ON OPTIMAL LEGAL STANDARDS FOR COMPETITION POLICY: A GENERAL WELFARE-BASED ANALYSIS†
*We would like to thank the JIE Editor and three anonymous referees for their extremely helpful comments. Also, the participants of seminars at OFT, the Paris School of Economics, Toulouse School of Economics, CERGE-EI (Prague), Cyprus University, the University of St. Andrews and at the Conference on ‘Innovation and Competition in the New Economy,’ University of Milan, Bicocca (May 4–5, 2007) and the 3rd CRESSE Conference on ‘Competition Policy: Procedures, Institutions, IPRs,’ Anavyssos, Greece (4–5, July, 2008). We are particularly grateful to A. Fletcher, V. Korah, P. Rey, M. Salinger, D. Spector and F. Verboven for their suggestions and/or comments on earlier versions. Of course all errors, ambiguities and inaccuracies remain our responsibility. Some of the research in producing this paper was undertaken when both authors were visiting the ESRC Centre for Economic Learning and Social Evolution (ELSE) at University College London (March, 2007 and February, 2008) and the Toulouse School of Economics (November, 2007), whose hospitality we gratefully acknowledge.
We present a new welfare-based framework for optimally choosing legal standards (decision rules). We formalise the decision-theoretic considerations widely discussed in the existing literature by capturing the quality of the underlying analysis and information available to a regulatory authority, and we obtain a precise necessary and sufficient set of conditions for determining when an Economics or Effects-Based approach would be able to discriminate effectively between benign and harmful actions and consequently dominate per se as a decision-making procedure. We then show that in a full welfare-based approach, the choice between legal standards must additionally take into account, (i) indirect (deterrence) effects of the choice of standard on the behaviour of all firms when deciding whether or not to adopt a particular practice; and (ii) procedural effects of certain features of the administrative process in particular delays in reaching decisions; and the investigation of only a fraction of the actions taking place. We therefore derive necessary and sufficient conditions for adopting Discriminating Rules, as advocated by the Effects-Based approach. We also examine what type of Discriminating rule will be optimal under different conditions that characterise different business practices. We apply our framework to two recent landmark decisions – Microsoft vs. EU Commission (2007) and Leegin vs. PSKS (2007) – in which a change in legal standards has been proposed, and show that it can powerfully clarify and enhance the arguments deployed in these cases.
In its landmark decision on leegin vs. psks, of June 28th, 2007, the Supreme Court of the United States overturned a nearly century old precedent of treating Resale Price Maintenance as per se illegal under Section 1 of the Sherman Act.1 The Court, following the advice of the brief of amici curiae economists in support of the petitioners, decided that all vertical price restraints should be judged by the ‘rule of reason’2. By adopting this change in the decision rule, or legal standard, used in assessing the practice of RPM, the Supreme Court essentially ruled that in the future in the U.S.A., with the exception of hard-core (horizontal) cartels, no business practice will be treated under a per se illegality standard.
In another recent landmark case, the European Court of First Instance (CFI) delivering on September 17th, 2007, its decision on Microsoft's appeal on Microsoft vs. Commission, concurred with the Commission that Microsoft's refusal to share with its competitors interoperability information for Windows (protected by IPR's) has adverse effects on innovation and ultimately on consumers and had to be addressed by compulsory licensing. To reach this conclusion, the Commission (and the CFI) proposed and adopted a new legal standard, one that significantly alters certain aspects of the ‘exceptional circumstances’ standard for handling refusals to license IP prevailing until then3.
Needless to say, in both these landmark cases the change in the proposed legal standard has raised substantial opposition. In the Leegin case, the Supreme Court decision was taken by a slim majority of four in favour to three voting against. The American Antitrust Institute filed an amicus brief urging that the per se illegality standard be upheld, emphasizing that procompetitive uses of RPM are not common and that the harm from anticompetitive uses is relatively substantial, and in addition pointed to the greater legal uncertainty and administrability disadvantages of ‘rule of reason’4. In the Microsoft case it has also been very forcefully argued that the change in the legal standard will increase the cost of decision errors as well as, again, involving greater legal uncertainty and administrability costs5.
These two examples demonstrate that the issue of the appropriate legal standard is extremely important in competition law and policy6, and over the years it has been the subject of considerable debate. In recent years the debate has been associated with the advocacy of a more ‘economics or effects-based approach’ in Europe, that is, the advocacy of relying more on ‘discriminating rules’7 in implementing competition policy. While under a ‘per se legal’ standard, an entire class of actions is allowed or disallowed without trying to identify more carefully sub-classes of actions that might generally be harmful or generally benign, a ‘discriminating rule’ requires the competition authority to establish explicit criteria for deeming some actions to be harmful and others benign and then to investigate each case to see which of these criteria it meets. It is important to note that this approach is not exactly the same as a ‘rule of reason’ approach: while the latter (U.S.) approach also advocates the use of ‘discriminating (effects-based) rules,’ it differs from the European approach in that it goes beyond that and proposes what essentially amounts to discretionary decision-making by the authority on the basis of a ‘case-by-case’ analysis. The analysis below essentially compares per se and discriminating legal standards8.
A key background factor that has emerged in the literature on legal standards is a recognition that our economic and legal understanding will always be imperfect, and, because of both this and data imperfections, it will be impossible to measure with precision many of the important factors that will determine the likely welfare consequences of a given action. It is therefore impossible to define a precise set of conditions under which a given action will be harmful (anti-competitive) and when it will be benign (pro-competitive). Consequently any legal standard is likely to make either Type I errors (false negatives or false convictions) or Type II errors (false positives or false acquittals) or both. Following the seminal contribution of Judge Easterbrook  it has been recognized that the ‘decision theoretic’ approach9 provides a useful framework for organizing the discussion. He put forward a decision error-cost framework – proposing the idea that legal standards should minimise the sum of the welfare costs caused by decision errors of Type I and Type II10.
In applying this ‘decision theoretic’ approach it has come to be recognised that there are two important considerations to be taken into account.
- (i)The first is the fraction of harmful actions in all possible circumstances, or what is sometimes referred to as the ‘base-rate probability of anticompetitive harm.’11 Thus it has, for example, been argued that when harmful actions are very rare a per se Legality rule should be applied12.
- (ii)Secondly, ‘Decision theory (also) implies that it is not just the relative frequency of pro and anti-competitive consequences that matters to the assessment of a per se rule, but the severity of resulting harm in either case.’13
However, despite the widespread recognition of the value of the decision theoretic analysis in the optimal choice of legal standards, it suffers from at least four major shortcomings.
- 1No formal model of the optimal choice of decision rules has emerged in the literature that takes into account the above decision-theoretic considerations and relates them systematically to the underlying quality of the information and economic models/analysis available to the competition authority (CA) and to various important aspects of the CA's administrative procedure. So there is no clear test of when the effects-based analysis available to the authority is sufficiently good to enable it to effectively discriminate between harmful and benign actions and so make decisions that are better than those produced by a per se standard, thus lowering the welfare costs of decision errors.
- 2The ‘decision theoretic’ approach focuses solely on the impact of different rules on the outcome of cases coming before the authority. It ignores the indirect (or deterrence) effects caused as all firms anticipate the potential consequences of different legal standards were they to come to the authority's attention and adjust their behaviour accordingly. This has been recognised by, among others, Joskow  who argues that these indirect effects are more important than the costs of decision errors as they include the (cost of) the responses and adaptations that target firms as well as other ‘firms and markets in general make to antitrust rules ….’14.
- 3In taking account of indirect effects, it is clear that it is not just the outcomes of the CA's decisions that matter to firms, but also other procedural aspects of the CA's investigation and enforcement processes. Three important such aspects are:
- a.the fact that only a proportion of firms taking the action will be investigated by the authority – this fraction is known as the ‘coverage rate’;
- b.delays in reaching decisions;
- c.the level and structure of any penalties, reputational costs, or costs of reversing the action that a firm might face if found to have acted in an anti-competitive fashion.
- 4The above dimensions of the administrative procedure are also very important for the CA in making optimal choices between different standards. Thus a satisfactory model has to specify how these are determined – it has to specify precisely the investigation process in relation to its notification, verification and analysis aspects.
The aim of this paper is to address these weaknesses of existing analyses by providing a systematic welfare-based framework for choosing between legal standards which:
- (i)formally captures the quality of the information/analysis available to the authority in reaching an ‘effects-based’ decision, and uses this to develop an explicit test for when this is sufficiently good to enable the authority to effectively discriminate between actions that are likely to be harmful or benign, thus lowering the welfare costs of decision errors relative to per se;
- (ii)takes into account and models indirect effects;
- (iii)takes into account and models the procedural effects mentioned above.
Though our focus will be on legal standards for competition policy, it will become immediately clear that the framework we propose has far more general applicability. In particular it can be applied in many other contexts (such as those faced by sectoral regulators, environmental agencies, tax authorities, etc.) characterised by the following conditions: (a) agents are taking actions that are privately beneficial but from a wider social viewpoint may be harmful or beneficial; (b) the degree of social harm/benefit varies with the circumstances under which the action is taken; (c) the authority/regulator cannot observe the precise circumstances under which any given action is taken.
The key results/messages of the paper are as follows:
- 1There is a simple but powerful condition for determining when the quality of the information and analysis available to the authority when using a discriminating (effects-based) rule is good enough to enable it to discriminate effectively between actions that are likely to be harmful and actions that are likely to be benign, thus lowering the welfare costs of decision errors relative to per se. The test depends on comparing a measure of the quality of the analysis/models available to the authority with what we call the ‘strength of the presumption’ of legality (or illegality) which in turn depends on the two factors identified by the existing decision-theoretic approach:
- (i)The frequency of harmful actions in the overall population
- (ii)The economic harm (benefit) that arises from harmful (benign) actions.
- 2Indirect/Deterrence Effects influence the choice between ‘per se rules’ and ‘discriminating rules,’ in two ways which operate in different directions. Thus, compared to per se, ‘discriminating rules:
- a. generate (absolute) deterrence effects that are too weak for actions which are on balance harmful (‘presumptively illegal’) and so should be deterred, but are too strong in the case of actions that are on balance benign (‘presumptively legal’), and so should not be deterred;
- b. generate a differential deterrence effect whereby harmful actions are more heavily deterred than benign actions.
- 3The magnitude of Type I and Type II errors, interpreted more broadly now as the wrongful prevention of beneficial actions and the failure to prevent harmful actions, depend on the factors identified above – decision-making quality; deterrence and administration effectiveness – but in a different way for each type of error. In particular administrative errors reduce Type I errors but increase Type II errors.
- 4How one improves the quality of the information/analysis that underpins ‘discriminating rules,’ (or, alternatively, the type of ‘discriminating rule’ chosen), matters. We distinguish between ‘low-false convictions’ or ‘low-Type I errors’ and ‘low-false acquittals’ or ‘low-Type II errors’ rules. Adopting one or the other is important in two crucial ways.
- (i)By affecting the welfare cost of decision errors. For actions that are ‘presumptively legal,’‘discriminating rules’ reduce false acquittals and increase false convictions relative to per se rules. In this case, the most effective way of reducing the welfare cost of decision errors is to adopt ‘low-false convictions’ discriminating rules. Indeed only such rules will be ‘effectively discriminating’ if the presumption of legality is strong. For actions that are ‘presumptively illegal,’ discriminating rules reduce false convictions and increase false acquittals relative to per se rules. In this case, the most effective way of reducing the welfare cost of decision errors is to adopt ‘low-false acquittals’ discriminating rules. Indeed only such rules will be effectively discriminating if the presumption of illegality is strong. When the presumption of legality (illegality) is not strong, both ‘low-false-convictions’ and ‘low-false-acquittals’ rules can be equally effective in reducing costs of decision errors: purely decision theoretic considerations are then not very helpful in choosing between alternative discriminating standards.
- (ii)By affecting deterrence. The impact of ‘low-false convictions’ and ‘low-false acquittals’ rules on deterrence effects is different. For ‘presumptively legal’ actions, reducing false convictions unequivocally improves deterrence effects and raises welfare, while reducing false acquittals may actually worsen deterrence effects and lower welfare. For ‘presumptively illegal’ actions it is not possible to make unequivocal predictions about the effect of reducing false convictions or false acquittals on deterrence.
We proceed as follows. In Section 2 we set out our model and in particular we describe our assumptions on the economic context and on the investigation and enforcement procedure followed by the authority. We also examine how firms' decisions are affected by the authority's analysis, decisions and procedures. In Section 3, we provide a welfare comparison of ‘discriminating’ and ‘per se rules’ and between various types of ‘discriminating rules.’ We start with a comparison to the first best that allows us to define clearly the various errors involved in the use of any given decision rule. Next, we provide a decision-error comparison that allows us to establish a central result that determines when a ‘discriminating rule’ produces lower costs of decision errors than a per se rule. We then turn to a full welfare comparison of different rules. In Section 4 we provide some extensions and then in Section 5 we outline a methodology for applying our framework to the choice of legal standards for handling specific business practices under competition law and provide a brief application to the cases of Leegin and Microsoft15– for both cases we identify a number of errors or inaccuracies in the arguments of both the proponents and the critics of the decisions. Section 5 provides conclusions and suggestions for future research.
II. THE MODEL
II(i) The Economic Context
There is a population of firms, whose size is normalised to 1, who could potentially take an action. If a firm does take the action there is a possibility that this could become the subject of an investigation by a CA, which could disallow it and could then require the firm to reverse it and/or impose a penalty. Anticipating this, firms have to decide whether or not to take the action.16
If there were no intervention, the action would confer on the firm taking it a positive private benefit which we take to be the present value of the expected change in profits from the action over its ‘natural’ lifetime17. Let b>0 denote the benefit accruing to a typical firm. However, the action can also cause wider social harm, which we take to be measured by the negative of the present value of the change in consumer surplus. The extent of the harm caused by any firm will depend on its environment, which encompasses various characteristics of both the firm and of the markets in which it operates. For simplicity we assume that there are just two environments – Harmful and Benign – and that if the action is taken by a firm from the harmful environment it will generate harm hH>0 – while if the action is taken by a firm from the benign environment it will generate harm hB<0 – i.e. will be socially beneficial. Let the fraction of firms in the underlying population of firms who could take the action that comes from the harmful environment be γ, 0<γ<1. We assume that the values of γ, hH and hB are common knowledge, as is therefore the value of average harm/benefit . We will say that the action is presumptively legal if and presumptively illegal if .
In principle, the distribution of private benefits could be different in each of the two environments, reflecting, inter alia, a positive or negative correlation between private benefit and social harm. In general there is no reason for presuming one correlation or the other, though, in specific contexts, it may be appropriate to do so. Accordingly we will initially impose the symmetry assumption that the two distributions are identical, and discuss in Section 4 how our conclusions are affected when this assumption is dropped. So we suppose that the private benefit has a positive continuous probability density f(b)>0 on [0, ∞), with cumulative distribution function .
II(ii). The Investigation Process
We assume that if the CA uses a ‘per se legal’ decision procedure under which all actions are allowed, then no actions are investigated. Under all other decision procedures the CA will ban at least some actions, and can do so only if there has been some process of investigation, which involves a number of stages.
Stage 1. Notification and Verification We assume that a fraction π, 0π1 of firms who have taken the action come to the attention of the CA and that these represent a random sub-sample of the population of firms taking the action. In Section 4 we will consider this assumption more fully. We refer to π as the coverage rate.
Before taking any decision the CA must first verify whether or not the firms coming to its attention have indeed taken the action. We assume that the CA can do so accurately. Under a ‘per se illegal’ procedure, decisions are made solely on the basis of the nature of the action, so once it has been verified that the firm has taken the action, the action will be banned and this will be the end of the investigation process. We recognise that this might take some time, so there will be a delay in reaching a decision. We capture this delay by assuming that under a ‘per se illegal’ process, firms taking the action will get a fraction of their private benefit before the action is terminated, while society gets the corresponding fraction of the harm/benefit.
Stage 2. Analysis
If the CA operates a ‘discriminating’ decision rule, then it will try to form a view about the likely effects on welfare of any action it investigates before deciding whether or not to disallow it. The CA does not know from which environment an action has come, so has to use whatever information and data it can gather, and applies to this a variety of tests and analytical techniques as a result of which it puts the action in one of just two categories:
- a.on balance likely to be welfare increasing (potentially benign);
- b.on balance likely to be welfare reducing (potentially harmful).
We assume that under a ‘discriminating rule’ it allows all actions in the first category and disallows all actions in the second.
Of course the data, tests and analysis available to the authority will typically be imperfect and lead it to classifying some genuinely harmful actions as potentially benign and some genuinely benign actions as potentially harmful. So we let be the probability of correctly identifying the environment from which an action has come. In the following, the quality of the information/analysis available to the CA is characterised by the two parameters (pB, pH). We will refer to (pB, pH) as the CA's model.
If pB=1−pH then the probability of an action's being classified as potentially harmful or benign is exactly the same whatever environment it comes from, and the CA's model has no discriminatory power. If pB=1; pH=1 then the CA's model allows it to identify perfectly the environment from which any firm taking the action comes. In the more general case where but , then firms from, say, the benign environment are more likely to have their actions classified as welfare increasing (potentially benign) than are firms from the harmful environment, so the CA's model has genuine discriminatory power.
In many cases there will be a range of models available to a CA, but we suppose that at any given time the CA uses the best model available to it and that this is reflected in (pB, pH). We identify an ‘economics/effects based’ approach to competition policy as one that employs such a ‘discriminating rule.’
Now, as noted by Ehrlich and Posner , the choice between decision rules ‘affects the speed, and hence indirectly the costs and benefits, of legal dispute resolution…’18 To capture this idea, we assume that if the authority disallows the action under a discriminating rule procedure, then the firm gets only a fraction of the private benefit b– and society gets the corresponding fraction of the harm/benefit. Since a discriminating rule requires both verification plus analysis while a ‘per se illegal’ procedure requires only verification, it follows that a discriminating rule has a longer litigation cycle and so .
Finally, as also emphasized in the literature,19 there are costs involved in collecting and analysing the information needed to form the judgments necessary to implement a discriminating rule – costs that would not be incurred under a per se rule. So a discriminating rule should only be chosen in preference to a per se rule, if any welfare advantages it has from all other respects are sufficient to outweigh these additional costs. However, since this point is well understood and we have nothing new to add, in what follows we will simply ignore these costs.
Stage 3. Enforcement
If an action is investigated and disallowed, then there are two possible consequences for the firm: it may have to pay a fine/penalty and it may have to reverse the action which could cause significant costs20. We capture both of these by assuming that if a firm's actions are disallowed, it has to pay a fine f>021.
II(iii). Firms' Decisions
In deciding whether or not to take an action, firms anticipate the possibility that they might be investigated and that, if investigated, the action may be disallowed, possibly after a delay, and, if disallowed, have to pay a fine. We assume that firms know:
- •the environment e=H, B from which they come22;
- •what type of decision rule the CA employs;
- •if the CA uses a discriminating rule, the quality of the model (pB, pH);
- •the coverage rate π;
- •the delay factors ;
- •the fine f.
Now, generically, we can think of any decision rule/procedure being characterised by the four parameters where:
- •ρ, 0ρ1 is the risk of being investigated;
- •δe, 0δe1, e=B, H is the probability that, if investigated, a firm from environment e will have its action disallowed;
- •is the delay in reaching a decision.
From the above discussion it follows that a ‘per se legal rule’ is characterised by r=(0, 0, 0, 0); a ‘per se illegal rule’ by r=(π, 1, 1, φPSI); and a ‘discriminating rule’ by r=(π, pH, 1−pB, φD).
For any given rule, the expected value of profits of a firm with private benefit b that comes from environment e will be
A firm will take the action if the expected value of profits is positive, i.e. if
Consequently the fraction of firms from environment e who will be deterred under a generic rule will be
Given (2) and Definition 1 above, it follows that, in an obvious notation:
There are two important features of this result:
- (i)Under ‘per se’ rules, the deterrent effect is the same for firms from each of the two environments, while under a discriminating rule there is a differential deterrence effect whereby the fraction of firms from the harmful environment that is deterred is greater than for firms from the benign environment.
- (ii)A discriminating rule generates greater deterrence than a per se legal rule but weaker deterrence than a per se illegal rule, and the latter for two reasons: (a) there is a smaller risk of having the action disallowed; (b) the decision will take longer to reach.
III. WELFARE COMPARISON OF THE RULES
Social welfare under any generic rule arises from the harm or benefit caused by the actions actually taken. So it is generated by firms that choose to undertake the action and either do not come to the attention of the authority, or, if they do, do not have their actions disallowed, or, if they are disallowed, there is a delay before the action is curtailed. In short it arises from the fraction of actions not deterred and not detected and not disallowed. It is easy to see that formally this implies that social welfare is:
This enables us to undertake two comparisons. We can first compare welfare under any generic rule with welfare in the first-best, and show how the resulting welfare loss can be decomposed into Type I and Type II errors, though, as we will see, these now have to be more widely understood than in the conventional decision-theoretic approach. Then we undertake a comparison between per se rules and discriminating rules and show when one decision rule welfare-dominates the other.
III(i). Comparison with the First Best
A first-best decision procedure is characterised by
- •perfect administration: all firms are investigated and decisions are instant –;
- •perfect discrimination: ,
which, from (2) and (3), implies that none of the benign actions are deterred while all of the harmful ones are, i.e.
Substitute these values into (5) and we see that welfare in the first-best is just that arising from benign actions: namely
Now any given rule will differ from the first best in terms of (i) its administrative effectiveness – coverage rate and delays in decision making; (ii) decision-making effectiveness – ability to correctly identify firms from each environment – and consequently in its deterrence impact. It follows that Type I and Type II errors have to be defined more widely than in the traditional decision-theoretic theoretic approach as:
- •Type I – erroneously preventing benign actions;
- •Type II – failure to prevent harmful actions.
Type I errors can arise by: erroneously deterring firms who should take the action, investigating too high a fraction of the remaining firms who do take it and then mistakenly disallowing the action of some of these and moreover, doing so too quickly. Type II errors arise by erroneously failing to deter enough actions; not investigating a high enough fraction of those firms who do take them, while for those who are investigated, either failing to disallow the action or taking too long to do so. So they arise through a combination of administrative, decision and deterrence effects. But it is clear from this discussion that administrative considerations affect Type I and Type II errors in completely the opposite way.
To examine this formally, we first measure the deviation between a generic rule and the first best in terms of these three dimensions as:
where we have combined the coverage rate and delay in decision-making into a single measure of administrative effectiveness:
which is higher the greater the likelihood of investigation and the shorter the delay in reaching a decision. Notice that in first-best .
By subtracting (5) from (7) the overall welfare loss from a generic rule is
is the welfare loss arising from Type I errors, and
is the welfare loss from Type II errors.
Consequently, as we argued above, Type I and Type II losses no longer depend on just decision errors – they also depend on deterrence errors and administrative errors, and reduce to decision errors only in the case where there is no deterrence – so – and perfect administration (Δa=0). While the welfare losses from both types of error are increasing functions of both decision and deterrence errors, the welfare loss from Type I errors, LI is a decreasing function of the administrative error, Δa, because failing to detect and rapidly disallow benign actions is a bonus, while welfare loss from Type II errors, LII, is an increasing function of administrative error Δa, because the failure to investigate and stop harmful actions rapidly enough is a cost. Finally, the way in which administrative, decision and deterrence effects combine to give the overall error varies significantly depending on whether we are dealing with Type I or Type II errors. Type I losses are zero if either both the deterrence error and the decision error are zero or if the deterrence error is zero and the administrative error is unity, whereas Type II losses will be zero if either there is no deterrence error (because if there is no deterrence error then no one takes the action and so the other errors are irrelevant) or if both the decision error and the administrative error are zero – because then no one is allowed to take the action and it doesn't matter how many people try to (though none will).
III(ii). Comparison of Discriminating Rules with Per Se Rules
We now undertake a full welfare comparison between per se and discriminating rules. Given our characterisation of per se rules and Lemma 1 it follows from (5) in an obvious notation that:
It is useful to begin by first establishing a central result that determines when a ‘discriminating rule’ produces lower decision error costs than a per se rule.
III(ii)(i). Decision-Error Comparison of Discriminating vs Per Se Rules In order to compare different rules purely in terms of their decision making ability (i.e., unaffected by any differential deterrence effects they might have) we consider the action of a firm picked at random from the underlying population of firms and ask what would be the Cost of Decision Errors (CDE) that would be generated if this were considered by the CA under both a per se and a discriminating rule. If the cost of decision errors for a discriminating rule is lower than under a per se rule we will call it an ‘effectively discriminating rule.’
To understand when this might arise, it is useful to consider separately actions that are presumptively legal and those that are presumptively illegal.
For a presumptively legal action expected harm is negative – i.e., – which implies that , where sL is what we call the ‘strength of presumption of legality.’sL provides a measure of how far an action is from being borderline legal/illegal which, unlike , is independent of the absolute magnitudes of the harm (hH>0) and benefit (−hB>0) caused by the action. Notice that the strength of presumption of legality depends on all the factors that have been identified in the existing literature as being relevant to decision as to whether or not to use per se rules – base-line probability of anti-competitive harm, and the magnitudes of the associated harm and benefiit.
Now the costs of decision errors under per se legality and a discriminating rule are, respectively,
Thus if and only if:
where qH is a measure of the quality of the model available to the authority which reflects its relative propensity to classify as welfare-reducing (potentially harmful) actions that are genuinely harmful and actions that are genuinely benign.
By an analogous argument, if an action is presumptively illegal, , and if and only if:
where qB is a measure of the quality of the model available to the authority that reflects its relative propensity to classify as welfare-increasing (potentially benign) actions that are genuinely benign and actions that are genuinely harmful, and sI is the strength of the presumption of illegality. So we have established:
A necessary and sufficient condition for a discriminating rule to be able to ‘effectively discriminate’ and so give lower decision error costs than a per se rule is that the quality of the rule is greater than the strength of the presumption of legality (for a presumptively legal action) or illegality (for a presumptively illegal action).
An important implication of Proposition 1 is that even though there is a clear sense in which a discriminating rule incorporates a degree of legal uncertainty that is absent from a per se rule provided the discrimination is effective the discriminating rule will still be superior to a per se rule. Put differently it is better to be uncertainly right than certainly wrong25.
To ensure that a discriminating rule can effectively discriminate it is necessary to raise its quality, and it turns out that there are clear predictions as to how this is best done. Consider again a presumptively legal action and notice that it follows from (15) that
Moreover if a discriminating rule does not effectively discriminate, and so, from (15),
then, if the strength of the presumption of legality is sufficiently high it may be that even if the CA could eliminate all false acquittals – thus making pH=1 – we may still have
and so the discriminatory rule is still unable to effectively discriminate.
Analogous results hold for the case of a class of actions that are presumptively illegal. Thus we have established:
Proposition 2. (i) If an action is presumptively legal, then the most effective way of ensuring that a discriminatory rule can effectively discriminate is by reducing false convictions – increasing pB. Indeed in some circumstances this is the only way of achieving effective discrimination.
(ii) If an action is presumptively illegal then the most effective way of ensuring that a discriminatory rule can effectively discriminate is by reducing false acquittals – increasing pH. Indeed in some circumstances this is the only way of achieving effective discrimination.
III(ii)(ii). Full Welfare Comparison of Discriminating vs Per Se Rules Let us now turn to a full welfare comparison of the two types of rule. Since the relevant per se rule is different depending on whether the action is presumptively legal or presumptively illegal the precise formula is somewhat different in the two cases, though the elements are precisely the same. If we substitute all the relevant variables for a discriminating rule into (8) and compare to (13) and (14) we get the following results.
- (i)If the action is presumptively legal then:
- (ii)If the action is presumptively illegal then:
From the RHS of these expressions26 we can see that the welfare difference between a discriminating rule and a per se rule comprises three separate terms.
The first is the decision error difference between the two rules. The term in square brackets is positive if and only if the quality of the CA's model enables it to effectively discriminate (inequalities (15) and, respectively, (16), hold), and is larger the better is the quality of the rule. Note that the magnitude of this term is modified by the fact that only a fraction of firms take the action and for these the administration is imperfect.
The second term is the (absolute) deterrence difference between the two rules and is always negative – i.e., per se is welfare superior to a discriminating rule27. This is because a discriminating rule has too strong a deterrence effect when the action is presumptively legal and so is on balance benign, while it has too weak a deterrence effect and is too slow in reaching a decision for actions that are presumptively illegal and so are on balance Harmful.
The third term is the differential deterrence effect and is always positive. This reflects the fact that the discriminating rule has a greater deterrence effect on harmful actions than on benign actions – a feature not shared by a per se rule.
One immediate consequence of this decomposition is the following:
Proposition 3. Ceteris Paribus, if the strength of the presumption of legality/illegality is weak then discriminating rules will be welfare superior to per se rules.
Proof. There are two implications of the fact that the strength of the presumption of legality/illegality is weak. The first is that the discriminating rule will be able to effectively discriminate and so will have lower decision error costs than a per se rule – see Proposition 1. So the first term on the RHS of (18) and (19) will be positive. Secondly will not be significantly different from zero, and so the absolute deterrence difference – the second term on RHS of (18) and (19)– will be approximately zero. Since the differential deterrence effect is always positive, the result now follows.
As already indicated in Proposition 2 above, increasing pB can have a markedly different impact on the decision-making quality of a discriminating rule than increasing pH, i.e., how one improves a discriminating rule can matter greatly. We can extend this discussion by examining the effects of increases in pB and pH on the welfare difference between a discriminating rule and a per se rule and hence on the choice between them.
If we start with a presumptively legal action then, from (18) we see that an increase in pB has two effects: (a) it reduces decision errors on firms from the benign environment, and (b) it reduces the number of firms from the benign environment who are deterred. This second effect in turn has three effects: (i) it increases the population of firms for whom the difference in decision error costs between the two rules matters; (ii) it reduces the loss from the absolute deterrence effect; (iii) it increases the differential deterrence effect. The first of these three effects is positive if the discriminating rule can effectively discriminate. On the other hand increasing pH has three effects: (a) it reduces decision errors on firms from the harmful environment; (b) it increases the number of firms from the harmful environment that are deterred – but this has just the one effect of increasing the differential deterrence effect; however (c) it reduces the population of firms for whom the differential deterrence effect matters. Formally
Because the action is presumptively legal, the decision error effect (a) – the first term on the RHS of (20) and (21)– is greater for increases in pB than for increases in pH. If the increase in pH had more or less the same impact on the differential deterrence effect as the increase in pB– i.e. if – and if the discriminating rule could effectively discriminate, then the second term on the RHS of (20) would also be greater than that in (21). So we have proved:
Proposition 4. For presumptively legal actions, if a discriminating rule is effective then:
- (i)Reducing false convictions (increasing pB) will unambiguously increase welfare from the discriminating rule relative to that from per se:
- (ii)Moreover if an increase in pH has more or less the same impact on the differential deterrence effect as an increase in pB, then reducing false convictions (increasing pB) increases welfare from using the discriminating rule relative to that from using per se by more than reducing false acquittals (increasing pH):
- (iii)Indeed reducing false acquittals may actually lower the welfare from using the discriminating rule relative to that from using per se.
Note that while Proposition 4 gives sufficient conditions for (22) and (23) to hold, it is clear from (20) and (21) that they will hold in a much wider class of cases.
It turns out that there are no such simple predictions for the case of presumptively illegal actions. In part this is because now the relative impacts on decision error costs get reversed, and in part because of the greater complexity of the expression for the absolute deterrence effect in (19). Any comparison therefore depends on a balancing of many effects going in different directions.
IV. SOME EXTENSIONS
In this section we discuss more fully the justification for some of the key assumptions of our model and the potential implications of dropping them.
IV(i). The Symmetry Assumption
The model presented so far incorporates the symmetry assumption that the distribution of private benefits is the same whether firms come from a harmful or benign environment. In general of course this will not be true and the distribution of private benefits from the harmful environment FH(b), will be different from that for firms from the benign environment, FB(b). In many contexts, however, the CA might have no robust empirical evidence to tell it how the two distributions differ, and so, on the principle of insufficient reason, the only reasonable assumption for it to make is that they are identical. Nevertheless, it is important to understand how our conclusions will be affected when we explicitly recognise that the two distributions are different.
Now whilst having two different distributions will mean that the precise magnitude of some of the effects discussed above could differ, it is clear from (18) and (19) that the only qualitative feature of our analysis that could be affected is the sign of the differential deterrence effect.
So now let where is, as before, the critical level of private benefit above which firms from environment e will take the action under a discriminating rule. Notice that these critical values are completely unaffected by the fact that there are now two different distributions of private benefit. We can decompose the difference between and into that arising through the fact that and that rising from the fact that the two distributions are different:
The first term on the RHS of (24) is still positive. So to overturn the sign of the differential deterrence effect, the second term will have to be negative, and moreover sufficiently negative to dominate the first term. So we can establish:
Proposition 5. The differential deterrence effect will be negative if and only if there is a sufficiently strong positive correlation between private benefit and social harm.
Corollary 2. If there is a strong positive correlation between private benefit and social harm, then, ceteris paribus, there is a stronger presumption in favour of using a per se rather than an effects based approach.
IV(ii). The Coverage Rate
In the model, we assume that a fraction, π, of the firms taking the action come to the attention of the CA and that these constitute a random sub-sample of that population. A number of inter-related considerations need to be addressed in relation to this.
The first concerns the nature of the ‘action’ we have in mind here. Clearly, for the distinction between ‘effects-based’ and ‘per se’ to be meaningful, ‘actions’ should not be defined too broadly (e.g., ‘agreements between undertakings’ or ‘mergers’) otherwise the assessment procedures adopted will always be ‘effects-based.’ Also, actions should not be defined too narrowly in terms of their formal characteristics and the context in which they take place (e.g., exclusive distribution agreements with a specific set of non-compete and other obligations by firms with specific product, market share and other market characteristics) otherwise the assessment procedures adopted will tend always to be ‘per se.’
Secondly, although there are a number of ways in which actions might come to the attention of authorities – there could be third-party reports, firms could be required to report their actions, the CA could select firms for investigation – in practice, in order to use resources effectively, the CA will always use some kind of screening procedure whereby the authority undertakes an initial check on the action and then, for a sub-population that meets certain criteria will take an action (allow or disallow) in a per se fashion while it remits the remaining sub-population for further investigation (i.e., essentially takes an effects-based approach).
We can think of our analysis as asking for each of these sub-population whether the chosen per se or an effects-based approach is right. We can then allow for the coverage rate from each sub-population to be different, and it is then less unreasonable to assume that the sub-sample investigated is a random sub-sample of the sub-population. Of course, a full analysis would endogenise the choice of the first screen by the authority. This would involve a multi-stage/multi-criteria decision framework, an extension that is it at the top of our research agenda with a first step contained in Katsoulacos & Ulph [2009b].
IV(iii). Assumption that Firms Know Their Type
In the model, we assume that firms know their type – i.e., whether their actions are harmful or benign. In many cases it may be reasonable to assume that firms do not know this. This assumption implies that firms perceive a common probability of having their action disallowed if investigated, equal to i.e., equal to the frequency with which actions are disallowed by the CA28. In this case , so the differential deterrence effect is zero. Whenever this is true, an ineffective discriminating rule will be welfare inferior to per se, while an effective discriminating rule will be welfare superior to per se only if it is so much better in reducing decision error costs than per se that the improvement in decision errors is large enough to compensate for the negative (absolute) deterrence effect.
V. APPLYING THE FRAMEWORK
The following methodology is suggested for applying the framework set out in the previous sections to the choice of legal standard for the handling of specific business practices for competition policy purposes.
- 1The first step is to examine whether actions associated with the practice should be considered as presumptively legal or presumptively illegal and to establish the strength of the presumption in either case. This would involve examining what economic theory tells us regarding how often actions are likely to be anticompetitive and about the potential harm/benefits of anticompetitive/precompetitive actions29. Note that if the practice under consideration contains more than one category of potential action and for each of these it is considered that the strength of the presumption of (il)legality is very different, then that indicates that the practice is too widely defined and that a potentially different legal standard should be considered for each action category30.
- 2If the presumption of legality (illegality) is considered very strong then the second step is to establish whether economic theory can nevertheless suggest effectively discriminating rules. Our analysis in Proposition 2 indicates that, in the first case, these must be very ‘low-false-convictions’ rules, while in the second case these must be very ‘low-false-acquittals’ rules31. Further, our analysis indicates that the existence of such rules is a necessary condition for discriminating standards being welfare superior to per se (unless differential deterrence affects are very large).
- 3If the presumption of legality is not very strong then, effectively discriminating rules are likely to exist and to be welfare superior to per se rules since they reduce substantially the cost of decision errors (Proposition 3). The important issue then becomes which is the optimal discriminating rule. To answer this, we must explore first whether theory suggests both ‘low-false-convictions’ and ‘low-false-acquittals’ rules that can be equally (or almost equally) good in reducing costs of decision errors. If this is the case then the optimal discriminating rule will be the one that produces the best deterrence effects. If the action is presumptively legal then ‘low-false-convictions’ are most likely to generate the best deterrence effects (Proposition 4).
V(i)(i). Leegin vs. PSKS (2007) In this case the U.S. Supreme court decided that the lower court was wrong to adopt a per se illegality standard to deal with RPM and remanded the case to be re-examined under ‘Rule of Reason,’ thus overturning nearly a century-old tradition.
However, certain aspects of the decision are characteristic of the incomplete assessment of the factors relevant to the choice of decision rules that the lack of a formal model can cause. Thus it is argued (p. 3) that ‘A per se rule should not be adopted for administrative convenience alone. Such rules can be counterproductive, increasing the antitrust system's total cost by prohibiting procompetitive conduct the antitrust laws should encourage.’ While this statement is correct, as the model above shows, one cannot judge the relative appropriateness of a rule solely on the basis of its relative rate of false convictions. Indeed, all discriminating rules will lower the rate of false convictions relative to per se illegality, though it may well be that none of these reduces the total cost of decision errors – i.e., it may well be that none of these discriminating rules is effectively discriminating. This is more likely to be so in the the case of RPM if the presumption of illegality of this practice is quite strong.
Consider an illustrative example. First, despite the Supreme Court's decision, it may nevertheless still be safe to assume that most economists would consider the practice of RPM as presumptively illegal, i.e., one for which . For example, while Vickers  argues that it is ‘hard to see how per se treatment of RPM is justified in economic logic,’ he declares himself ‘no great fan of RPM’32. If this is true, a discriminating rule would be effective and thus superior to per se illegality in minimising the cost of decision errors if . Though those arguing for a PSI rule would propose that the value of γ is very large, assume for the sake of argument, and given what recent advances in economic theory suggest33, that quite a large proportion of RPM cases (about one third) is benign, or that γ=0.7. Also, let the gain from disallowing a harmful action be just one and a half times as large as the loss from wrongly convicting a benign action. The latter can be justified as harmful RPM acts are likely to be associated with collusive horizontal practices. Then the presumption of illegality (at 3.5) exists but is not very strong.
Coming to the quality of models that a CA can use to discriminate, critics of the decision, such as Judge Breyer, have pointed out (p. 8–10) that given available evidence it is very difficult to recognise when an RPM practice might be on balance benign (i.e., that pB is very low). But again, for the sake of argument, assume that pB=0.5. Even under these conditions there would still be no effectively discriminating rule as long as pH0.86. That is, our models, criteria and empirical evidence must be sufficiently good that we can correctly classify harmful RPM actions as harmful in at least 86% of the cases examined in order for a discriminating rule to be able to effectively discriminate and so be superior to per se in decision error terms.
And even this is not enough for the discriminating rule to be welfare superior. To see this, note that a low pB value suggests that a large fraction of benign actions will be deterred by the discriminating rule ( will be large). This, plus the greater delay entailed by using a discriminating rule, can greatly mitigate the decision error advantage of the rule (reducing the effect of the first term on the RHS of (19)). If, also, the differential deterrence effect were sufficiently small and thus dominated by the absolute deterrence effect of the discriminating rule, then even without taking into account its higher implementation costs it seems highly unlikely on the basis of the analysis provided in this paper that an effects-based approach – which is at the heart of ‘rule of reason’– would be the optimal rule.
V(i)(ii). Commission vs. Microsoft (2007) In the Microsoft case the Commission has been criticized for altering the legal standard for dealing with refusals to license IPR's. Specifically, Ahlborn, Evans and Padilla  have argued that the ‘exceptional circumstances’ decision rule that was adopted in previous cases such as Magill  and IMS Health  is superior to the new rule34. They identify a number of differences between the two rules in terms of the criteria that need to be satisfied for establishing that refusal is abusive35. Perhaps the most novel aspect of the new rule concerns the part dealing with ‘objective justification.’ In the new rule the Commission suggests that this should be based on ‘an incentives to innovate for the whole industry’ test. While the ‘exceptional circumstances’ test is, in our terms, a ‘low-false-convictions’ rule, the Commission proposed a rule that lowers the likelihood of false acquittals – a ‘low-false-acquittals’ rule.
Now, economic theory suggests that refusals to license IP rights are on average benign, and thus presumptively legal, taking into account both long-run and short-run considerations36. However, as the opposing views of the contributions by Ahlborn et al.  and Ritter  suggest, this presumption is not unequivocally accepted as being very strong.
Our analysis suggests that if the presumption of legality is quite strong, the optimal type of discriminating rule will be a low-false-convictions rule such as EU's ‘exceptional circumstances’ one: it is most effective in reducing the cost of decision errors and generates optimal deterrence effects. However, even such a discriminating rule may be welfare inferior to per se legality if the presumption of legality is very strong: the latter should then be adopted, as the U.S. authorities did in Xerox .
If, on the other hand, the presumption of legality is not strong – the Commission's point of view regarding interoperability information in Microsoft, endorsed recently by the CFI – then as we have seen above, both ‘low-false-convictions’ and ‘low-false-acquittals’ discriminating rules are likely to be welfare superior to per se legality. Comparing these two types of discriminating rule, and contrary to what Ahlborn, Evans and Padilla  suggest, the ‘low-false-acquittals’ standard adopted by the Commission in Microsoft is not necessarily inferior to the ‘low-false convictions’‘exceptional circumstances’ test in cost of decision errors terms. The latter is, however, likely to be the optimal discriminating standard in welfare terms. The reason is that, as shown above37, ‘low-false-convictions’ rules generate optimal deterrence effects for presumptively legal actions while ‘low-false-acquittals’ rules may actually reduce welfare due to their deterrence effects.
VI. CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH
This paper provides a systematic formal welfare-based analysis for choosing legal standards taking into account and modelling decision error, deterrence and procedural considerations, with potential applications in a variety of regulatory contexts. It is motivated by a number of very important recent competition decisions in U.S. and the EU questioning established legal standards, and by the emphasis that has been placed in recent years by academics, policy makers and practitioners on the use of a more effects- or economics-based approach in competition policy.
An important general policy lesson of our analysis is that due to the lack of a systematic framework for comparing legal standards, in practice there could be cases where CA's may be using the wrong standard. Thus they could be using discriminating rules when in fact they should be using per se rules and vice versa. Another important general implication that emerges once procedural aspects of the investigation process are taken into account, aspects which are likely to vary between institutions/countries, is that it will not be wise to assume that the same legal standard is always optimal irrespective of the context in which or of the institution by which it will be applied.
There are a number of important directions for future research.
First, as discussed in section 4, it is important to extend the analysis to look at the use of multi-criteria/multi-stage decision rules that combine elements of both per se and effects-based approaches.
Second, as with all the literature, we have focused on a single action and so have implicitly assumed that if a firm is deterred from taking this action it does nothing at all. Of course firms can take other substitute actions which could themselves be subject to oversight by a competition authority. This could include taking the same action in a different jurisdiction. This raises interesting questions about the appropriate design of a portfolio of decision rules.
Thirdly a number of writers have argued that CA's should use a total welfare standard – e.g., Carlton – and it is important to extend our framework to consider the implications of doing so.
1 Supreme Court of U.S.A. ‘Leegin vs. PSKS Inc.’ Decision No. 06-480, June 28th, 2007.
2 Ab.cit. p. 1.
3 See for example J. Killick  and Ahlborn et al. .
4 See for a summary Vickers , p.10.
5 See Ahlborn et al.  and Killick . For opposing views see Ritter  and Leveque .
6 As it is in many other contexts - see also below.
7 See for example, EAGCP Report , Vickers [2005, 2007b] and for an early analysis Markham . Vickers [2007b] is the only author that we are aware of that makes the distinction between an economics-based and a ‘case-by-case’ approach. Quite often expressions such as ‘rebuttable per se (il)legality,’‘modified per se (il)legality,’‘structured rule of reason,’ and ‘rule of reason,’ are used in the literature to refer to different types of discriminating rules.
8 Discretionary decision-making on the basis of ‘case-by-case’ analysis raises very interesting issues of deterrence and legal uncertainty that are dealt with in a companion paper (Katsoulacos and Ulph [2009a]).
9 See for example Hylton and Salinger , Hylton and Salinger , Ahlborn et al. [2004, 2005] and Salinger .
10 See also Beckner and Salop , Tom and Pak , Joskow , and related analyses on legal standards, enforcement procedures and applications by Evans and Padilla [2004, 2005], Hylton and Salinger , Ahlborn, Evans and Padilla , A. Christiansen and W. Kerber , Salinger . Immordino and Polo  and Sørgard  also consider deterrence effects.
11As Whinston  mentions, ‘the justification of the per se rule is really nothing more than an application of optimal statistical decision making.’
12 Vickers, ab.cit. p.4, quoting Easterbrook in U.S. Court of Appeals case Schor vs. Abbott Labs.
13 Vickers, ab. cit. p.10.
14 Page 98.
15 For an extensive application to Microsoft see Katsoulacos .
16 Note that this is an ex-post investigation process: firms first take the action and then the CA may undertake an investigation. An alternative decision process involving ex ante intervention by the Competition Authority is a prior clearance process whereby all firms contemplating taking an action (e.g., to merge) have to get prior approval before proceeding.
17 This captures the idea that firms operate in a changing environment and that an action taken at a particular time might be modified or even reversed at some later date.
18 Page 265-6.
19 For example, Christiansen et al.  p. 223/224, 231.
20 These include many sunk costs involved in implementing an action potentially including R&D costs, costs in unbundling products, rearranging contractual commitments, modifying price lists, as well as the managerial effort involved in redirecting the firm's strategy. Such costs can be quite substantial as they may involve difficult to reverse technological, marketing and/or other contractual commitments.
21 In practice, CA's impose fines on the basis of imperfect criteria related to revenue or profit which are likely to bear little relation to the amounts suggested by the literature on optimal fines. Wils  discusses the possibility of estimating optimal fines. Commissioner Kroes'speech on ‘Developments in Competition Policy in 2006’ of 20/3/2007 gives an indication of the current emphasis on the deterrent effects of fines.
22 Katsoulacos and Ulph  provide an analysis where this assumption does not hold.
23 Clearly under PSL the only costs are cost of false acquitalls (CFA) – i.e., costs of Type II errors – while costs of Type I errors (costs of false convictions (CFC)) are zero.
24 The first term on the RHS is the cost of Type II errors and the second term the cost of Type I errors with a discriminating rule.
25 In Katsoulacos & Ulph [2009a] we formalise this idea and explore a second notion of legal uncertainty which can affect the choice between per se and an effects based approach.
26 There are alternative ways of decomposing the welfare difference between per se and discriminating rules. For example (18) can also be written as:
The first term on the RHS captures the difference in decision error costs between a discriminating rule and a per se rule for the population of firms taking the action under the discriminating rule. The second term is negative and captures the welfare loss arising because a discriminating rule falsely deters some benign action, while the third term is positive and captures the welfare gain from using a Discriminating Rule because it deters some harmful actions. However, while this might seem like quite a natural decomposition, the problem with this approach is that steps taken by the CA to improve its decision rules – by increasing pB and/or pH– can sometimes make the cost of decision errors as measured this way grow because of the differential impact of these changes on the deterrence effects for harmful and benign firms. This is a feature of the approach taken to measuring decision errors adopted by Sørgard . The decomposition we provide separates out deterrence and decision issues more cleanly.
27 This is true for both (18) and (19) given and (4).
28 See Katsoulacos & Ulph  for an analysis based on this. The assumption that firms do not know whether their action is socially benign or harmful may be reasonable for many unilateral practices, such as refusal to license IP, the implications of which, for welfare, depend on a very complex weighing of anticompetitive and precompetitive effects.
29 See also Salinger – who advocates a decision theoretic approach and stresses taking into account these considerations. As he notes ‘No one seriously supposes that we can objectively measure all of these factors. In particular, there is no practical way to take a random sample of instances of a particular practice … and assess the relative frequency of … anticompetitive instances. Still, any policy implicitly rests on judgments about these factors, so it is useful to form subjective estimates of the answers when objective measures are not available.’ See also his paper with Hylton .
30 A good example may be that of refusals to license IPRs' when IPRs' are defined as encompassing patents, copyrights, trademarks and data/information subject to protection as trade secrets.
31 Note that minimising false convictions (resp. acquittals) would require putting very high thresholds on showing that an action is not benign (resp. harmful).
32 Ab.cit. p. 11. The views of Comanor and Scherer mentioned by Vickers [2007a; footnote 20] are also consistent with this interpretation.
33 See for example the Supreme Court of U.S.A. ‘Leegin vs. PSKS Inc.’ Decision No. 06-480, June 28th, 2007 and Vickers [2007a].
34 See also Killick  and Geradin . For counterarguments see Ritter .
35 Ahlborn et al. , p. 1110.
36 See also Katsoulacos .
37 See Corollary 3 of Proposition 3 above. For details on applying the above framework to optimal standards for refusals to license IP see also Katsoulacos .