The effect of leniency programs on endogenous collusion

Economics Letters 122 (2014) 326–330

Contents lists available at ScienceDirect

Economics Letters journal homepage: www.elsevier.com/locate/ecolet

The effect of leniency programs on endogenous collusion✩ Sangwon Park ∗ Hankuk University of Foreign Studies, Department of International Economics and Law, 270 Imundong, Dongdaemungu, Seoul, 130-791, Republic of Korea

highlights • • • • •

The effect of leniency programs on collusion is studied. This model extends the previous literature in two ways. First, the collusion degree depends on the detection probability. Second, the equilibrium selection in the reporting stage is endogenized. We reveal that the maximum reduction is the best policy without any condition.

article

info

Article history: Received 12 August 2013 Received in revised form 4 December 2013 Accepted 13 December 2013 Available online 22 December 2013 JEL classification: K21 D43 L41

abstract The objective of a leniency program is to reduce sanctions against collusion if a participant voluntarily confesses his behavior or cooperates with the public authority’s investigation. Constructing a model in which the detection probability varies over time, Harrington (2008) pointed out that there are three channels through which the leniency program can affect the collusion amount; furthermore, he presented a sufficient condition under which the maximum leniency is optimal. After extending the model by endogenizing the degree of collusion as well as equilibrium selection in the self-reporting stage, we revealed that the Race to the Courthouse effect disappears and that the maximum reduction is always optimal. © 2014 Elsevier B.V. All rights reserved.

Keywords: Collusion Antitrust Leniency program Self-reporting

1. Introduction Collusion is an agreement to limit open competition among firms. In most countries, a great deal of public resource is used to detect and prevent collusion. The leniency program is one of the newly developed policies under which sanctions against collusion are to be reduced if a member voluntarily confesses his illegal behavior or cooperates extraordinarily with the investigation authority. Two types of reductions should be noted. One is offered to a firm which spontaneously self-reports a collusion even before the initiation of any investigation by the public authority. The

✩ This work was supported by Hankuk University of Foreign Studies Research Fund. We gratefully acknowledge many helpful comments and suggestions from an anonymous reviewer. The development of this paper has benefited substantially from his/her comments. ∗ Tel.: +82 2 2173 3197; fax: +82 2 965 9147. E-mail addresses: [email protected], [email protected].

0165-1765/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econlet.2013.12.014

other is applied to a firm which cooperates when investigation is underway, e.g. by providing hard evidence to the public authority. Leniency programs were first introduced by the US and then spread out to the European Union and other countries, such as Japan, Korea and so on. The effect of the programs and the optimal design under various conditions have been the subject of recent research, such as by Motta and Polo (2003), Brisset and Thomas (2004), Buccirossi and Spagnolo (2006), Spagnolo (2000a,b, 2004, 2006), Harrington (2005, 2008, 2013) and Ishibashi and Shimizu (2010). In particular, the most comprehensive analysis of self-reporting prior to an investigation is by Harrington (2008), who assumes that the chance of being detected by the public authority changes over time. It points out three effects—the Deviator Amnesty Effect, the Cartel Amnesty Effect, and the Race to the Courthouse Effect. The Deviator Amnesty Effect captures the reduction in fines by applying the leniency program right after a firm undercuts the collusive price. Because this effect helps the deviator, the collusion becomes more difficult to sustain. The Cartel Amnesty Effect arises

S. Park / Economics Letters 122 (2014) 326–330

as colluders utilize the leniency program when the chance of detection is high. Because more lenient programs reduce sanctions to colluders, this effect plays a pro-collusive role. The Race to the Courthouse Effect observes that it can be in equilibrium for no firms to confess when the reduction is minimal. With the more generous treatment, the reporting game becomes a Prisoner’s Dilemma and it is the unique equilibrium for all firms to apply for amnesty. This effect is counter-collusive in that the expected present value of penalty from continuing to collude increases with transition from ‘self-reporting by nobody’ to ‘self-reporting by everybody.’ After presenting the three effects, Harrington (2008) provided a sufficient condition whereby the antitrust law should waive all penalties for the first firm to come forward. By extending the previous model in the following ways, this paper proves that the Race to the Courthouse Effect disappears and maximum leniency is always optimal. First, we allow the collusion degree to be flexible depending on the detection probability. Second, the reporting strategy is a part of collusion and the colluders are assumed to select any equilibrium of the selfreporting game to maximize collusion profit. 2. Model 2.1. Set up We adapt a standard model of repeated auction. There is one buyer and n sellers (firms) who repeatedly interact with each other. Each seller maximizes his/her life time profit and δ ∈ (0, 1) is the discount factor. The buyer wants to consume one unit of goods at each period. The cost of production is normalized to be 0 and the reservation price is denoted by m. We take the standard tiebreaking rule of determining the winner so that equal probability will be given to all the highest bidders. The firms are supposed to choose whether to apply for leniency as well as their bidding at each period. As to the timing of selfreporting to the public authority, two different assumptions have been made in the literature. Some assume that a firm can set the price and apply for leniency before other firms observe his bidding. In other models, leniency decisions are made after the bidding outcome is realized. To make a comparison with the result in Harrington (2008), we follow the assumption that it is possible for the firms to apply for leniency at the same time of presenting their bid. This reporting opportunity will be called the ‘with-bidding stage’ in this paper. The ‘after-bidding stage’, as it will be called in this paper, is one in which firms can also choose to self-report simultaneously after the bidding outcome is realized. In the case that nobody self-reports in two reporting stages, they face a risk of being detected by the public authority.1 The detection occurs probabilistically, which varies period by period. Specifically, let ρt be the probability of successful detection at time t which is a random variable drawn independently from a continuous distribution at the start of every period. The distribution function is denoted by G which has the support of [0, 1]. The realization of ρt is public information and can be utilized by the collusion members. F is the fine against collusion imposed on every colluder. In the case of a confession before detection, only the first one to come forward receives amnesty and his penalty reduces to θ F where θ ∈ [0, 1]. If k ≥ 1 firms confess together, then each  firm has the expected fine of θ (k)F = k−k 1 + 1k θ F . The following sums up the sequence of actions in each period.

1 Because we want to focus on an amnesty program for self-reporting before investigation is underway, the process of verifying at court is ignored and the detection immediately connects to the proof.

327

• ρt is realized and observed by every seller. • n sellers show their bid. • At the time of presenting the bid, each firm has a chance of confessing to the public authority (with-bidding stage).

• If nobody confesses at the time of bidding, the colluders simultaneously choose ‘confess’ or ‘no confess’ after observing the bidding outcome (after-bidding stage). • If nobody has confessed, the detection is made with probability ρt . To describe the strategic situation in the reporting stage, the following simultaneous game, RG(ρ), is defined. The colluders are the player and the set of their strategy is {confess, no confess}. Each player’s payoff is −ρ F if nobody chooses ‘self-report’. If k players choose ‘self-report’, then the players with self-reporting strategy will get −θ (k)F and others will get −F . In principle, collusion can be any anti-competitive agreement. However, we impose structures for a meaningful conclusion. Let D(θ ) be the set of subgame perfect equilibrium with the following properties (a)–(g). The generic element of D(θ ) is denoted by d ∈ D(θ ). (a) There are two states, a collusive state and a competitive state. The initial period is collusive. (b) At a collusive state of t, the agreed winning bidder is determined with an equal probability. The agreed winner is supposed to bid mt (ρt ) where mt (ρt ) ∈ [0, m]. Every bidder other than the agreed winner bids strictly more than mt (ρt ). Nobody applies for leniency at the with-bidding stage. If the bids are the same as the agreed ones, they do not self-report at the afterbidding stage. (c) At a collusive state, if any bid is different from the agreed one and no self-report is made at the with-bidding stage, then any (pure strategy) equilibrium of RG(ρt ) is played at the afterbidding stage. (d) Suppose that t − 1 was a collusive state. If, at t − 1, the agreed bids were presented, no self-report was made at the withbidding and after-bidding stage, the public detection did not occur and ρt ≤ ρ , then t continues to be a collusive state. Otherwise, t becomes the competitive state. (e) Suppose that t − 1 was a collusive state but t has become a competitive state due to ρt > ρ , Then at the with-bidding stage, any (pure strategy) equilibrium of RG(ρt ) will be played.2 (f) At a competitive state, the sellers present the stage Nash equilibrium bid which is 0. In addition, if t − 1 was a competitive state, then t becomes a competitive state regardless of the outcome of t − 1. (g) If t − 1 and t are competitive states, then nobody self-reports at the with-bidding and after-bidding stage of the t period. We say that a collusion exists at time t if t is a collusive state of any d ∈ D(θ ). Several remarks are worth mentioning. First, a grim-trigger strategy is used. One deviational bid will trigger permanent competition. Theoretically, the players may organize another collusion in the future after finite punishment periods, and the argument will still be applied even with the revival of collusion; however, we exclude it for ease of exposition. Moreover, the permanent punishment provides the highest incentive to participate in the collusion. Not only a deviational bid but also a self-report or public detection causes a permanent transition to competition. Another possibility of collusion in the future is unlikely given that the market with a collusion history will be the subject of thorough monitoring by the public authority.

2 If no self-report is made at the with-bidding stage, any (pure strategy) equilibrium of RG(ρt ) will be played at the after-bidding stage, again.

328

S. Park / Economics Letters 122 (2014) 326–330

Second, it is a cut-off strategy. If ρt is higher than the threshold level, ρ , then the firms give up the collusion and a competitive state begins. Nobody has an incentive to abide by the collusive agreement if the chances for getting caught are high. Third, following Harrington (2008), we assume that if t − 1 was a collusive state, then the colluders face the detection possibility even though they bid competitively at time t.3 In contrast, if the buyers did not collude in the previous period, there will be no detection at time t and it is meaningless to consider a self-report strategy. In reality, the public authority may punish past collusive behavior. However, we stick to the current assumption in order to obtain a stationary structure. Fourth, as the reporting strategy is a part of collusion, the colluders can choose one to maximize the collusive profit. In other words, though any type of equilibrium selection is accepted in the reporting stages of (c) and (e), the one with the maximum collusion profit will be driven. Because no future collusive profit is expected, the strategic situation at the reporting stage of (c) and (e) is represented by RG(ρt ). Note that if θ ≥ ρt , then two equilibria exist; that is, self-report by everybody and self-report by nobody. If θ < ρt , then the unique equilibrium is to self-report by everybody. For future reference, let −x(ρt )F and −y(ρt )F be the equilibrium payoff used in (c) and (e), respectively. Fifth, the collusion degree changes over time depending on ρt . Suppose that ρt is high. Because the expected future payoff from collusion is low, the colluders need to cut down the benefit from the deviation in order to sustain the collusion. A higher mt commands larger benefit from the deviational bid, leading to a conclusion that the degree of collusion must have a negative relation with ρt . The firms want the maximum payoff with collusion while the government needs to minimize the expected payment to the buyers. Let W (d) and V (d) be each firm’s (normalized) expected revenue (=payment from the government) and payoff along d,  (θ ) as respectively.4 We define W

 (θ) = max W (d∗ ) s.t. d∗ ∈ arg max V (d). W d∗

d∈D(θ)

Then the optimal leniency program is defined as θ ∗ = arg minθ  (θ). W 2.2. Optimal leniency This section will characterize the collusion with maximum expected profit given the leniency program. If a non-winner conforms to the collusion in a collusive state, his life-time payoff will be (1 − δ)(−ρt F ) + δ(1 − ρt )V where V is the normalized life time payoff to each firm from collusion. The supremum payoff he can get with a deviational bid and self-reporting strategy at the with-bidding stage is (1 − δ) (mt − θ F ). If he deviates and waits until the bidding outcome is publicized, then the payoff he can get is (1 − δ) (mt − x(ρt )F ) where x(ρt ) is θ (n) or ρt , depending on the equilibrium selection in the after-bidding stage. If a deviator chooses to self-report at the with-bidding stage after conforming the collusive bid, then his payoff will be (1 − δ)(−θ F ). To prevent a deviation, (1 − δ)(−ρt F ) + δ(1 − ρt )V must be bigger than any of the above deviational payoff. Because θ (n) ≥ θ and the deviator will take the best deviation, we can merge three deviational payoffs into (1 − δ) (mt − min

{x(ρt ), θ}F ). Hence, (1) below is the key incentive compatibility conditions in the case of ρt ≤ ρ : (1 − δ)(−ρt F ) + δ(1 − ρt )V ≥ (1 − δ) (mt − min{x(ρt ), θ}F ) .

(1)

Obviously, the firms want ρ and mt to be as high as possible. If ρt is small enough, even mt = m will satisfy (1). Let  ρ be the threshold level of ρt which makes mt = m hold. As ρt increases, the firms cannot achieve m and set mt to satisfy (1) as equality. As explained before, the equilibrium selection in the after-bidding stage should be a part of collusion the participants design. Because the larger min{x(ρt ), θ} implies the bigger mt , the colluders want to form a collusion with the larger min{x(ρt ), θ}. If θ ≤  ρ < ρt , then min{x(ρt ), θ} = θ regardless of the equilibrium selection. In addition, if  ρ < θ , then with positive probability  ρ < ρt < θ holds. Hence θ (n) should be selected as the equilibrium payoff to make min{x(ρt ), θ} as large as possible. Therefore, min{x(ρt ), θ} = θ must be satisfied in order to maximize the collusion profit. As ρt approaches 1, (1 − δ)(−ρt F ) + δ(1 − ρt )V becomes close enough to (1 − δ)(−F ). Therefore (1) will be violated eventually, which means that ρ is determined by (1 − δ)(−ρ F ) + δ(1 − ρ)V = (1 − δ)(−θ F ). To sum up, there are two thresholds,  ρ and ρ , such that the structures of the maximum collusion are5 :

ρt ≤  ρ : mt = m  ρ < ρt ≤ ρ: mt = (θ − ρt )F +

δ 1−δ

(1 − ρt )V .

δ Note that θ ≤ ρ holds because ρt = θ and mt = 1−δ (1 − θ )V 6 satisfy (1). In addition, θ ≤ ρ < ρt implies that ‘self-reporting by everybody’ is the only equilibrium in the with-bidding and afterbidding game of (e), that is y(ρt ) = θ (n). From the above argument, we can conclude that the following conditions fully characterize the collusion with maximum profit given θ :



mt (ρt ) ≡ max m, θ F − ρt F +

δ (1 − ρt )V 1−δ



(1 − δ)(− ρ F ) + δ(1 −  ρ )V = (1 − δ)(m − θ F ) (1 − δ)(−ρ F ) + δ(1 − ρ)V = (1 − δ)(−θ F )     ρ  m V = (1 − δ) − ρ F + δ(1 − ρ)V dG n 0    ρ δ (θ − ρ)F + 1−δ (1 − ρ)V + (1 − δ) − ρF

(2) (3) (4)

n

 ρ

 + δ(1 − ρ)V dG −

1

 ρ

 ρ

(1 − δ)θ (n)F dG. ρ 

(5)

δ m dG(ρ) +  Let M = 0 ρ (θ F − ρ F ) + 1−δ (1 − ρ)V dG(ρ), which is the expected current-period payment. Then the buyer’s (normalized life time) expected payment, Φ , is



Φ = (1 − δ)M + δ G(ρ)Φ (1 − δ)M ⇒Φ= . 1 − δ G(ρ)

3 The conclusion in this paper only strengthens with the assumption that firms face no detective challenge with competitive action at the current period. 4 Though the production cost is 0, the expected revenue to the sellers is different

5 We can define  ρ = 0 if m can be never obtained. In addition, we can say ρ = 1 if the collusive bidding will be sustained regardless of ρt . Then it is clear that 0 ≤  ρ < ρ ≤ 1. 6 V ≥ 0 because, otherwise, the firms will not participate in the collusion in the

from their payoff because of the fine after detection.

beginning.

S. Park / Economics Letters 122 (2014) 326–330

Harrington (2008) pointed out three channels through which θ affects the expected duration of collusion.7 The Deviator Amnesty Effect operates anti-collusively, which can be explained by the observation that a more lenient program will reduce mt (ρt ) in (2). The Cartel Amnesty Effect, which is pro-collusive, works though V . Smaller θ (n) makes V in (5) larger, which in turn forces mt (ρt ) to be bigger in (2). The Racing to the Authority Effect may arise in the period in which the detection probability is high. When the collusion breaks down due to high ρ , a more lenient program may destabilize the equilibrium of ‘no-reporting by everybody’ which would have been sustainable with a large θ . The last effect disappears in this model because ‘no-reporting by everybody’ cannot be an equilibrium at all. Due to flexibility of the collusion degree, the condition of collusion collapse is not  ρ < ρt , but ρ < ρt . In addition, ‘self-reporting by everybody’ is the only equilibrium when ρ < ρt since ρ < ρt implies θ < ρt .

The following proposition confirms that maximum leniency is always optimal without any sufficient condition. In other words, without the Racing to the Authority Effect, the Deviator Amnesty Effect dominates the Cartel Amnesty Effect. Simply put, while the former directly appears as θ F in M, the latter operates indirectly through V and happens only when the detection probability is high. The proof is not straightforward because the effect of θ on  ρ and ρ should also be considered. It turns out to be positive, which supports the intuition too. Proposition 1. The optimal leniency program is θ = 0. Proof. Define ρ (θ , α, β), ρ(θ , α, β), V (θ , α, β), M (θ , α, β)), ( given α ∈ [0, 1] and β ∈ [α, 1], as follows:

(1 − δ)(− ρ (θ , α, β)F ) + δ(1 −  ρ (θ , α, β))V (θ , α, β) (6)

(1 − δ)(−ρ(θ , α, β)F ) + δ(1 − ρ(θ , α, β))V (θ , α, β) = (1 − δ)(−θ F )    α m V (θ, α, β) = (1 − δ) − ρF

(7)

n

0



+ δ(1 − ρ)V (θ , α, β) dG +

β

 α

β 1 ∂ V (θ , α, β) (1 − δ)F α dG − β dG = β α ∂θ n 1 − 0 δ(1 − ρ)dG − 1n α δ(1 − ρ)dG dρ(θ , α, β)

∂θ

n



+

α



δ + 1−δ

0

δ(1 − ρ)dG − 1n

β α

β



Suppose now that θ0 < θ∗ . Let ( ρ0 , ρ 0 , V0 , M0 , Φ0 ) and ( ρ∗ , ρ ∗ , V∗ , M∗ .Φ∗ ) be the variables of the corresponding collusion with maximum profit given θ0 and θ ∗ , respectively. By definition,

 ρ0 =  ρ (θ0 , ρ0 , ρ 0 ), V0 = V (θ0 , ρ0 , ρ 0 ),  ρ∗ =  ρ (θ∗ , ρ∗ , ρ ∗ ), V∗ = V (θ∗ , ρ∗ , ρ ∗ ),

ρ 0 = ρ(θ0 , ρ0 , ρ 0 ), M0 = M (θ0 , ρ0 , ρ 0 ), ρ ∗ = ρ(θ∗ , ρ∗ , ρ ∗ ), M∗ = M (θ∗ , ρ∗ , ρ ∗ ).

Define a sequence of ( ρn , ρ n , Vn , Mn ) as follows (n = 1, 2, . . .):

 ρn =  ρ (θ∗ , ρn−1 , ρ n−1 ) ρ n = ρ(θ∗ , ρn−1 , ρ n−1 ) Vn = V (θ∗ , ρn−1 , ρ n−1 ) Mn = M (θ∗ , ρn−1 , ρ n−1 ).

n

0

ρ0





(1 − δ)

+

β

α



∂ ρ (θ , α, β) >0 (10) ∂θ   β ∂ M (θ , α, β) δ ∂ V (θ , α, β) = F+ (1 − ρ) dG(ρ) ∂θ 1 − δ ∂θ α > 0. (11)

(8)

 ρ0

(θ − ρ)F +

+ δ(1 − ρ)V1 dG −

(9)

<

 ρ1



(1 − δ)



0

δ(1 − ρ)dG > 0,



ρ1

+  ρ1 7 In Harrington (2008), the degree of collusion is fixed at m. Therefore, minimizing the expected duration of collusion is equivalent to minimizing the expected buyer’s payment to the colluding firms.





m n



(1 − δ)

δ 1−δ

(1 − ρ)V1

n



Specifically, (8) defines V (θ , α, β), which again is used to determine ( ρ (θ , α, β), ρ(θ , α, β), M (θ , α, β)) through (6), (7) and (9). Then, as long as 1 −

1

Using the same method, we can show

m dG + 0

α

∂ V (θ ,α,β) ∂θ

1 − 0 δ(1 − ρ)dG − n α δ(1 − ρ)dG    β   1  F +δ dG ( 1 − ρ(θ , α, β))   n α    1   1 −δ (1 − ρ(θ , α, β)) dG n β   =  β α δ F + (1−δ) V 1 − 0 δ(1 − ρ)dG − 1n α δ(1 − ρ)dG



 (θ F − ρ F ) α  (1 − ρ)V (θ , α, β) dG. 

δ F + (1−δ) V





β

M (θ, α, β) =

δ (1 − ρ(θ , α, β)) F + (1−δ)

=

Because θ0 < θ∗ , (10) implies that  ρ0 =  ρ (θ0 , ρ0 , ρ 0 ) <  ρ (θ∗ ,  ρ0 , ρ 0 ) =  ρ1 . By the same token, ρ 0 < ρ 1 as well as M0 < M1 can be driven. From (1 − δ)(− ρ1 F ) + δ(1 − ρ1 )V1 = (1 − δ)(m − θ∗ F ) and (1 − δ)(−ρ 1 F ) + δ(1 − ρ 1 )V1 = (1 − δ)(−θ∗ F ),       ρ0 m V1 = (1 − δ) − ρ F + δ(1 − ρ)V1 dG

   1 (1 − δ) (θ − ρ)F

 δ (1 − ρ)V (θ , α, β) − ρ F 1−δ   1 + δ(1 − ρ)V (θ , α, β) dG − (1 − δ)θ (n)F dG

the following holds:

> 0.

Lemma 1. There is no Racing to the Authority Effect.

= (1 − δ)(m − θ F )

329



(1 − δ)θ (n)F dG

− ρF



 + δ(1 − ρ)V1 dG

(θ − ρ)F +

 + δ(1 − ρ)V1 dG −

δ 1−δ

(1 − ρ)V1

n



1

ρ1

− ρF



1

ρ0



 − ρF

 (1 − δ)θ (n)F dG .

(12)

330

S. Park / Economics Letters 122 (2014) 326–330

(12) and V2 = V (θ∗ , ρ1 , ρ 1 ) imply that V1 < V2 .8 Then V1 < V2 again leads us to  ρ1 <  ρ2 , ρ 1 < ρ 2 and M1 < M2 . By repeating the above process, we can conclude that ( ρn , ρ n , Mn ) is an increasing and bounded sequence, which means the limit exists. It is obvious that the limit is ( ρ∗ , ρ ∗ , M∗ ). Therefore M0 < M∗ and ρ 0 < ρ ∗ , which means that Φ0 < Φ∗ . Because the expected payment is larger with a bigger θ , θ = 0 is the optimal policy.  3. Conclusion The purpose of this paper is to analyze the effect of leniency programs on collusion, aligned with more flexibility than the previous literature has assumed. A standard model of repeated procurement auction is used in which the collusion can be detected probabilistically by the public authority and firms’ strategic decisions about whether to self-report or not are a part of the collusion scheme. In particular, the collusion degree, and the agreed winning bid, can depend on the detection probability which can vary over time and the colluders are assumed to select an equilibrium of the self-reporting game to maximize the collusion profit. This paper has shown that among the three different effects pointed out by Harrington (2008), the Racing to the Courthouse Effect disappears and the maximum leniency program is always optimal without any sufficient condition. This result strengthens

8 This comes from that the partial derivative of the right side of (8) with respect to θ is between 0 and 1.

the lesson that the pro-collusive effect of the program is dominated by the anti-collusive one. References Brisset, K., Thomas, L., 2004. Leniency program: a new tool in competition policy to deter cartel activity in procument auctions. Eur. J. Law Econ. 17, 5–19. Buccirossi, P., Spagnolo, G., 2006. Leniency policies and illegal transactions. J. Public Econ. 90, 1281–1297. Harrington, J.E., 2005. Optimal cartel pricing in the presence of an antitrust authority. Internat. Econom. Rev. 46 (1). Harrington, J.E., 2008. Optimal corporate leniency programs. J. Ind. Econ. 56, 215–246. Harrington, J.E., 2013. Corporate leniency programs when firms have private information: the push of prosecution and the pull of pre-emption. J. Ind. Econ. 61 (1), 1–27. Ishibashi, I., Shimizu, D., 2010. Collusive behavior under a leniency program. J. Econ. 101 (2), 169–183. Springer. Motta, M., Polo, M., 2003. Leniency programs and cartel prosecution. Int. J. Ind. Organ. 21, 347–379. Spagnolo, G., 2000a. Optimal leniency programs. In: F.E.E.M. Nota di Lavora, Vol. 42.00. Fondazione ENI enrico Mattei, Milano. Spagnolo, G., 2000b. Self-defeating Antitrust laws: how leniency programs solve Bertrand’s paradox and enforce collusion in auctions. In: F.E.E.M. Nota di Lavora, Vol. 52.2000. Fondazione EnI enrico Mattei, Milano. Spagnolo, G., 2004. Divide et impera: optimal leniency programs. CEPR Discussion papers 4840. Spagnolo, G., 2006. Leniency and Whistleblowers in Antitrust. CEPR Discussion Papers 5794. C.E.P.R. Discussion Papers.