HORIZONTAL RESTRAINT REGULATIONS IN THE EU AND THE US IN THE ERA OF ALGORITHMIC TACIT COLLUSION

: The fast development and improvement of e-commerce through various tools such as data mining, artificial intelligence and complex pricing algorithms has not gone unnoticed. Concerns about how new technologies can impact competition law have started to be raised by the academic world and various regulatory authorities. Specifically, the degree to which computer algorithms have the effect of inducing or enhancing tacit collusion is one of the most challenging topics for enforcement. Notwithstanding the question of whether algorithms should be per se regulated and how this can be achieved, in regard to tacit collusion scenarios enhanced by algorithms, we do have available tools that may be used to tackle it. This article will discuss whether the current regulation on horizontal restraints in the EU and the US could be appropriate for dealing with an algorithmic tacit collusion if such cases appear today.

not escape the reach of competition law.As Commissioner Vestager stated, firms could not ''hide behind computers'' and enforcers should watch over the advance of algorithms. 10reover, the Organisation for Economic Co-operation and Development ('OECD') has concentrated on technological developments and competition law.In November 2016, a Policy Roundtable on the use of Big Data was held, 11 and as recently as June 2017, there was another Policy Roundtable about algorithms and collusion. 12Likewise, several competition agencies have also addressed this issue, as seen in their participation in the aforementioned OECD Roundtables.Scholars have also alerted of the dangers and have proposed possible solutions to the problems that might arise. 13ere are several areas of antitrust that are directly affected by firms implementing algorithms in their processes, as can be seen in the Google case, 14 and the collusion of poster sellers on Amazon. 15The use of algorithms has the potential to make collusive outcomes easier to achieve and more stable. 16This may affect the entire spectrum of collusion scenarios, from the absolutely explicit to the completely tacit. 17In an explicit collusion case, the firms agree on colluding and could use the algorithms to achieve or enhance this collusion, but the analysis of this scenario should not create major challenges for the authorities because it presupposes an agreement and therefore the already-existing regulation will be enough to prosecute it as a traditional cartel.The higher risks and enforcement challenges arise in the area of tacit collusion, which is an already-controversial topic, as will be explained further in this article. 18e use of pricing algorithms could make tacit collusion more achievable and easier to sustain, but at the same time an algorithm implemented with innocent intent could result in entirely unintentional collusion, making prosecution difficult.10 It remains to be seen if and how this new scenario should be regulated. 19However, we do have available tools in the form of those regulations which deal with agreements between actual or potential competitors to restrain any aspect of their rivalry, more commonly known as horizontal restraints.This article will discuss whether the current regulations on horizontal restraints in the EU and in the US could be appropriate for dealing with an algorithmic tacit collusion.In Section B, I will explore how algorithms work and their impact as a potential enhancer of tacit collusion.Subsequently, in Section C, I will address the concept of tacit collusion and in Section D, I will address the interaction between algorithms and tacit collusion.
Finally, in Section E, I will critically analyse how the substantive horizontal restraint rules both in the US and in the EU, as they are currently understood, could tackle the possible tacit collusion scenarios intensified by the use of pricing algorithms.Finally, this article will conclude that, despite the alarming voices, the existing regulations on horizontal agreements could be applied in a tacit collusion scenario, notwithstanding the recognised difficulties in doing so even in a non-algorithmic case.

B. ALGORITHMS: WHAT ARE THEY?
To begin with, it is necessary to understand algorithms. 20An algorithm is a 'set of step by step instructions, to be carried out quite mechanically, so as to achieve some desired result'. 21This definition is a simple answer to a difficult question, as elucidating what an algorithm is has proved to be a challenging problem. 22gorithms are not new; they have been used by ancient cultures such as the Babylonians and Romans. 23The word itself dates back to the ninth century and comes from the mathematician Al-Khwarizmi. 24The concept of the algorithm has evolved through centuries; it went from being a mathematics concept related to any method of systematic calculation to today's understanding, which is closely linked to computer science. 25Basic concepts 19 Ezrachi and Stucke (n 1) ch 18. 20 Le Chen, Alan Mislove and Christo Wilson, 'An Empirical Analysis of Algorithmic Pricing on Amazon Marketplace' (2016), 2 <https://mislove.org/publications/Amazon-WWW.pdf>accessed 27 August 2017. 21Jean-Luc Chabert and E Barbin (eds), A History of Algorithms: From the Pebble to the Microchip (Springer 1999) 1. 22 Yiannis Moschovakis, 'What Is an Algorithm?' in Björn Engquist and Wilfried Schmid (eds), Mathematics unlimited: 2001 and beyond (Springer 2001) 919.23 Chabert and Barbin (n 21) 1. 24 ibid 2. 25 ibid.
In computer science, an algorithm is 'any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or sets of values, as output'. 26wadays computer algorithms are used in almost all industries to improve efficiency in their processes, for example by measuring future results based on the analysis of historical data or reducing transaction costs. 27 is necessary to understand that all algorithms are, at their heart, essentially just very complicated decision trees. 28Computer logic is binary, meaning all decisions made by a computer take the form 'IF x, THEN do y, ELSE do z'. 29Despite this apparent simplicity, predicting the outcome of a given algorithm can be difficult, because the processing power of modern computers means that a computer is capable of making billions of such decisions each second, and all but the simplest algorithms make heavy use of recursive functions -that is to say, logical loops where the outcome of a step of the calculation is fed back into the same calculation repeatedly. 30For a human being to 'follow along' with the logical steps that the algorithm is performing is therefore extremely difficult, and indeed most modern algorithms are written using tools that abstract away much of the low-level detail. 31This abstraction, while essential to productivity, does mean that there is a substantial chance that not even the person who actually coded the algorithm in question will know exactly what results it will produce in every scenario. 32 is also necessary briefly to define some other concepts that are in widespread use as part of the functioning of many algorithms.Firstly, the term 'Big Data' is related to the collection, processing and exploitation of personal data for commercial use.Big Data can be defined as a dataset characterised by such a high volume, velocity and variety, that traditional data processors are not capable of processing it. 33The use of Big Data can bring several benefits to consumers and the economy, notably in the area of finding patterns that traditional analysis would not identify. 34'Data Mining', which is a sub-concept of Big Data, can be explained as 'the automated or convenient extraction of patterns representing knowledge implicitly stored or captured in large databases, data warehouses, the web or other massive information repositories or data streams'. 35other relevant concept is 'Artificial Intelligence' (AI) which is a branch of computer science that 'studies and designs an intelligent agent who should be able to carry out tasks of significant difficulty in a way that is perceived as intelligent.' 36A subfield of AI is 'Machine Learning', which aims to grant computers the capacity to learn without having been programmed to do so. 37Machine learning is very important for the use of Big Data as it allows going deeper into the information, in ways not necessarily originally imagined by the designer. 38ese concepts seem futuristic, but they are not.Many companies have been using and developing these technologies and continue to do so. 39For example, Walmart uses Big Data to improve operational efficiencies, 40 and Google uses the data it collects to develop new products and invests in deep learning and AI. 41

Pricing algorithms
Algorithms can be used to create dynamic pricing tools, which are the focus of this paper.Dynamic pricing 'responds to market fluctuation in a real-time basis to achieve specific sale objectives such as maximize profit, maximize sales volume and minimize sales time'. 42From a business perspective, for an e-commerce firm having a pricing algorithm is essential, 43 considering that they are already present in many areas of e-commerce 44 and that (freed from the limits of physical storefront space) e-commerce sellers are able to offer a far wider range of distinct products than was historically the case.In addition to using the seller's internal information, pricing algorithms are used, inter alia, for collecting data from competitors, mainly their prices (but where possible, other information such as sales volumes, reported profits and so on), for then setting one's own price to maximise profit and/or sales. 45pricing algorithm may seem an abstract concept, as the design varies from one to another; it could almost be said that there are infinite possible algorithms.For explanatory purposes, I will provide an example of a basic structure that will be useful to understand the legal analysis made in Section E. First, as contained in the definition, an algorithm needs input to produce an output.Simply put, the algorithms need to be fed with information in order to produce a result, in this case, a product's price.The information provided to the algorithm could be divided into internal input and external input, and this is where the concept of Big Data becomes useful.Internal input would be the seller's own information, for instance: i) its costs (fixed, variable, marginal, distribution, etc); ii) the desired profit margin; iii) willingness to forgo profit due to a foreseeable future loss (e.g. a sales season).
The external input is the information that the firm collects from the market.Examples of this could be: i) current information about competitors and customers such as price profile, currently known market prices, and customer information data; and ii) heuristic data 46 (information from past experiences that can be used for self-learning to predict future outcomes; for instance, the behaviour of the market the last time the price increased).External input would also include new governmental regulation that prohibits certain conduct or sets certain limits, which the algorithm could be set to take into account.
Having this input, the algorithm can be programmed to execute the functions desired by the firm, which in this example would be to collect data from the market, analyse it and set a price that would maximise the profits of the firm.The process herein described is of course an oversimplification compared to what a real-world algorithm would do, but it fulfils the purpose of explaining it.Having done so, it is necessary to introduce the legal framework and related economic concepts on which this article will focus.

C. TACIT COLLUSION
Both in the EU and in the US, the concept of collusion is associated with coordination by competitors to achieve supra-competitive benefits.In the EU, collusion is defined as 'actively conspiratorial behaviour of the kind captured by the expressions of agreement and concerted 45 Hwang and Kim (n 42) 149. 46 practices of Article 101 Treaty on the Functioning of the European Union ('TFEU').' 47 In the US, collusion has been defined as the 'joint action to divide markets or fix prices, (...).Such collusive action is the substance of the conspiracy in restraint of trade which Section 1 of the [Sherman Act] makes a crime'. 48Collusion can be explicit or tacit, as will be explained below.
Explicit collusion is achieved through an agreement (which itself can be explicit or tacit), and this agreement is a central matter to regulatory enforcement, either under article 101 TFEU 49 or Sherman Act §1. 50Other notions included under these statutes are those of concerted practices in the EU, or conspiracy in the US. 51Any of the aforementioned situations are straightforward in their enforcement.On the other hand, tacit collusion has been harder to define and enforce as it does not encompass an agreement, but generally arises from the interdependence associated with an oligopoly, and the enforcement of measures against it is ultimately a policy choice. 52

The oligopoly problem
When discussing what tacit collusion is, it is necessary to address the oligopoly problem.An oligopoly is a market where few firms compete and the actions of each are considered by each other. 53It is in this context where the oligopoly problem or the theory of oligopolistic interdependence appears. 54e oligopoly problem theory proposes that in an oligopolistic market, the competitors are interdependent.Interdependence in this setting means that the rivals are aware of each others' existence and adapt their strategies to achieve a stable non-competitive environment without the necessary incentives to compete. 55The result of such behaviour is that, without the existence of an agreement between competitors, the competitive price that could exist is replaced by an oligopolistic price and thus supra-competitive profits. 56However, this is not the only possible outcome, as firms in an oligopoly can be competitive, 57 a point discussed further in the second part of this Section. 47 There are certain conditions for tacit coordination to emerge.Firstly, firms need to have the capacity to monitor competitors and the ''parameters that lend themselves to being a focal point of the proposed coordination'' (such as pricing or output levels); 58 and this is why price transparency enhanced by algorithms plays a relevant role, as will be discussed later.Then, to incentivise firms to continue adhering to the coordinated position, there has to be a 'deterrent punishment mechanism which requires that the detected cheats could be sanctioned both credibly and effectively'. 59Such punishment could be, for example, going back to competitive prices.
The pricing system in an oligopolistic market 'can be described as a rational individual decision in light of the relevant economic facts'. 60As can be seen, the outcome of interdependence is similar to the one that could be achieved with explicit collusion and it should be equally undesired.Economists refer to the result of the oligopoly problem as tacit collusion, whereas lawyers refer to it as conscious parallelism. 61There are also other (roughly synonymous) concepts used in this regard, such as parallel conduct, parallel pricing, oligopolistic pricing suits, implicit collusion, imperfect cartels, non-cooperative collusion, tacit coordination, coordinated effects, or self-enforcing collusion. 62om an economic perspective, the outcome of oligopoly can be explained through game theory, as firms play 'repeated games'. 63This means that the players can analyse previous games to make their future decisions, which translates into studying the previous pricing strategies of the competing firms to make the next pricing decision. 64However, for maintaining tacit collusion, the information has to be complete and perfect 65 (and as will be seen, this is where algorithms that aid in the completeness and perfection of the information become problematic).
The factors that facilitate the occurrence of tacit collusion can be either structural or not. 66The structural factors are, inter alia, concentration, entry, cross-ownership and other links among competitors, regularity and frequency of orders, buyers' power, demand elasticity, the evolution of demand, product homogeneity, symmetry, multi-market contacts, inventories and excess capacities.The non-structural factors are price transparency and exchange of information. 67

The legal challenge of tacit collusion
The oligopoly problem poses the following question: should tacit collusion be prevented or subjected to enforcement action even if it is rational conduct of a firm in an oligopolistic market?Tacit collusion has not been an uncontroversial subject among scholars, nor in the courts, both in the EU and in the US, as explained below.The challenge resides in the fact that there is a gap in the regulation of horizontal restraints, because what such regulation prohibits are agreements or concertation, and in the case of tacit collusion, such agreement does not exist.
Introducing algorithms in this already controversial topic will relight this discussion, as they make the risks of tacit collusion more likely to occur.
The legality of tacit collusion 68 has been discussed by scholars and a common understanding on the matter has yet to be reached.Donald Turner analysed whether conscious parallelism could be considered an agreement regulated under §1 of the Sherman Act.His view on the matter was that 'conscious parallelism is devoid of anything that might reasonably be called agreement when it involves simply the independent responses of a group of competitors to the same set of economic facts -independent in the sense that each would have made the same decision for himself even though his competitors decided otherwise'. 69An oligopolistic firm takes into consideration the reaction of the other firms in the market to any price adjustment that it executes since the other firms will surely react because of the potential loss in their sales. 70 contrast, Richard Posner argued that a firm might initiate a reduction of the price because of the time lag between such reduction and the response by the other oligopolistic firms, in which case there is a possibility that the price reduction could be profitable until it is matched, which could be understood to be a economically rational conduct. 71Thus, it can be understood from the absence of such reductions in an oligopoly that there is an effort to jointly 67 Marc Ivaldu and others, 'The Economics of Tacit Collusion, Final Report for DG Competition (European Commission, March 2013) <http://ec.europa.eu/competition/mergers/studies_reports/the_economics_of_tacit_collusion_en.pdf>accessed 5 March 2018. 68Please note that the expression 'conscious parallelism' will also be used here as the legal scholars' equivalent to 'tacit collusion'. 69Turner (n 60) 665. 70ibid. 71Richard A Posner, Antitrust Law (2 nd edn, University of Chicago Press 2001) 57.maximise the price.Nevertheless, Turner concluded that if firms in an oligopolistic market consider the probable conduct of their competitors when establishing their prices 'without more in the way of agreement than is found in conscious parallelism, [they] should not be held unlawful conspirators under the Sherman Act'. 72Posner disputed such an approach, considering it inadequate. 73He proposed an economic approach to collusion, either tacit or explicit. 74If there is enough economic evidence to infer collusive pricing, 'there is neither legal nor practical justification for requiring evidence that will support the further inference that the collusion was explicit rather than tacit'. 75Thus, Posner argued that tacit collusion should be analysed as a tacit meeting of minds, 76 to which the Sherman Act would be applicable.
Kaplow provides a more organic analysis of the concept of tacit collusion by giving a different classification and re-categorisation of the interaction among firms. 77He starts by making a clear-cut distinction between independent behaviour, 78 interdependent behaviour 79 and express agreement, and notes that these terms may lead to confusion when they are not well-defined. 80Under this view, the concept of plain interdependence falls within the idea of 'agreement', 81 and is therefore subject to enforcement action under § 1 of the Sherman Act.
However, he recognises that there should be a balance between the deterrence of misconduct and the 'chilling of desirable economic activity'. 82Lastly, writing in relation to the EU regime, Petit is of the view that 'the fact that tacit collusion is rational conduct cannot, and should not, be a cause for excuse under the competition rules'. 83nally, in the context of these debates as to the appropriate regulatory response to oligopoly, it should be noted that even if tacit collusion appears to be a very probable outcome in an oligopolistic market, there are some caveats.Firstly, a collusive outcome arising from pure interdependence is unlikely to occur, as in real life markets there are other variables to consider such as product differentiation, lack of information about competitors (which could 72 Turner (n 60) 671. 738 Independent behaviour can be defined as 'behavior by two or more parties that has no relationship whatsoever as well as behavior that has similarities yet is motivated by considerations that do not depend on others' reactions.' 79Interdependent behaviour can be defined as: 'behaviour that involves coordination with others'.incentivise cheating) and potential new entrants. 84Second is the fact that many oligopolistic markets are competitive, not only in terms of price competition, but also non-price competition, such as after-sales services, quality of products and loyalty schemes. 85Moreover, Motta argues that in a tacit collusion scenario it would be difficult for firms to effectively coordinate as they 'cannot communicate with each other, they can make mistakes, and select a price (or quantity) which is not jointly optimal for the firms.' 86 The result of trying to coordinate without communication could be too expensive 87 and may affect the willingness of the firms to participate in the collusive outcome.
As can be seen, the theory of oligopoly interdependence is a controversial topic among economists and lawyers, who have different positions on whether such interdependence should of itself provide a basis for enforcement action. 88The trend in Courts both in the US and in the EU has been not to condemn conscious parallelism as illegal in an oligopolistic market unless it can be proved that there was an agreement. 89

D. HOW COULD ALGORITHMS CHANGE TACIT COLLUSION?
The discussion of oligopoly interdependence may take a new approach when algorithms are put in the picture.Even if tacit collusion, in theory, is a possible outcome in an oligopolistic market, in practice it is unlikely to occur, for the reasons discussed in Section C. 90 As noted by Stucke and Ezrachi, algorithms could create a so-called 'tacit collusion on steroids' scenario. 91e reason to assert this is that 'industry-wide use of pricing algorithms leads to higher prices, without any clear or implied human anticompetitive agreement.' 92The use of pricing algorithms could make tacit collusion more common in the already oligopolistic markets and even extend 'the oligopoly problem to non-oligopolistic markets structures'. 93In particular, pricing algorithms allow: i) greater speed in detection of and reaction to competitor price movements; ii) improved accuracy in such detection and reaction (since algorithms will be 84 William Page, 'Communication and Concerted Action' (2007) 38 Loyola University Chicago Law Journal 405. 85Whish and Bailey (n 47) 600. 86 more efficient in studying the price fluctuations and the probabilities of deviation); and iii) minimization of human factors (the removal of human decision-making from the pricing strategy may lead to more stable cartels, because of the better understanding of the market that algorithms might have). 94gorithms may also have procompetitive effects that are connected with the efficiencies both in the supply side and the demand side. 95For example, on the supply side, algorithms improve transparency in the market. 96Nevertheless, this factor could also lead to collusion in markets with limited players. 97Transparency of prices is a 'double edged sword', 98 and the overall effect of the transparency should be measured on a case by case basis, to determine if this attribute is a benefit or not.With pricing algorithms firms have more information about market trends and can better assess the optimal price level and change it accordingly. 99This has the effect of levelling the playing field for smaller companies to directly compete with firms that may have more resources for such purpose.On the other hand, it could be argued that this feature may render tacit collusion more feasible, due to the enhanced capacity of firms to rapidly adjust to the price changes of competitors.The critique Posner made to Turner's approach to tacit collusion was based on the time it took firms to change their prices.If a firm reduces its prices, the other competitors could be able to match such price reduction much faster if they use algorithms, reducing the firm's incentive to undertake a price reduction strategy. 100The Posner approach to tacit collusion would not therefore be applicable to an environment where algorithms are used to implement a pricing strategy, especially when they are programmed to maximise profits, as there would not be a time lag in which the price cut could be profitable given that the price matching by the other firms might be immediate.
The way in which algorithms are set to function, and the capacity they have to process information and change the data (prices) provided to the market, are practically unlimited.
There are many ways in which in the data collection phase can be carried out depending on how easy it is to access the information of the competitor.For example, when a 'robot' (i.e. the 94 ibid. 95 automated piece of software that is tasked with fetching the prices) of firm A looks for the prices of firm B, the robot may have access to a specifically-published data web service provided by firm B (firm A would need to be subscribed to it, and firm B would need to allow this), or the algorithm could carry out a data scraping function, 101 which is much more complicated, but which can be done without firm B's knowledge or consent.Firm B could however take measures to prevent easy access to its prices, even if they are posted online.
Accordingly, from the way data is collected, firm B's attitude towards competition may be inferred, depending on the technique used to extract data.If firm B allows firm A to subscribe to its data web services, and therefore get instant access to price information, it could be thought that firm B is deliberately exchanging sensitive information with firm A through an algorithm, the implications of which will be discussed later in this piece.
Other factors worth considering are: how often the algorithm of firm A is programmed to collect data, and how fast the pricing decision is made.In this sense, the frequency in which firms obtain information from their competitors may have effects in the market as stated by the Finnish competition agency in regard to the ScanTrack service offered by AC Nielsen. 102Many features of an algorithm should be studied and tested to understand the real effect it may have on the market and to qualify it as competitive or anticompetitive.
High quality input data is fundamental for a pricing algorithm to be effective. 103Thus, the capacity to collect consumer and market information is very relevant, as this is what makes it possible for firms to effectively use algorithms as pricing tools. 104However, it is argued that in determining how the algorithm finally sets the price to be charged to consumers, the firm should avoid programming algorithms that could (for example by introducing too-frequent price changes, by gathering the information in a method designed to ensure that competitors are working from the same data set, or by having any other feature from which anticompetitive intent could be understood) eventually lead to tacit collusion.Nonetheless, it would be possible to argue that in programming an algorithm, there are many actions that could be taken to avoid creating a potential collusion scenario and still maintain the benefits of using it due to the efficiencies it can bring to the market.Thus, understanding how algorithms work is crucial both to analyse the risks and the benefits and to adequately assess them.
Algorithms could thus have a huge impact in tacit collusion.However, for this to occur, it has to be assumed that the algorithms are programmed to work with similar parameters and achieve a common aim of maximising profit, and even in that case, outcomes could be variable, due to chaos theory, in the sense that tiny changes in the starting conditions can lead to massive differences in outcomes. 105Moreover, the use of algorithms also has an impact on price discrimination, which could be thought of as a limit to tacit collusion. 106Nevertheless, in theory under certain assumptions pricing algorithms could lead to a tacit collusion outcome more easily by ''facilitating a non-competitive equilibrium by working as instruments that eliminate the need for explicit communication or interaction between competitors''. 107Thus, the optimal use of pricing algorithms could be an effective means of effecting tacit collusion. 108

E. HORIZONTAL RESTRAINT REGULATIONS: HOW COULD THEY BE APPLIED IN A TACIT COLLUSION SCENARIO EXACERBATED BY ALGORITHMS?
Since algorithms are already present in the economy, and thus it is possible to encounter a tacit collusion scenario enhanced by algorithms, I will now discuss how the existing regulations on horizontal restraints could be applied in such a case and whether it would be necessary to introduce any other regulatory alternative.If there were a case now involving algorithms and tacit collusion, how could Article 101 TFEU and §1 of the Sherman Act be applied?
In the bigger picture, there are two questions to answer regarding the regulation of algorithms and collusion: first, whether the use of algorithms should be regulated from a competition law perspective; and second, what tools could be used for such purposes.I consider that the regulation challenge in this topic is twofold.On one hand, the existing gap in the regulation of tacit collusion could make it more difficult to enforce a pure case of tacit collusion aided by algorithms.On the other hand, the consequences of pricing algorithms are still not yet well understood 109 (nor are they likely ever to be in full), and it is a field where innovation is of the essence; furthermore, competition authorities do not have sufficient knowledge on 105 Christos Skiadas and Charilaos Skiadas, Handbook of Applications of Chaos Theory (CRC Press 2016) 228. 106For a detailed explanation of this point see Ezrachi  algorithms. 110However, these challenges to regulation should not be considered as an insurmountable impediment for competition authorities.The existing regulation on horizontal agreements could be applicable, in conjunction with the facilitating practices or plus factors doctrine, which will be further explained. 111Before considering other possible tools, such as auditing algorithms 112 or creating new laws, the ones already available should be given a chance.Moreover, regulations affecting related areas of innovation could indirectly affect the topic of tacit collusion.For example privacy and other laws governing the handling of Big Data will be particularly relevant to the collection and use of the data on which the effectiveness of algorithms depends.
Before describing the enforcement options under the current horizontal regulations in the EU and in the US to tackle an undesired outcome, it should be reiterated that, as explained earlier, algorithms have different designs and purposes and can work in very diverse ways.
Additionally, it is a fast-evolving area.Studying algorithms could be very complex due to the dynamism of the area and the constant development of new technologies.For example, AI, the evolution of Big Data and deep learning could render obsolete any potential regulation within a short period of time.This issue of fast evolution is particularly relevant in relation to the e-commerce market.
The dynamism in the market has been previously considered by competition authorities when studying a market.For example, when Microsoft bought Skype, the EU Commission took this factor into account when it approved the transaction. 113However, the EU Commission has also investigated situations where there was anticompetitive conduct in a dynamic market: examples of this are the Microsoft v. Commission case and the AstraZeneca v. Commission case. 114In this regard, some argue that courts and agencies should rarely, if ever, intervene in dynamic industries. 115Innovation should be considered a factor that encourages firms to compete more intensely, due to the rewards that they can attain. 116 can be seen, the challenge to regulate algorithms is not minor, and companies are adopting business models that rely on algorithms either for data collection, data analysis or 110  pricing purposes.117However, that does not mean it is impossible.The extensive use of pricing algorithms could clearly make coordination easier, cheaper and faster, and thus lead to more cases of tacit collusion.Even now, with the existing tools and regulations, it could be possible to tackle in some way these effects. 118 The notion of agreement under Article 101 TFEU and §1 of the Sherman Act From the enforcement perspective, as noted previously tacit collusion is considered a gap because the illegality of collusion depends on the existence of an agreement (or concerted practice, as discussed in the next sub-section below).119 In enforcement proceedings relating to explicit collusion, the authorities will usually be able to establish the existence of an agreement or a concerted practice, and therefore the application of Article 101 TFEU or §1 of the Sherman Act is very straightforward.By contrast, and even if criticised, 120 it has been recognised by courts both in the US and in the EU that tacit collusion (understood as conscious parallelism), is not per se unlawful.121 Thus, one would think that the first option for enforcing tacit collusion enhanced by the use of pricing algorithms would be to revisit the concept of agreement or concerted practice.122 When addressing agreements, there is a very relevant evidentiary factor to consider.123 Much has been discussed on what qualifies as an agreement and how it has to be proven.124 When dealing with oligopolies, it has been difficult for competition authorities to set the adequate evidentiary standard for proving an agreement, especially in cases of conscious parallelism, as it is not assumed that it is a concerted action.125 In the EU, Article 101 includes both agreements and concerted practices.A (pricefixing) agreement 'centres around the existence of a concurrence of wills between at least two parties, the form in which it is manifested being unimportant so long as it constitutes the faithful expression of the parties' intention.'126 Concerted practice is 'a form of coordination between undertakings which, without having reached the stage where an agreement properly so-called has been concluded, knowingly substitutes practical cooperation between them for the risks of competition'.127 This criterion has been applied in other cases, such as in the Suiker Unie v.
Commission. 128Even if agreements and concerted practices are conceptually diverse, there is no need to set a point on which one ends and the other one starts. 129 the US, the concept of agreement and concerted action are employed interchangeably as constituting a joint action prohibited by §1 of the Sherman Act. 130The concept of agreement does not explicitly appear in §1 of the Sherman Act, as it uses the terms contract, combination and conspiracy. 131These three concepts encompass a single term 132 which is one of 'agreement' with an anticompetitive purpose. 133In the Socony case, 134 the Supreme Court precluded all types of price-fixing agreements, including as such any combination or conspiracy to fix prices.The concept of concerted action is also covered by the Sherman Act, 135 as can be seen in the the Container Corp case. 136Thus, both in the EU and the US, the requirement for an agreement to be found is the concurrence of wills, and in the case of tacit collusion, that requirement is not satisfied.
It is thus clear that tacit collusion is not included in the pure concept of agreement.
Posner and Kaplow have advocated for this to change, suggesting that oligopolistic behaviour encompasses an understanding with other competitors, as explained in Section C. The reason for not including tacit collusion in the concept of agreement may be the risk of chilling competition by over-deterring conduct that could be the result of normal business behaviour, as stated above.Nevertheless, revising the notion of 'agreement' (whether by legislative change or further development in the interpretation of existing rules) could be a possibility to expand the concept's scope as predicated by Posner and Kaplow, 137 so tacit collusion could be prevented by enforcement.The difference now, which raises concern, is that algorithms could make tacit collusion more effective and plausible in oligopolistic markets, and even feasible in non-oligopolistic markets.As algorithms theoretically increase the risk of collusion, it may occur more frequently, and therefore, amending the current regulation on horizontal restraints may be an option, but the benefits and risks should be carefully analysed to avoid undesired effects, such as deterring competitive conduct.
It should be noted that in accordance with the EU Guidelines on Horizontal Cooperation138 exchanges of information between competitors (including pricing information) could be tackled under Article 101 TFEU, if there is an agreement or concerted practice to exchange such information. 139The theory of harm of such information exchanges is that they facilitate the occurrence of tacit collusion in markets where the existing transparency of prices as between competitors would otherwise be insufficient to maintain tacit collusion. 140As argued by Wagner-von Papp, the impact of information exchanges is better understood through game theory. 141The underlying argument is that in an oligopoly, the main challenge to the oligopolists is that there is no complete information about the game, and exchanging information helps overcome this challenge. 142However, as it remains necessary to prove an agreement or concerted practice in such a tacit collusion case, we fall into the same problem addressed above about the difficulties of enforcing in respect of other forms of tacit collusion.
The possible exception to this would be scenarios where one player in a market takes active steps to deliberately share its pricing information with a direct competitor, which may in itself be seen as an intentionally anticompetitive step.

Concerted practices and plus factors in general
The question to be answered now is whether parallel behaviour can be identified with a concerted practice or not.In the EU, the European Court of Justice ('ECJ') set forth in the Dyestuff case 143 that 'although parallel behaviour may not in itself be identified with a concerted practice, it may however, amount to strong evidence of such practice … '. 144 Since then, and until the case Woodpulp II, 145 the ECJ was reluctant to accept the possibility that Article 101 TFEU was applicable to tacit collusion, 146 as seen in other cases such as the Züchner case 147 and the Zinc Producers case. 148This approach was later revised in Woodpulp II, which marked a departure from the previous case law as it did not exclude the possibility that Article 101 could be applicable to tacit collusion. 149This was later confirmed in the CISAC case in 2013. 150The result of these cases, as mentioned by Stroux, was that concerted practice could be 'inferred from parallelism of behaviour if it is the only plausible explanation for it.' 151 the US, so far courts have set the limit between conscious parallelism and unlawful concerted action by means of common law development, as the Sherman Act provides no guidance on this matter. 152In the Brooke Group case, the Supreme Court provided that tacit collusion (understood as conscious parallelism) ''describes the process, in itself not unlawful, by which firms in a concentrated market might in effect share monopoly power, setting their prices at a profit-maximizing, supracompetitive level by recognizing their shared economic interests and their interdependence with respect to price and output decisions''. 153 has been held that conscious parallelism could be a violation of §1 of the Sherman Act, if additional evidence consistent only with a concerted action scenario is provided, such evidence comprising the so-called 'plus factors'. 154Thus, the plus factors doctrine is used in the US for the prosecution of certain types of parallel conduct and can be defined as 'the body of economic circumstantial evidence of collusion, and beyond parallel movement of prices by firm in an industry'. 155They are operational criteria by which courts allow an agreement to be proved by circumstantial evidence, beyond merely the economic evidence of parallel pricing behaviour. 156Stroux classifies plus factors in five categories, and for the analysis of parallelism and algorithms, the relevant ones are the factual, the economic and the facilitating practice plus factors. 157However, even with the existing judicial experience and the contributions that lawyers and economists have made to this area, the proof of concerted action remains a disputed topic in cases under §1 of the Sherman Act. 158 the other hand, in the EU, the plus factors approach is not present in the case law.Kovacic and others (n 125) 395. 157Stroux (n 57) 51. 158Kovacic and others (n 125) 399. 159Stroux (n 57) 80.

Algorithms as plus factors or facilitating practices
An agreement or concerted practice is thus pivotal for the triggering of the horizontal restraint rules, both in the US and the EU.As has been seen, this formalistic approach (focusing on the existence of an agreement rather than the outcome) does not include a situation where competitors engage in parallel conduct unless it complies with the evidentiary requirements above described.However just as the involvement of algorithms may increase the risk of tacit collusion, it may also provide additional grounds for enforcement action, which will now be considered.

a) Algorithms as plus factors
When faced with tacit collusion involving algorithms, it could be considered that having a pricing algorithm with certain characteristics could be treated as a plus factor, that helps to achieve a parallel outcome.Notwithstanding that the universe of types of algorithms is almost infinite, there are a variety of algorithmic patterns that can be identified as aiding tacit collusion.Comparison could be drawn with certain pricing systems which have been considered as potential enhancers of tacit collusion in several cases, and have been treated as plus factors. 160In the General Electric and Westinghouse case (which ended with a settlement), the DOJ stated that even if there was no evidence proving that there was some sort of communication between the companies, 'the independent yet parallel adoption of the new policy by GE and Westinghouse had brought about a meeting of the minds and facilitated the elimination of price competition'. 161In Wall Products v. National Gypsum, a private enforcement case, the court found that the firms involved 'combined and conspired among themselves and others to stabilise and maintain the price level of Gypsum wallboard through a course of interdependent conscious parallel action pursuant to a tacit understanding by acquiescence coupled with assistance, whereby they mutually agreed [...].' 162 Taking a pricing system called the posted prices system 163 as an example of a plus factor, Harrington evaluates four variables: i) whether before adopting a posted pricing system, the prices were below any publicly announced list, or did not have a publicly announced list price; ii) whether having this system only serves the interest of the firm if the competitors adopt the same strategy; iii) whether after implementing the new pricing strategy, the prices are higher and more uniform; and iv) whether there are market conditions that make collusion 160 Joseph E Harrington Jr., 'Posted Princing as a plus Factor' (2011) 7 Journal of Competition Law & Economics 1; Stroux (n 57) 52. 161Harrington Jr (n 160) 5. 162 357 F Supp 832 (ND Cal 1973). 163Public announcement by firms of a policy to set a list price with no discounting off of that list price.feasible. 164This evaluation focuses on 'identifying circumstances under which the adoption of posted pricing is the basis for inferring that firms have entered into an agreement to coordinate their prices'. 165e decision to adopt an algorithm could be scrutinised through the same lens: competition authorities should study the pricing situation from an economic perspective before having algorithms (for industries that are also present in the brick-and-mortar market), or the situation before the competitor entered into the e-commerce market (for firms that have always been e-commerce ones, like Amazon).Moreover, it should be examined whether the algorithmic maximising profit function is only effective if other firms take the same action, and discard other pricing strategies such as price discrimination or discounts, and it is critical to understand 'if some practice is only in a firm's best interest when it anticipates coordinated pricing'. 166To conclude whether the conduct in question amounts to an unlawful concerted practice, it is necessary to consider the economic analysis of the case.
Another element to be assessed as a plus factor is the exchange of information.It is important to consider the input of the algorithm, as it is fed with already-existing information, either internal or external.The way in which data collection is carried out is of vital importance.
The access that a firm can give to another firm through data web services could be a sign of willingness to enter into tacit collusion.There are various safeguards that firms could take in order to prevent a competitor's robot or web crawler from collecting price data effectively, and a company with competitive intent would usually be expected to attempt to use these safeguards so as to gain a favourable position of informational asymmetry (gaining competitive advantage through being better-informed).
It is for this reason that I am proposing that failing to implement such safeguards should be considered a plus factor.This may be extending the concept of exchange of information, but what firms are doing by allowing other firms to know their prices and feed them into their own pricing algorithms is exactly that.The means of going about the exchange are innovative, but the act itself is not.Information exchange has been considered a plus factor in the Petroleum Products 167 case and Exxon Corp. 168 A mentioned by Harrington, 'communication is an economically appropriate basis for distinguishing interdependent and concerted action'. 169By 164 Harrington Jr (n 160) 14. 165 ibid 18. 166 ibid 21. 167 Re Coordinated Pretrial Proceedings in Petroleum Products Antitrust Litigation [1990] 906 F2d 488 (9 th Cir). 168Todd v Exxon Corporation 275 F3d 191 (2ndCir 2001). 169Harrington Jr (n 160) 434.applied differently, in the shape of facilitating practices, to face such problems. 177Nevertheless, the current legal assessment of this matter is still ambiguous. 178 to the facilitating practices that could fall within the scope of Article 102 TFEU, the current approach dates back to 1965, when a group of professors were commissioned by the predecessor of the EU Commission to study the application of what is now Article 102 TFEU.
They suggested 'the possibility of applying an abuse of dominance law to oligopolistic price leadership'. 179This collective dominance theory (also called joint dominance and oligopolistic dominance) is highly controversial. 180e facilitating practices covered by Article 101 TFEU can be considered as circumstantial evidence of an agreement and be an infringement of that article, and are also per se illegal when adopted by agreement or concerted practice and prevent competition. 181It is relevant for this purpose to address information exchanges, for the same reasons as mentioned above for plus factors in the US.In the EU, information exchanges have great importance, as the ECJ has consistently ruled that information exchanges can provide an artificial transparency to the market that may lead to tacit collusion, as it subverts the aim of having competitors act independently. 182This is precisely the case of algorithms; they create an enhanced market transparency through their functions, such as data collection.In concentrated markets, information exchanges are very dangerous, and even in less highly concentrated ones, as stated in the Thyssen Stahl case, 183 they are also not risk neutral. 184Those dangers may be considerably exacerbated given the capacity that algorithms have to immediately adapt their conduct to match that of competitors or to punish deviation from the oligopolistic price.
As previously stated, facilitating practices, such as the adoption by an industry of a certain pricing system, can be plus factors. 185In the US, a facilitating practice is defined as 'one that makes it easier for parties to coordinate price or another behaviour in an anticompetitive way'. 186There is a clear difference between agreements that are tantamount to naked price-fixing agreements and other types of horizontal behaviours. 187The approach that the FTC and the DOJ have taken towards facilitating practices differs, as such practices have been treated as autonomous misconduct or have gone unchallenged, due to the benefits they bring to the market. 188When enforcing conduct as an autonomous facilitating practice -an infringement in itself -this has been done under §1 of the Sherman Act, usually for exchanges of information, or under §5 of the Fair Trade Commission Act (''FTC Act''), for other facilitating practices. 189 previously suggested (concerning plus factors), a pricing algorithm could be considered a facilitating practice, but only when certain conditions are met.In the US, to treat a pricing practice as a facilitating practice is not new.Advance price announcements in some situations have been assessed as facilitating practices. 190In the EU, the treatment of pricing systems that lead to information exchange as facilitating prices is similar to the position in the US. 191The proposed approach of considering certain patterns of algorithms as plus factors in the US can thus effectively be replicated in relation to facilitating practices related to information exchange in the EU.It is argued that there is space in the current regulation of information exchange to undertake enforcement action in an algorithmic tacit collusion case when the necessary collusion-facilitating features are found in the algorithms used by the firms.
Moreover, the lack of taking certain precautions to prevent the free flow of information between algorithms could also be investigated, as suggested earlier in the context of plus factors.
Nevertheless, as stated by Petit, the scope of Article 101 is limited to reciprocal contacts between competitors, thus, the facilitating practices should include a link to another competitor. 192Also, he argues that 'Article 101 TFEU has no teeth in situations of "pure" tacit collusion, where no facilitating measures are needed to tacitly collude'. 193However, in the case of algorithmic tacit collusion, it could be understood that the function of the algorithm is what creates the collusive outcome, and the algorithms are fed with the information they receive from the market.Therefore it would not be exaggerating to say that, depending on the information characteristics of the algorithm and how fast prices are adapted, it could be considered an information exchange case.Nonetheless, it should be noted that information 188 ibid. 189 exchange does also bring procompetitive effects to the market, 194 and thus, a thorough assessment of algorithms and their impact in the market should be carried out in each such case.
The facilitating practices that amount to unilateral conduct covered by Article 102 TFEU are related to the concept of abuse of a collective dominant position. 195According to Petit, the term of collective dominance has to be understood as a 'situation of observable, exteriorised tacit collusion'. 196Laurent Piau v. Commission affirmed that 'there is a collective dominant position where firms present themselves or act together on a particular market as a collective entity'. 197Petit also contends that the concept of a 'collective entity' requires a degree of effectiveness of the result of the tacit collusion, thus, to have joint dominance the relevant entities must have colluded. 198As is the case in a unilateral abuse of dominance case, what is sanctioned is not having this joint dominance, but the abuse of it. 199The type of abuse required for this to be triggered is not clear, and scholars have proposed different types of abuses. 200One of these is applying the concept of collective dominance to facilitating practices, for example unilateral price signalling. 201Stroux argues that by adopting facilitating practices, it would be easier to achieve the collusive outcome because elements such as market transparency could be increased.It is submitted that this interpretation would allow authorities to enforce facilitating practices that escape the scope of Article 101 when such practices are parallel, and there is no agreement or concerted practice whatsoever. 202However, such an approach has not been judicially endorsed. 203When dealing with algorithms, this approach could be useful, for instance, if the exchange of information between algorithms was not caught by Article 101, as it was not possible to prove the concerted action.Thus, there is still a possible enforcement option when dealing with algorithms that by any of their characteristics have a negative effect on the market and that lead to tacit collusion.
In the US, §2 of the Sherman Act deals with unilateral conducts, as does Article 102 TFEU.However, §2 of the Sherman Act has proved to be unfit in dealing with an oligopoly. 204he reason for such an approach is that no oligopolist has monopoly power, 205 even if the US courts had suggested it in, for example, the United States v American Airlines, when the Fifth Circuit provided that 'the two airlines at the moment of acceptance, would have acquired monopoly power [...] the offense of joint monopolization would have been complete'. 206C Act, Section 5 In the US, there is still one other piece of legislation that needs to be addressed when discussing tacit collusion.The FTC Act §5 was enacted in 1914 to deal with unfair methods of competition, and it also precludes unfair or deceptive practices. 207FTC Act §5 empowers the FTC to enforce misconduct that violates the Sherman Act 208 by interpretation of what unfair conduct is. 209The broad language of §5 of the FTC Act has made it useful to enforce in respect of conduct that escapes the scope of the Sherman Act, and it has been used to try tackling oligopolistic interdependence. 210In the 1970s, 211 the FTC attempted to do so under the concept of shared monopoly but failed, for example in the Kellogg Co. case. 212Moreover, in the Ethyl case, it was held that 'the mere existence of an oligopolistic market structure in which a small group of manufacturers engage in consciously parallel pricing of an identical product does not violate the antitrust laws.' 213 §5 of the FTC Act may seem useful to provide a solution to the algorithmic tacit collusion, due to its theoretical application to oligopolistic behaviour.However, the case law proves that it is not possible to apply it, and therefore it is not an effective tool. 214Nevertheless, it could be used as a means of dealing with unilateral conduct that amounts to facilitating practices, specifically information exchanges. 215

F. CONCLUSION
Technological developments are having an impact on the way we live, and e-commerce has changed and will change our consumer behaviour.Together with this revolution come regulatory challenges, and competition law is not oblivious to them.One of the problems that scholars and academics have identified is the possibility of algorithms enhancing the risk of tacit collusion.One may agree or disagree as to the likely future extent of algorithm-driven tacit collusion, but we cannot deny it is a possibility.In this sense, this article has focused on explaining how algorithms have the potential to affect the conditions that make tacit collusion possible, such as monitoring and transparency.Further, it has analysed the enforcement tools currently available to EU and US authorities for tackling horizontal conduct, and how they could be interpreted if faced with algorithmic tacit collusion scenario today.
There is already a dispute as to how to deal with tacit collusion, as can be seen through the positions of commentators such as Turner and Posner.Ultimately, the approach depends on a policy decision to alter the possible rational business behaviour in an oligopolistic market.
In dealing with this issue, so far, in the EU we encounter Article 101 TFEU which relies on the existence of an agreement, concerted practices or facilitating practices.Also in certain cases it has been pleaded that Article 102 TFEU could serve for confronting tacit collusion.In the US, similarly, the basic requirement of an agreement or meeting of the mind complicates prosecuting cases of tacit collusion.However, the aforementioned does not mean that oligopolistic coordination cannot be subject to enforcement processes, due to the concepts of plus factors and facilitating practices.
Pricing Algorithms have many features that could be deemed as plus factors or facilitating practices; for example, if we consider that certain techniques of data collection are equivalent to pernicious information exchanges.The challenge in this regard is to adequately assess the risks and benefits that the algorithms bring to the market.We cannot forget that algorithmic pricing is an efficiency tool that has business justifications, and their presence does not necessarily mean that there is an anticompetitive aim behind them. 216ter critically analysing the different approaches to tacit collusion and its enforcement through Article 1 TFEU and §1 of Sherman Act, I consider that current regulations are fully capable of tackling potential cases of algorithmic tacit collusion, with the caveat that some cases may escape enforcement, in much the same way that certain non-algorithmic collusion scenarios do, where regulators are limited by policy considerations.Nonetheless, the interaction between algorithms and tacit collusion is a developing area, and in the future, policy makers may need to reconsider the current antitrust toolkit in order to adequately tackle misconduct. 217216 Mehra (n 104) 1362. 217Capobianco and Gonzaga (n 111) 4.
Robert C Marshall and Leslie M Marx, The Economics of Collusion: Cartels and Bidding Rings (MIT Press 2012) 213. 155