Using Network Theory to Detect Dominant Cartel Firms

Journal of Competition Law & Economics, 12(3), 541–555 doi:10.1093/joclec/nhw016 Advance Access publication 20 September 2016

USING NETWORK THEORY TO DETECT DOMINANT CARTEL FIRMS

Pilar Grau-Carles* & Miguel Cuerdo-Mir† Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021

ABSTRACT Despite multiple applications of network theory in different fields of social and legal sciences in general, the possibility of applying this theory to the economic analysis of the antitrust law and, more specifically, to the study of cartels has not yet been considered. Nevertheless, the study of cartels as networks can advance some general elements and measurements that can help the detection and elimination of these organizational forms that cause evident harm to general well-being. This is the first time that the approach of network theory has been used to analyze cartels. This article uses a set of classical measures such as clustering and centrality measures, taken from network theory, and applies them to a specific case of a cartel sanctioned as such by the European Commission. This approach has enabled us to quantify some characteristic elements of the cartel, such as, for instance, a remarkable asymmetry between operators (nodes in the network), its different degree of influence (study of links), as well as the critical importance of some operators versus other cartelized agents, such that their elimination from the organization would not enable them to create their own cartel. This finding warrants reconsidering the antitrust policy based on leniency programs. JEL: K21; D85; L22

I. INTRODUCTION Antitrust law considers cartel formation to be the most serious infraction. A cartel is an illegal, and therefore secret, agreement among competitors in the same market that is generally complex and continued over time, the pur- pose of which is to impose monopoly-like conditions on the market in question, resulting in effects on quantity and price equilibrium, in detriment of

* Universidad Rey Juan Carlos, Campus Vicálvaro. Facultad de Ciencias Jurídicas y Sociales. Departamento Economía Aplicada I. Paseo Artilleros s/n 28032 Madrid, Spain. Email: pilar. [email protected]. † Universidad Rey Juan Carlos, Campus Vicálvaro. Facultad de Ciencias Jurídicas y Sociales. Departamento Economía Aplicada I. Paseo Artilleros s/n 28032 Madrid, Spain. Email: miguel. [email protected]. This article was supported by grants from the Research Project, “La Potestad Sancionadora de los Organismos Reguladores’ (Ref. DER 2011-22549, Spanish Education Ministry) and “Gobierno Corporativo, Mercados de Capitales y Crisis Financiera” (Ref. ECO2012-32554, Spanish Economic Ministry).

© The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] 542 Journal of Competition Law & Economics general wellbeing. This is because there is no longer competition among them.1 Different cartel organizations might be more suitable than others to apply entry barriers or fulﬁl the agreements on which they are based. Also critical is the weight and position of each cartelist in the organization, often determin- ing its very existence. If we assume that there has to be one operator or organization with greater responsibility in the cartel, then its elimination

could be expected to put an end to the cartel itself. According to this reason- Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 ing, the organization of cartels can determine different levels of centrality and different role for each of the members. It is clear that a study of centrality structure could show how decisions are made inside the cartel, which could differ depending on the type of organization. If we consider cartels as organizations, they can be viewed as networks. These networks change the rate of substitution among competitors into a cooperative one. Somehow, cartelists turn each other into complementary agents. Cartelists do not already face a given price alone and in line with their costs. Extra revenue arises as all of them capture an externality from this cooperative behavior. What type of network is required for cartelization? For instance, a new node in the network will have an effect on other nodes in the shape of the marginal externality (the network effect), but also it will increase competition among nodes to get extra profits (the competitive effect). In case of a cartel, an increase in the size of the network leads to a problem of distribution with a monopoly price, although the cartel can be more effective (capture more of the externality) if it controls a larger market share. There will also be limited compatibility, determined by the marginal contribution of the last operator who enters the cartel to make the monopoly price effective. To be able to capture these extra profits, one interesting aspect is the study of the cartel’s degree of cohesion and stability. Sometimes, the role played by certain agents is explained by their market position, which makes them central agents in the cartel itself. Without them, cartels can be said to lose economic significance, or at least the ability to be successful. From this perspective, the study of some measures taken from network theory enables us to identify the cohesion and efficiency of these networks, focusing on the nodes that are network effective, resulting in a positive difference in relation with the competitive effect that they generate. Frank Schweitzer, Giorgio Fagiolo, Didier Sornette, Fernando Vega-Redondo, Alessandro Vespignani, and Douglas White underline the need to study economic networks through a better understanding of these frameworks over time, with a closer analysis of the role, function, and influence of each agent

1 Richard A. Posner, ANTITRUST LAW:AN ECONOMIC PERSPECTIVE (Univ. Chicago Press 2d ed. 2001). Using Network Theory to Detect Dominant Cartel Firms 543 in the cartel organization.2 In social and economic networks, other research- ers3 have shown that there is a selection inside the network of the members that obtain higher profits, who become leaders and make the network more hierarchical. This finding would mean that sustainable cooperation depends critically on these leaders, creating asymmetric collaboration structures.4 This question is connected to the traditional practice of antitrust law in which different obligations are defined for each operator, depending on its

importance in the market. So it has to be known which of them are critical Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 for the survival of the network and which are not, at least in terms of ability to affect effective competition. The above perspective could be relevant for reviewing all competition policies based on the idea of a leniency program related to the detection of cartels. The idea of reviewing leniency program using different methodologies is not new. For instance, by means of game theory several studies have tried to evaluate the impact of such leniency programs.5 To a certain extent, it is clear that leniency programs should not only consider when the cartelists decide to collaborate and to what extent. Indeed, it is not so peculiar that the main market operator, the most active cartel member, would be totally exempted from the fine. This leniency program result creates an incentive for those who are capable of better and more directly controlling the cartel’s dynamics, who report the cartel’s existence when con- venient. These agents would be able to weaken their competitors, avoiding administrative sanctions and generating an administrative cost for their competitors, especially those with financial difficulties.6 In this regard, network theory can be used to study cartels, allowing, on one hand, to find the most important or central nodes within it and, on the other, measuring the network cohesion, and studying the possibilities of network partitioning. Regarding the use of network theory in market cartelization, this article studies a case file, using a set of measures derived from network theory to

2 Frank Schweitzer, Giorgio Fagiolo, Didier Sornette, Fernando Vega-Redondo, Alessandro Vespignani & Douglas R. White, Economic Networks: The New Challenges, 325 SCIENCE 593422 (2009). 3 Martín G. Zimmermann & Víctor M. Eguíluz, Cooperation, Social Networks, and the Emergent of Leadership in a Prisoner’s Dilemma with Adaptive Local Interactions,72PHYSICAL REV. E 056118 (2005). 4 See Sanjeev Goyal & Sumit Joshi, Networks of Collaboration in Oligopoly (Tingergen Institute Discussion Paper, Paper No. TI 2000-092/1, 2000). 5 Nathan H. Miller, Strategic Leniency and Cartel Enforcement,99AM.ECON.REV. 750 (2009); see also Cécile Aubert, Patrick Rey & William E. Kovacic, The Impact of Leniency and Whistle- Blowing Programs on Cartels,24INT’L J. INDUS.ORG. 1241 (2006). 6 Miguel Cuerdo-Mir & Pilar Grau-Carles, Networks, Cartels, and Antitrust Policy, (unpublished manuscript) (Oct. 30, 2014), http://dx.doi.org/10.2139/ssrn.2518988; see also Pilar Grau- Carles & Miguel Cuerdo-Mir, Stability and Cohesion of Cartels Through Network Theory (URJC Working Paper, 2014), http://hdl.handle.net/10115/12272. 544 Journal of Competition Law & Economics study this ﬁle from a novel approach. The object of our analysis is the vitamin cartel, European Commission case ﬁle COMP/E-1/37.512—Vitamins.7 The results of the study can be used as a basis for subsequent approaches more appropriate for cartel formation and organization. It seems that these new approaches could be increasingly useful, not only for better development of an effective competition policy against such pernicious agreements, but also as a new instrument for their detection, prosecution, and sanction.

The structure of this article is as follows: Part II contains the information Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 and the resulting network obtained by the study of the agreements of the cartelized companies explained in the case ﬁle. Part III presents the characterization of the network vertex and edges by means of centrality measures. Part IV studies the network cohesion by means of connectivity and clustering properties, enabling an analysis of the role played by each undertaking inside the cartel. Part V compares the cartel network with a random graph model.

II. DATA The information used for studying the structure of a cartel network comes from European Commission Decision of November 21, 2001, “Vitamins,” relating to a proceeding pursuant to Article 81 of the EC Treaty and Article 53 of the EEA Agreement.8 Thirteen companies are involved, with market shares distributed around the world for 12 different products and markets related to vitamins. In this Commission Decision, all the members of the cartel are described, as are the vitamin markets affected by the agreement. Summarizing, the agreements were intended to fix prices and to agree how to share the world market for each vitamin. Obviously, the main part of this administrative decision is about how this cartel was detected—the firms who reported the existence of the cartel agreements—and which were the agreements made. A fundamental principle of the agreement is the historic existence of distribution of market shares, on a fixed date that cartel members decide to respect as a basis for the agreement, for different products, in this case vitamins; in other words, each product has a cartel, but with a common organization, so that each product is produced by a variable number of firms, depending on the vitamins in question. The aforementioned agreements took place from 1989 to 1999. After 10 years, one of the companies decided to report its existence. Over this period there was an increasing number of growing inlets in the industry, despite which there were attempts to imple- ment the cartel agreements with their historical quotas. Social network analysis can be used to explore interactions among different network nodes and to analyze the economic phenomena constrained by

7 Commission Decision of 21 November 2001 Relating to a Proceeding Pursuant to Article 81 of the EC Treaty and Article 53 of the EEA Agreement (Case COMP/E-1/37.512 — Vitamins), 2001 O.J. (C 2001) 3695. 8 Id. Using Network Theory to Detect Dominant Cartel Firms 545 the structure.9 To study this cartel as a network it is necessary to focus on the essential elements defined for any network: nodes and links. In this case file, the nodes represent companies that appear as members of this cartel. The links between nodes can be defined by some type of price-fixing or market-sharing agreement. The studied network presents 13 nodes or companies named: F. Hoffmann-La Roche AG (Switzerland), BASF AG (Germany), Rhone-Poulenc, SA (France), Solvay Pharmaceuticals BV

(Netherlands), Takeda Chemical Industries Ltd (Japan), Eisai Co Ltd Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 (Japan), Daiichi Pharmaceutical Co Ltd (Germany), Lonza AG (Germany), Merck KgaA (Germany) Kongo Chemical Co Ltd (Japan), Sumitomo Chemical Co Ltd (Japan), Sumika Fine Chemicals Ltd (Japan) and Tanabe Saiyaku Co Ltd (Japan) and 34 links. Formally, we deﬁne the network graph by G = {N,E}, where N is the number of nodes, N = {n1, n2,...n13}, and E is the number of links or edges, E = {e1, e2,...e34}. The links between the nodes are shown in the graphical representation of the network (Figure 1).

III. NETWORK CHARACTERIZATION This Part analyses the structure of this cartel network. The aim is to identify the main features that help to characterize the cartel structure, as well as its characteristics, especially those related to the node characterization and those that allows capturing the “importance” of the node. We therefore begin by

EISAI RHÔNE

SOLVAY

SUMIMOTO BASF

LONZA ROCHE DAIICHI

TANABE MERK TAKEDA

SUMIKA

KONGO

Figure 1. Graphical representation of the vitamin cartel network

9 Stanley Wasserman & Katherine Faust, 8 SOCIAL NETWORK ANALYSIS:METHODS AND APPLICATIONS (Cambridge Univ. Press 1994). 546 Journal of Competition Law & Economics analyzing the centrality position of some operators, which could be relevant for explaining the main factors of stability and duration of the cartel. This requires a calculation of the most common measures of this centrality. Centrality measures might be used to assess the importance of each node. In network theory, centrality refers to a group of measures that aim to quantify or measure the importance of a particular node within the network. In our case, it should be interpreted as the measurement of the importance of

each of the companies in the cartel. We consider four measures of centrality: Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 degree, eigenvalue centrality, closeness, and betweenness.

A. Degree The degree is the most basic measure in the study of a network and the traditional version measures the number of nodes that are connected to the node under consideration.10 This measure can be formalized for a focal node v as:

dxv =()∑ vj, 1 jN∈ where j represents all other nodes, N is the total number of nodes, and x is the adjacency matrix, in which cell xvj is defined as 1 if node v is connected to node j, and 0 otherwise. The idea is that the node or company that has more links will be in a better position than the rest, as it has better connection and can reach more resources of the network than companies with less links. Thus, the degree allows us to measure the level of influence of every node. In the case of a cartel, this influence involves knowing which are the companies with the greatest influence in the network, because they are involved in a fuller flow or exchange of information, as required to reach agreements on prices and the distribution of markets. In other words, degree shows which nodes are more likely to influence others. It could be said that its presence makes the network more effective when they decide to operate on markets as a cartel. The results of this measure are in the first column of Table 1.Accordingto the Figure 1 and this table, Roche company has connections with all the nodes, with a degree of 12. It is followed by firm BASF, which has 10 connections. Depending on this measure, both firms should be considered as those which have the greatest influence. It is also shown that the lowest number of connections is three. This minimum degree of connection means that, for any differentiated product in this cartel, the minimum number of companies that agree on prices or market shares is three. Table 1 also shows the statistics for the distribution of this measure. The average is 5.2, a high result considering

10 Linton C. Freeman, Centrality in Social Networks I: Conceptual Clariﬁcation,1SOC. NETWORKS 215 (1979). Using Network Theory to Detect Dominant Cartel Firms 547

Table 1. Measures of network centrality

Firm Degree Eigenvector centralities Closeness Betweenness

ROCHE 12 1.00 0.08 26.17 BASF 10 0.92 0.07 11.17 RHÔNE 5 0.50 0.05 1.00 TAKEDA 6 0.58 0.06 3.33 EISAI 3 0.38 0.05 0.00

DAIICHI 4 0.47 0.05 0.33 Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 KONGO 3 0.30 0.05 0.00 SUMIKA 3 0.30 0.05 0.00 MERK 6 0.68 0.06 1.00 SOLVAY 3 0.38 0.05 0.00 LONZA 5 0.60 0.05 0.00 SUMIMOTO 5 0.60 0.05 0.00 TANABE 12 1.00 0.08 26.17 Mean 5.42 0.56 0.06 3.58 Standard Deviation 2.87 0.22 0.01 7.80 Maximum 12.00 1.00 0.08 26.17 Minimum 3.00 0.30 0.05 0.00 that the network only has 13 nodes. The variability measured by the standard deviation (2.83) is also quite high, showing that the degree of influence of each of these companies, measured by number of links, is heterogeneous. One way to examine whether variability, in terms of the importance of each firm, is large or small is to calculate the coefficient of variation, as the standard deviation divided by the mean and multiplied by 100, where we obtain a coefficient of 54.14, which is quite high. However, digging deeper into these differences, we see that the importance of a node depends not only on having many connections with its neighbors (that is, a high of degree centrality), but also because its neighbors are also important.

B. Eigenvalue Centrality The importance of the neighbors of each node can be quantiﬁed by eigenvector centrality. This measure aims to ﬁnd the most central nodes in the network overall, focusing less on local patterns. Eigenvalue centrality is calculated by assessing how well connected an individual is to the parts of the network with the greatest connectivity. So individuals with high eigenvector scores have many connections, and their connections have many connections, and so on. To calculate this score we can use the following equation:11

cnEi ()=α ∑ cuEi (),2 () {}∈un, E

11 Phillip Bonacich, Power and Centrality: A Family of Measures,92AM.J.SOC. 1170 (1987). 548 Journal of Competition Law & Economics

T where the vector cEi=(ccN Ei (1, ) … , Ei ( n )) is the solution to the eigenvalue −1 problem, knowing that AcEi= α c Ei, where A is the adjacency matrix for the network graph G. The results of this measure are also shown in the second column of Table 1. Again, Roche and BASF are more central, while nodes Kongo and Sumika have less inﬂuence, showing that these companies are more peripheral. The distribution statistics also show that there is variability (standard deviation 0.1) with regard to the average (0.26). In this case,

a lower variability is conﬁrmed, with a coefﬁcient of variation of 39.9. Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 Degree only considers the immediate links that a node has with other nearby nodes, so that a node can be linked to a large number of nodes but these nodes might be disconnected from the network as a whole; the initial node might have a high degree of centrality, but it could be very local.

C. Closeness Therefore, the previous analysis should be completed with the closeness measure,12 which takes into account the distance of a node to all the rest of the network. Closeness relies on the identiﬁcation of the length of the path from a node to all the rest of the nodes and is deﬁned as the inverse of the total length:

⎡ N ⎤−1 ⎢ ⎥ Cvc ()=∑ dujv (,, ) () 3 ⎣⎢ ⎦⎥ uN∈ where d(u,v) is the geodesic distance between the vertices uv, ∈ N. We can say that the higher the measurement, the greater the influence on the other nodes. According to the results of the Table 1, Roche has the highest degree of centrality according to this measure, so Roche and BASF are the most influential, and Eisai, Kongo, Sumika, and Solvay are the less influential. That is to say, it supports the characterization obtained by means of degree, but with some shades of interest. For example, the distribution of this closeness shows less dispersion than the measure of degree.

D. Betweenness The last measure of centrality that we are going to present here is betweenness,13 which quantiﬁes the number of times that a node operates as a bridge, as the shortest way between other two nodes. Betweenness centrality is measured with

12 Freeman, supra note 10. 13 Id. Using Network Theory to Detect Dominant Cartel Firms 549

gstv(), CivB ()= ∑ ,4() stvV≠≠ ∈ gs(), t where g(s,t|v) is the number of binary shortest paths between s and t that pass through v, and g(s,t|v) is the total number of shortest paths between s and t, regardless whether or not they pass through vi. In the last column of the Table 1, Roche and BASF are again those companies that present the greatest degree of betweenness. It might be thought that these companies have Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 greater power in the cartel organization. There is also a group of companies that do not act as bridges for any links, so their degree of betweenness is zero. That is why dispersion is large, with a coefﬁcient of variation of 231.4, conﬁrming again that Roche and BASF are central to the achievement of the cartel, as they act as a bridge to the other companies.

IV. NETWORK COHESION One property of a network that requires exploring in this case is the distance between nodes. In our case, these nodes are individual ﬁrms that participate in the cartel. When the distances are large, the information can take a long time to propagate among these nodes—cartel members—and the effective- ness of the agreements can diminish. This fact would make the continuity of the cartel uncertain, resulting in a more vulnerable and unstable agreement. In some nodes, although the links are technically attainable, the exchange with others is likely to be costly. On the other hand, the companies that are closer to all the rest can exercise stronger power than those that are more remote. Indeed, multiple connections between companies can indicate a stronger connection among them than when there is only one connection. The analysis of the cohesion of the network shows which of the network companies tend to be more close to each other. There are several ways to deﬁne cohesion. We examine three: subgraphs, connectivity, and clustering.

A. Subgraphs The canonical representation of a subgraph is a clique. Cliques are complete subgraphs, showing all the nodes of the subgraph that are connected by edges. Table 2 shows the maximum clique census of the network. These cliques are subgroups of companies with information transmission that is autonomous; that is to say, information transmission among companies of the same clique that ﬂows among them and does not need the existence of other companies or cliques to work. On the other hand, Roche is the only cartel member that appears in all the maximum cliques. 550 Journal of Competition Law & Economics

Table 2. Maximum cliques census

Max. clique size Companies

Size 6 TANABE ROCHE SUMIMOTO LONZA MERK BASF Size 4 TAKEDA ROCHE BASF DAIICHI TAKEDA ROCHE BASF MERK TAKEDA ROCHE KONGO SUMIKA RHÔNE ROCHE BASF EISAI

RHÔNE ROCHE BASF DAIICHI Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 RHÔNE ROCHE BASF SOLVAY

B. Connectivity Many networks of different nature show non-homogenous connected structure, with groups of nodes that are more densely connected among them than with the rest of the network. This kind of structure has been found in networks such as social networks14 or flight transportation network,15 among others. A way to measure the cohesion of the network comes from the possibility of graph partitioning, thus graph division is a way of finding subsets of edges that show a special form of cohesiveness. In this sense, group or community identification is a useful tool because nodes that belong to the same community usually share several characteristics and dynamics. Furthermore, both the number and the characteristics of the groups provide information about the network and allow understanding of the organization and possible evolution of the network. In addition, the subsets show nodes that are well connected among them and indicate a higher separation from the rest of the edges of the network. Using the technical methodology of agglomerative hierarchical clustering,16 we find three different communities in the network, as shown in Figure 2. The dendogram is another way to observe the hierarchical partitioning. In Figure 3, the dendogram shows the asymmetry of the node groups that can be formed in the cartel. The clustering shows the extent to which the network is more or less compact, as some nodes are more strategically positioned than others. This measure of clustering reveals the unequal importance between nodes, showing some nodes without which the network makes no sense, whereas the presence or absence of other nodes has no effect on the network’s structure.

14 Alex Arenas, Leon Danon, Albert Diaz-Guilera, Pablo M. Gleiser & Roger Guimer, Community Analysis in Social Networks,38EUR.PHYSICAL J. B-CONDENSED MATTER & COMPLEX SYS. 373 (2004). 15 Roger Guimera, S. Mossa, A. Turtschi & L. A. N. Amaral, The Worldwide Air Transportation Network: Anomalous Centrality, Community Structure, and Cities’ Global Roles, 102 PROCEEDINGS NAT’L ACAD.SCI. 7794 (2005). 16 Aaron Clauset, Mark E.J. Newman & Cristopher Moore, Finding Community Structure in Very Large Networks,70PHYSICAL REV. E 066111 (2004). Using Network Theory to Detect Dominant Cartel Firms 551

RHÔNE EISAI SOLVAY

BASF TANABE DAIICHI

ROCHE LONZA Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021

SUMIMOTO MERK TAKEDA

SUMIKA

KONGO

Figure 2. Partition of the network using fast agglomerative hierarchical clustering Height 024681012 EISAI BASF MERK LONZA ROCHE RHÔNE DAIICHI KONGO SUMIKA TANABE SOLVAY TAKEDA SUMIMOTO

Figure 3. Dendogram showing agglomerative hierarchical clustering

C. Clustering Finally, another important property of social networks cohesion is clustering, Duncan Watts and Steven Strogatz show that in real-word networks the probability of a link between two nodes is much greater if the two actors in question have more mutual contacts and they define a clustering coefficient, C, which is the probability that two acquaintances of a randomly chosen per- son are themselves acquainted.17 They showed for a variety of networks that this clustering coefficient took values anywhere from a few percent to 40 or

17 Duncan J. Watts & Steven H. Strogatz, Collective Dynamics of ‘Small-World’ Networks, 393 NATURE 440, (1998). 552 Journal of Competition Law & Economics

50 percent. Other studies have since shown similar results for other networks.18 In many cases, this clustering makes the probability of contact between people greater if they have a common friend than if they do not. In the network under study, the global clustering coefficient is 0.58. This value is obtained calculating the number of triangles in the entire network and dividing it by the number of possible triangles. In this cartel network, more than half of the edges are connected in this way. Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 V. NETWORK INTERFERENCE Once the network has been represented and its centrality characterized, the question must be asked whether the results obtained would be different when the organization and functioning of the cartel is not based on the leading role of one of the cartelized companies. In other words, what would be the results of a cartel network with the same number of companies or nodes and the same number of links or agreements, but distributed randomly. One way of answering the question is by means of random networks. The random network concept was introduced by Paul Erdös and Alfréd Rényi and is defined as a network comprised of a specific number of nodes and links which assigns a connection between nodes with a determined probability.19 This enables the creation of random networks with the same number of nodes as the network studied, but in a way in which the connections between nodes are distributed randomly. If the actual network studied were random, the measures of the simulated and actual networks would coincide. However, the non-coincidence is an indication that the network is in some way unique. To contrast this, we generated 5,000 Erdös-Rényi type random networks, distributed randomly. With each generated network, we calculated the maximum values of degree, betweenness, closeness and clustering. Figure 4 shows the results on a frequency graph and enables a comparison of the maximum values we obtained using the actual network, which are marked with a black dot on the graph. It can be observed, for example, that for the degree measure, only one of networks reaches a value of 12, which is that obtained by the cartel network. In the case of the clustering coefficient, only 10 of the 5,000 networks reached a value equal to or higher than 0.58, for the maximum value of closeness only one network reached a value above 0.08 and, finally, no network reached the value of 26.17 obtained by the actual network. As a result, we can conclude that the network resulting from the modeliza- tion of the vitamin cartel shows centrality and clustering values that are sub- stantially higher than expected from a random network of a similar

18 Mark E.J. Newman, Steven H. Strogatz & Duncan J. Watts, Random Graphs with Arbitrary Degree Distributions and Their Applications,64PHYSICAL REV. E 026118 (2001). 19 Paul Erdös & Alfréd Rényi, On the Evolution of Random Graphs,5PUB.MATHEMATICS INST. HUNG.ACAD.SCI. 17 (1960). Using Network Theory to Detect Dominant Cartel Firms 553 2000 Frequency Frequency 500 1000 1500 0 500 1500 2500 0 6789101112 0.2 0.3 0.4 0.5 0.6

Max Degree Clustering Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 Frequency Frequency 0 500 1000 1500 0 500 1500 0.03 0.04 0.05 0.06 0.07 0.08 0.09 5 10152025 Max Closeness Max Betweenness

Figure 4. Distribution of the maximum values of degree, clustering, closeness, and betweenness, together with the actual value of such measures in the network studied, as represented by the black dot magnitude (number of nodes and links). Therefore, the role of some of the nodes, or companies in the network, is signiﬁcantly relevant in the network studied.

VI. INTERPRETATION Despite being eminently empirical and based on one single cartel, this research enables the use of the network theory for the first time to provide a different explanation of damaging cartel organizations, in addition to further- ing the economic analysis of antitrust, especially in relation to the different degrees of liability of the companies in the creation and stability of national or international cartels. The application of the network theory to this case allows a global perspective of the vitamins cartel, resulting from the central role of some of its nodes and the lack of importance of other nodes or companies with respect to the existence or stability of the cartelized group. In other words, without these central or dominating nodes, it is highly likely that the cartel would not exist. In any event, without the central nodes, the cartel would not be stable enough to affect a possible alternative competitive balance, given the important role they play in the use and transfer of information, in addition to being in a decision-making position, in contrast to the more peripheral nodes. Observing the nodes responsible for this centrality, the eigenvector centrality measure confirms that there are two companies that sustain the cartel 554 Journal of Competition Law & Economics organization, thanks to their direct and multiple links with the other cartel operators. Nevertheless, the closeness value of Roche in relation to BASF proves its relative importance among the dominant or central nodes, although it is true that the resulting value of betweenness highlights the com- bined importance of both companies within the organization, while the relative insignificance of the others is also observed. Also of importance are other aspects of the analysis of the network cohe-

sion. For example, there is no single clique that enables the information on Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 all nodes to be shared. Only Roche is present in the level 6 clique, the highest number of companies independently sharing certain information, and in the six other level 4 cliques. This means that only Roche has access to all the information circulating through the different subgraphs, which shows its unequalled capacity to keep the cartel together. BASF also has relevant capacity from a subgraph perspective, but is not present in all of them. In addition, the clustering value shows the close link between the two, which clearly contributes to the high degree of cohesion. Finally, using the Erdős and Rényi concept of random networks, the difference between the type of network produced by a cartel and the random networks obtained with the same number of nodes and links can be inferred through centrality measurements. This evident difference suggests that there are major forces of a corporate nature functioning within the cartel, which we consider to be intentional.

VII. CONCLUSION When a cartelized organization is analyzed as a network using a series of centrality and cohesion measures such as those used in this study, and one or more operators appear to hold a central position in the organization, which we could call dominant inside the cartel, the meaning is that without them, the cartel would not be viable and, in any case, the dominant operators in the cartel have critically more liability than the other cartel operators. As a result, antitrust policies, especially those based on leniency programs in cases of cartels, need to consider not only the moment at which a member of the cartel decides to report its existence to the competition authorities, but also the role played by the reporting member, especially when the cartel would not have been possible without it. Leniency policies basically consist in pardoning the members of a cartel that report it from paying the fine and severely punishing the others, in order to eliminate the incentives to obtaining unlawful profits. The problem is that there are cartels, as shown in this article, that are structured on the decisions and control of one or more dominating members, to the extent that they control the design of the organization and the information flows that the others would not be able to produce. Using Network Theory to Detect Dominant Cartel Firms 555

Furthermore, these central operators, because of their control, deﬁne the time for the other competitor members when the cartelized collaboration will end. By means of this timing, they can impose exit costs from the cartel— indirectly, through Competition Authority sanction. Nevertheless, the dominant cartel operators are able to minimize these costs using the leniency program. Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021 Downloaded from https://academic.oup.com/jcle/article/12/3/541/2236264 by guest on 27 September 2021