)}{N-1}\cdot(N-1)(1-F(x))^{N-2}f(x)dx\end{aligned} $$
where $ T(\hat{c}) $ is the total transfer to the other losing bidders and $ (N-1)(1-F(x))^{N-2}f(x) $ is the density of the lowest cost among N-1 bidders. By the revelation principle without loss of generality we can restrict attention to truthful report. By McAfee and McMillan (1992), we easily obtain an incentive compatible transfer. $ ^{5} $

Lemma 3.1 (McAfee and McMillan (1992)) In a symmetric, ex post efficient, ex post budget balance, and an incentive compatible cartel, the total transfer from a winning cost-c bidder to losing bidders is given by

$$ T(c)=\int_{c}^{r}(r-x)\frac{(N-1)(1-F(x))^{N-1}f(x)}{(1-F(c))^{N}}dx\qquad for c\in[\underline{c},r). $$

Proof: By Guesnerie and Laffont (1984), to show incentive compatibility we check two conditions:

$$ \frac{\partial^{2}\pi^{m}(\hat{c},c|r)}{\partial\hat{c}\partial c}\Big|_{\hat{c}=c}>0\quad\mathrm{a n d}\quad\frac{\partial\pi^{m}(\hat{c},c|r)}{\partial\hat{c}}\Big|_{\hat{c}=c}=0. $$

By (4),

$$ \frac{\partial\pi^{m}}{\partial\hat{c}}=-T^{\prime}(\hat{c})(1-F(\hat{c}))^{N-1}-(N-1)(r-c-T(\hat{c}))(1-F(\hat{c}))^{N-2}f(\hat{c})+ $$

We easily get $ \partial^{2}\pi^{m}(\hat{c},c|r)/\partial\hat{c}\partial c>0 $ . Furthermore,

$$ \begin{align*}\frac{\partial\pi^{m}}{\partial\hat{c}}\bigg|_{\hat{c}=c}=-T^{\prime}(c)(1-F(c))^{N-1}+T(c)N(1-F(c))^{N-2}f(c)-\ $ N-1)(r-c)(1-F(c))^{N-2}f(c)\\=(N-1)(r-c)(1-F(c))^{N-2}f(c)\\-N(N-1)(1-F(c))^{-2}f(c)\int_{c}^{r}(r-x)(1-F(x))^{N-1}f(x)dx\\+N(N-1)(1-F(c))^{-2}f(c)\int_{c}^{r}(r-x)(1-F(x))^{N-1}f(x)dx\\-(N-1)(r-c)(1-F(c))^{N-2}f(c)=0.\end{align*} $$
The other properties are obvious.

When $ \hat{c}=c $ , we simply write $ \pi^{m}(c|r) $ . We characterize collusive payoffs.

Lemma 3.2 In a symmetric, ex post efficient, ex post budget balance, and an incentive compatible cartel, the expected payoff for a cost-c bidder is given by

$$ \pi^{m}(c|r)=\left\{\begin{aligned}&\pi^{m}(r|r)&&(\text{if}c>r)\\ &\pi^{m}(r|r)+\int_{c}^{r}(1-F(x))^{N-1}dx&&(\text{if}c\leq r)\end{aligned}\right. $$

where

$$ \pi^{m}(r|r)=\int_{c}^{r}(r-x)(N-1)(1-F(x))^{N-2}F(x)f(x)d x. $$

The proof is contained in Appendix A. We note that the second term of $ \pi^{m}(c|r) $ for $ c \leq r $ is equal to the noncooperative payoff (1). This stems from incentive compatibility. $ ^{6} $ Since the mechanism must give an incentive to the most inefficient firm to tell the true cost, cost-r firm is given by a transfer and his profit is positive. $ ^{7} $ Since the density of the second-lowest order statistic among N is $ N(N-1)(1-F(x))^{N-2}F(x)f(x) $ , the fixed term $ \pi^{m}(r|r) $ is equal to the expected value of 1/N times the profit that the second most profitable firm would earn when he quotes price r on the item. Therefore, the highest-cost firm must receive an equal share of the expected profit when the second-lowest-cost firm supplies the item. The winning bidder's total rent for the auctions is the difference between the winner's (lowest) cost and the second-lowest cost. The winner takes the rent.
remaining surplus, which is the difference between the reserve price and the second lowest cost, is split equally among the cartel members (including the winner). This collusion mechanism can be implemented by a “preauction knockout,” which Graham and Marshall (1987) analyze.

Obviously, $ \pi^{m}(r|r)>0 $ in Lemma 3.2 and $ \pi^{k*}(r|r)=0 $ for noncooperative profit in each k. The collusive profits are higher than the noncooperative profits for each cost.

Lemma 3.3 $ \pi^{m}(c|r) > \pi^{k*}(c|r) $ for k = 1, 2 and all $ c \in [\underline{c}, \overline{c}] $ .

We assume that the government knows the existence of the cartel, but cannot crack down on it. Welfare $ W^{m} $ under the collusive scheme is reduced to

$$ W^{m}=N\int_{\underline{c}}^{r}\left(S-\lambda r-c\right)\left(1-F(c)\right)^{N-1}f(c)d c. $$

We assume the concavity of $ W^{m} $ . If the government optimally responds to the cartel, the optimal anticartel reserve price $ r^{m} $ is given by

$$ S=(1+\lambda)r^{m}+\lambda\frac{1-(1-F(r^{m}))^{N}}{N(1-F(r^{m}))^{N-1}f(r^{m})}. $$

The formula is similar to (3). We can deduce the implication from the latter. Remember that in the case of competitive bidding the problem is to find a “marginal supplier” at an appropriate reserve price. Since under the collusion all N bidders potentially quote a reserve price, the probability that some bidder sells the item at price $ r^{m} $ is $ 1 - (1 - F(r^{m}))^{N} $ and its density is $ N(1 - F(r^{m}))^{N-1}f(r^{m}) $ . The ratio of the probability to the density is the second term in the right-hand side. This implies that the anticartel reserve price decreases with the number of cartel members and is lower than the optimal reserve price under the same shadow cost $ \lambda^{8} $ .

## 4 Ratifiability

In the previous section we see that collusive profits are higher than competitive bidding profits. However, we sometimes observe a voluntary deviation
from bid-riggings. While deviators may be threatened by a competition authority, there may be a problem with the stability of cartels.

Since a winning deviator does not need to pay transfers to losers in bid-riggings, a low-cost firm with a high possibility of winning may prefer competitive auctions to bid-rigging. Although the collusion scheme is incentive compatible, a competition after the deviation could possibly change bidders' beliefs. The others can infer his cost by observing his deviation. They may anticipate that he has low cost. Thus, they may leave the auction. If he successfully makes them believe him to be low cost, he may gain a monopoly profit. In the following sections we introduce the concept of ratifiability to analyze the possibility of the above situation. We examine whether a difference in auction formats can influence collusion in the presence of the opportunity not to take part in collusion and to learn from deviation.

Cramton and Palfrey (1995) formulate the following two stage game to present ratifiability in a mechanism design environment. After firms know their own costs, at the first stage each firm votes for the proposed mechanism (bid-rigging). At the second stage the mechanism or the status quo game (first- or second-price auctions) is played. If they are unanimously for the mechanism, it is played. Otherwise, the status quo is played with the knowledge that some player vetoes the mechanism. Therefore, when firm i decides whether to veto the mechanism, he must consider how the others' beliefs about i might change as a result of the veto. There are many possibilities about beliefs and refinement concepts. $ ^{9} $ One of possibilities for beliefs is passive belief. When we adopt passive belief as off-equilibrium belief and in equilibrium the mechanism is preferable to the status quo game for any type for any player, unanimous ratification of the mechanism is a
sequential equilibrium in the two stage game. $ ^{10} $ In this case the mechanism is called individually rational relative to the status quo game. By Lemma 3.3 the bid-rigging mechanism is individually rational relative to competitive auctions.

However, this cannot formulate the learning from a veto. We now introduce more subtle beliefs and a refinement concept. If firm i vetoes the mechanism, the others believe that a type of i is in $ V_{i} \subset [\underline{c}, \overline{c}] $ and each type in $ V_{i} $ vetoes with positive probability. We call such a set a $ V_{i} $ veto set for i. The veto belief $ F_{v} $ is induced by the prior F and the veto probabilities. Let $ \pi_{i}^{k*}(c|r) $ be cost-c bidder i's payoff in post competitive k-auctions (k = 1 for first-price and k = 2 for second-price auctions) and $ U_{i}^{k}(c|r) = \pi^{m}(c|r) - \pi_{i}^{k*}(c|r) $ .¹¹

Definition 1 Fix k = 1 or 2. The veto set $ V_{i} $ is credible about i relative to the mechanism and the status quo game k if there exist an equilibrium in the status quo game, veto probabilities, and posterior beliefs such that

(1) there exists a positive veto probability in some type,

(2) $ c \in V_{i} $ for $ U_{i}^{k}(c|r) < 0, $

(3) $ c \notin V_{i} $ for $ U_{i}^{k}(c|r) > 0, $

(4) the posterior beliefs of the others about i are updated by his prior belief and veto probabilities using Bayes' rule.

A type in a credible veto set has an incentive to veto the mechanism. By his veto the others believe that his type is in $ V_{i} $ and he benefits from it. We note that we put no restriction on types that are indifferent between vetoing and not. The ratifiability concept depends on the indifference.

Definition 2 Fix k = 1 or 2. The incentive compatible mechanism is rati-fiable against the status quo game k if the mechanism is individually rational relative to the status quo game and for all i either