Leniency Programs and Cartel Organization of Multiproduct Firms

Emilie Dargaud; Armel Jacques

doi:10.1515/rle-2018-0060

Article

Leniency Programs and Cartel Organization of Multiproduct Firms

Emilie Dargaud and Armel Jacques

Published/Copyright: January 25, 2020

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From the journal Review of Law & Economics Volume 16 Issue 3

Abstract

When multi-product firms make simultaneous price-fixing agreements in different markets, they may compartmentalize these agreements by having different individuals manage them so as to avoid the contagion of antitrust authority investigations. Leniency programs can overcome this strategy but may also lead to procollusive effects for centralized firms. The introduction of US amnesty plus programs can have different competitive effects, and leniency programs may modify firms’ choice of internal structure.

Keywords: collusion; antitrust policy; leniency programs; multimarket contact; organizational form

JEL Classification: K42; L22; L41

Acknowledgements

We received useful feedback during conferences or seminars at the Association Française de Sciences Economiques (Lyon 2014), European Association for Research in Industrial Economics (Lisbon 2016), external seminar in Paris Ouest Nanterre (Paris 2016), International Industrial Organization Conference (Boston 2017) and Société Canadienne de Sciences Economiques (Ottawa 2017). We thank participants for helpful comments and discussion. We thank the anonymous reviewer and editor for their comments and suggestions. We have benefited from discussions with Richard Ruble. This article supersedes an unpublished working paper Dargaud and Jacques (2015a). The usual disclaimer applies.

Appendix A: Computations related to sustainability conditions

We set ρ‾=1−ρ to abridge mathematical expressions.

Threshold values of fines under the different scenarios are reported in the Tables 1 and 2.

Table 1:

Threshold values of fines – Scenarios No leniency, SL-S and SL-L.

	No leniency	SL-S	SL-L
F₂	1−δρ‾πicU2−πicM−δρ‾ρπ˜ic1−δρ‾ρ	1−δρ‾πicU2−πicM−δρ‾ρπ˜ic1−δρ‾ρ	1−δρ‾πicU2−πicM−δρ‾ρπ˜ic121−δ−δρρ‾ρ
[3mm] F₃	πicU2−πicMρ‾ρ	πicU2−πicMρ‾ρ	πicU2−πicM12ρ‾ρ
[3mm] FUsim	δρ‾2−12δρ‾2ρ2−ρπicU	2δρ‾2−12ρ2−ρπicU	2δρ‾2−13−ρρπicU
[3mm] F_Ms	2δρ‾2−1δρ‾2ρπicM	2δρ‾2−1ρπicM	2δρ‾2−1ρπicM
[3mm] F˜	2δρ‾−1δρρ‾π˜ic	2δρ‾−1ρπ˜ic	2δρ‾−1ρπ˜ic
[3mm] F_report	⊘	⊘	⊘
[3mm] F_Mc	1−δρ‾2δρ‾2−1πicM+δρρ‾π˜ic1−δρ‾2δρρ‾	1−δρ‾2δρ‾2−1πicM+δρ‾ρπ˜ic1−δρ‾2ρ	1−δρ‾2δρ‾2−1πicM+δρ‾ρπ˜ic1−δρ‾2ρ
[4mm] F_Useq	−1+3δ−2δρ−2δ2ρ‾21−δρ‾2δρπ˜ic	3δ−2δρ−2δ21−ρ2−11−δ+2δρρπ˜ic	3δ−2δρ−2δ21−ρ2−11−δ+2δρρπ˜ic
[4mm] F₁	1−δρ‾2πicU−1−δρ‾21−δ+2δρπ˜ic3−2ρ−δρ+3ρ−6δρ‾+3δ2ρ‾2ρ	1−δρ‾2πicU−1−δρ‾21−δ+2δρπ˜ic3−2ρ−δρ+3ρ−6δρ‾+3δ2ρ‾2ρ	1−δρ‾2πicU−1−δρ‾21−δ+2δρπ˜ic1−δρ‾23−ρ−1−δρ‾21−δ+2δρρ

Table 2:

Threshold values of fines -Scenarios AP-S + and AP-L +.

	AP-S+	AP-L+
F₂	1−δρ‾πicU2−πicM−δρ‾ρπ˜ic1−δρ‾ρ	1−δρ‾πicU2−πicM−δρ‾ρπ˜ic121−δρ‾τ−δρρ‾ρ
[3mm] F₃	πicU2−πicM1−12τρ‾ρ	⊘
[3mm] FUsim	2δρ‾2−12ρ2−ρπicU	2δρ‾2−12+τ−ρτρπicU
[3mm] F_Ms	2δρ‾2−11+12ρ‾τρπicM	2δρ‾2−11+ρ‾12τρπicM
[3mm] F˜	2δρ‾−1ρπ˜ic	2δρ‾−1ρπ˜ic
[3mm] F_report	δπ˜ic1−δρ‾1−τ+δρ	δπ˜ic1−δρ‾1−τ+δρ
[3mm] F_Mc	1−δρ‾2δρ‾2−1πicM+δρ‾ρπ˜ic1−δρ‾2ρ	1−δρ‾2δρ‾2−1πicM+δρ‾ρπ˜ic1−δρ‾2ρ
[4mm] F_Useq	3δ−2δρ−2δ21−ρ2−11−δ+2δρρπ˜ic	3δ−2δρ−2δ21−ρ2−11−δ+2δρρπ˜ic
[3mm] F₁	1−δρ‾2πicU−1−δρ‾21−δ+2δρπ˜ic3−2ρ−δρ+3ρ−6δρ‾+3δ2ρ‾2ρ	1−δρ‾2πicU−1−δρ‾21−δ+2δρπ˜ic1−δρ‾22+τ−ρτ−1−δρ‾21−δ+2δρρ

Appendix B: Computations related to imperfect compartmentalization (Section 3.4)

Without leniency and considering µ₃ > 0 expected profits and sustainability conditions are reported in the Table 3. Note that ρ‾≡1−ρ.

Table 3:

Imperfect compartmentalization.

Strategy	Expected profit	Sustainability conditions
M_s	ΠiMs=πicM−ρF−ρ‾ρμ3F1−δρ‾2	FMs=2δρ‾2−1δρ‾21+ρ‾μ3ρπicM
[3mm] M_c	ΠiMc=πicM−ρF−ρ‾ρμ3F+δρ‾ρ1−μ3Π˜i1−δρ‾2	FMc=1−δρ‾2δρ‾2−1πicM+δρ‾ρ1−μ3π˜icρ1−μ3+1−δρ‾ρ‾1+ρ‾μ3ρ‾δρ
[3mm]		F˜=2δρ‾−1δρρ‾π˜ic
[3mm] Seq	ΠiSeq=1−δ+2δρπ˜ic−ρF1−δρ‾2	F˜

Scenario L – Expression of FReportμ3>0:

1−μ3δΠ˜i−μ3F<0⇔FReportμ3>0=δ1−μ3π˜icδρ1−μ3+1−δρ‾μ3<F⇔δπ˜ic−ρF1−δρ‾F+δπ˜ic−ρF<μ3

Appendix C: Graphical representation for decentralized firms

Figure 7 displays collusive strategies of decentralized firms considering µ₃ = 0: n: no collusion; s: strategy Ms; c: strategy Mc. The first letter is the strategy without leniency, the second one is the strategy under scenarios S and L and the last one is the strategy under scenarios S + and L +. We plot the border lines without leniency, with simple leniency (-SL) and with amnesty plus (-AP).

Figure 7:

Impact of SL and AP on collusive strategies for decentralized firms.

If we focus on the first two letters we identify the following shifts c→s, s→n and c→n: SL can deter some cartel agreements (s→n and c→n) and may reduce the lifetime of others (c→s). If we focus now on the last two letters we observe that AP strengthens efficiency of leniency (s→n, c→n and c→s).

Appendix D – Discrepancies between CEO and managers and internal audits

Robustness of previous results Concerning the Mc strategy, each CEO has to decide between applying for leniency (with an immediate decrease in fine of 1−τF) or continuing to collude in the second market (expected profit Π˜i). A CEO will apply for leniency if: 1−τF≥δΠ˜i⇔F≥Freport.

If a CEO does not intend to request leniency then managers of each division has no reason to do so because they can keep colluding if they don’t cheat and obtain δΠ˜i.^[45] In the opposite case manager has an interest to cooperate if he believes that the other manager also does it. If he believes that the other manager is not willing to cooperate, then the profit of his own division is 0−12σF if he collaborates and 1−σ2δΠ˜i−σ1−σF−12σ2F in the other case. Consequently a manager desires to pass on hard evidence to his CEO if:

1−σ2δΠ˜i−σ1−σF−12σ2F≤0−12σF⇔δΠ˜i≤12σ1−σF

If σ>2−2τ3−2τ, then 1−τF≥δΠ˜i implies 12σ1−σF≥δΠ˜i. If σ>2−2τ3−2τ managers always cooperate when CEO wish to apply for leniency.

Ineffective audits If F∈Freport,Fcoop expected profit is:

ΠiMc=πicM−1+1−ρ1−12σστρF+δ1−ρρ1−σ2Π˜i1−δ1−ρ2

and:

∂ΠiMc∂σ(.)=−1−στ1−ρρF−2δ1−ρρ1−σΠ˜i1−δ1−ρ2<0

Costly audits If k = 0 firms playing the Ms strategy systematically apply for leniency once the first cartel has been detected. If k > 0 and the other firm does not apply for leniency then firm applies only if k<1−τF . But if the other firm applies for leniency, firm applies as well if:

−F<−12F+121−τF−k⇔k<122−τF

Under the Mc strategy and facing the other firm not applying for leniency a CEO launches an internal audit and applies for leniency if:

1−τF−k≥δΠ˜i⇔k≤1−δ(1−ρ)1−τ+δρF−δπ˜ic1−δ(1−ρ)⇔F≥δπ˜ic+1−δ(1−ρ)k1−δ(1−ρ)1−τ+δρ≡Freport

An higher value of k yields to an increased value of F_report and makes the Mc strategy easier to sustain.

It is straightforward to see that if a firm benefits from applying for leniency then the other firm benefits too.

1−δ(1−ρ)1−τ+δρF−δπ˜ic1−δ(1−ρ)≤122−τF⇔2δπ˜ic−ρF≥−1−δ(1−ρ)τF

This inequality is always checked.

Appendix E – Imperfect detection in the centralization case (μ2<1)

Note that ρ‾≡1−ρ. F_MsF_Mc and F˜ are the same that in appendix A.

About the Uc strategy- Scenario AP-L+ If firms playing the Uc strategy do not choose to cooperate with the antitrust authority at stage 3, firms can expect a global pay-off: 1−μ2δΠ˜i−μ2F, in the opposite case a firm obtains a reduced fine for the first cartel of 1−τF and avoids the second fine (if the other firm does not cooperate). Firms apply for leniency if:

1−τF>1−μ2δΠ˜i−μ2F⇔F>1−μ2δπ˜ic1−δ(1−ρ)1−τ+μ2+1−μ2δρ

Threshold values of fines under the different scenarios are reported in the Tables 4 and 5.

Table 4:

Threshold values of fines – Scenarios No leniency, SL-S and SL-L.

	No leniency	SL-S	SL-L
F_2a	1−δρ‾πicU2−πicM−μ2δρ‾ρπ˜ic1−δμ2ρ‾ρ	1−δρ‾πicU2−πicM−μ2δρ‾ρπ˜ic1−δμ2ρ‾ρ	1−δρ‾πicU2−πicM−μ2δρ‾ρπ˜ic1−δμ2ρ‾ρ
[4mm] F_2b	⊘	⊘	1−δρ‾πicU2−πicM−δρ‾ρπ˜ic121−δ−δρρ‾ρ
[4mm] F₃	πicU2−πicMρ‾μ2ρ	πicU2−πicMρ‾μ2ρ	πicU2−πicM12ρ‾ρ
[4mm] F_Us	δρ‾2−12δρ‾21+ρ‾μ2ρπicU	δρ‾2−121+ρ‾μ2ρπicU	2δρ‾2−13−ρρπicU
[4mm] F_Uc	1−δρ‾δρ‾2−12πicU+δρρ‾1−μ2π˜icρ1−μ2+1−ρ−δρ‾21+ρ‾μ2δρ‾ρ	1−δρ‾δρ‾2−12πicU+δρρ‾1−μ2π˜icδρρ‾1−μ2+1−δρ‾1+ρ‾μ2ρ	1−δρ‾δρ‾2−12πicU+δρρ‾1−μ2π˜icδρρ‾1−μ2+1−δρ‾1+ρ‾μ2ρ
[4mm] F˜	2δρ‾−1δρρ‾π˜ic	2δρ‾−1ρπ˜ic	2δρ‾−1ρπ˜ic
[4mm] F_report	⊘	⊘	δ1−μ2π˜icδρ1−μ2+1−δρ‾μ2

Table 5:

Threshold values of fines – Scenarios AP-S + and AP-L +.

	AP-S+	AP-L+
F_2a	1−δρ‾πicU2−πicM−μ2δρ‾ρπ˜ic1−δμ2ρ‾ρ	1−δρ‾πicU2−πicM−μ2δρ‾ρπ˜ic1−δμ2ρ‾ρ
[3mm] F_2b	⊘	1−δρ‾πicU2−πicM−δρ‾ρπ˜ic121−δρ‾τ−δρρ‾ρ
[3mm] F₃	πicU−2πicM2−τρ‾μ2ρ	⊘
[3mm] F_Us	2δρ‾2−12−τρ‾μ2+2+τ−ρτρπicU	2δ1−ρ2−12+τ−ρτρπicU
[3mm] F_Uc	1−δρ‾δρ‾2−12πicU+δρρ‾1−μ2π˜icδρρ‾1−μ2+1−δρ‾1+ρ‾μ2ρ	1−δρ‾δρ‾2−12πicU+δρρ‾1−μ2π˜icδρρ‾1−μ2+1−δρ‾1+ρ‾μ2ρ
[3mm] F_report	δπ˜ic1−δρ‾1−τ+δρ	1−μ2δπ˜ic1−δρ‾1−τ+μ2+1−μ2δρ

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Published Online: 2020-01-25

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https://doi.org/10.1515/rle-2018-0060

Keywords for this article

collusion; antitrust policy; leniency programs; multimarket contact; organizational form