Contributions to Economic Analysis & Policy

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1 Contributions to Economic Analysis & Policy Volume 3, Issue 004 Article 8 Selective Enforcement of Coyright as an Otimal onoolistic Behavior Danny Ben-Shahar Assaf Jacob The Interdiscilinary Center, danny@idc.ac.il IDC, jacoba@ost.tau.ac.il Coyright c 004 by the authors. All rights reserved. No art of this ublication may be reroduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, hotocoying, recording, or otherwise, without the rior written ermission of the ublisher, beress, which has been given certain exclusive rights by the author. Contributions to Economic Analysis & Policy is roduced by The Berkeley Electronic Press (beress). htt://

2 Selective Enforcement of Coyright as an Otimal onoolistic Behavior Danny Ben-Shahar and Assaf Jacob Abstract We resent a erfect Nash equilibrium in which the creator of a work, motivated by economic considerations, selectively enforces her own coyright. In fact, the creator may not only ermit, but may strategically romote infringement of the coyright, thereby articiating indirectly in redatory ricing, and so raising barriers to entry. Our model is highly alicable to the software industry, where relatively high entry costs and the relatively low cost of coyright infringement make this henomenon likely. We further show the conditions under which exogenous intervention, through intensive enforcement of coyrights, increases social welfare. inally, we exlore some otential strategies for such legal intervention. KEYWORDS: Antitrust, Coyright, Predatory Pricing, onooly, icrosoft, Nash Equilibrium, Price Discrimination *The Arison School of Business, The Interdiscilinary Center Herzliya; P.O. Box 67, Herzliya 4650, Israel; telehone: , fax: , danny@idc.ac.il **The Radziner School of aw, The Interdiscilinary Center Herzliya; P.O. Box 67, Herzliya 4650, Israel; telehone: , fax: , ajacov@idc.ac.il #We thank Omri Ben-Shahar, Alon Harel, Ariel Porat, Yoram Shachar, Gerald Willmann, the editor (Aaron Edlin), and two anonymous referees as well as the articiants of the Antitrust Economics and aw Session at the American aw and Economics Association Annual eeting, Georgetown 00, the ourth Kiel Worksho on icroeconomics of the New Economy, Germany 00, the Economics of Coyright Piracy session at the American Economic Association Annual eeting, Atlanta 00, and law school seminars at the Hebrew University and the Interdiscilinary Center Herzliya for constructive comments. The authors are resonsible for any remaining errors.

3 Ben-Shahar and Jacob: Selective Enforcement of Coyright. Introduction The traditional economic analysis of intellectual roerty rights, and of coyright in articular, relies on the ex ante and ex ost ersectives discussed, for examle, by andes and Posner (989). rom an efficiency asect, it is argued that social welfare will rise if, ex ost, a creative work may be coied without limitations. According to this argument, use of the roduct benefits many, while the cost of making additional coies is insignificant. What is more, new roducts often build uon their redecessors. or this reason, free distribution is likely not only to encourage direct use of the work, but also to serve as a basis for new works and ideas, thus maximizing future social welfare. On the other hand, from an ex ante oint of view, creators who are not assured the rotection of future coyrights may lack the incentive to create new works. This is articularly so when the cost of creating an original work is considerably higher than that of making each additional coy.,3 One straightforward imlication of the ex ante view, often emhasized by researchers, is the imortance of making available legal remedies for coyright violations. Allowing the creator to fully recover rofits lost due to infringement rotects the creator s remium and maintains the incentive to create. The State s role, according to this view, is to rovide a clear registry of right. Coyright holders, for their art, have a strong incentive to take action rivately against any detected infringement. This aer challenges this standard view. Secifically, we show that there exist circumstances in which creators maximize their rofit under the threat of cometition by selectively enforcing coyrights. While shrinking short-term rofits, this strategy generates a long-term benefit in the form of reduced cometition. The underlying strategy is to deter otential cometitors from entering the market by lowering rices, even at the cost of immediate rofit loss. Because antitrust laws are sensitive to redatory ricing and unlawful monoolization, 4 lowering rices directly is not an otion. But the incumbent may achieve the same result by strategically failing to enforce coyrights. In markets where coyright violation is widesread, this olicy may enable incumbents to legally maintain their monoolistic osition. An examle Also see Nordhaus (969), Besen et al. (99), Hadfield (99), and Nethanel (996). This is, for instance, true in the software industry, which is the rimary examle for our model, where the cost of creating software is generally huge, while the cost of coying it is negligible. 3 or other motivations that substantiate coyright laws, see, among others, Goldstein (996), Abrams (983), Brown (985), Yen (990), isher (988), Kalan (967), add (983), and Patterson and indberg (99). 4 See Section of the Sherman Act, 5 U.S.C.A.. Published by The Berkeley Electronic Press, 004

4 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 for this alleged henomenon comes from the software industry: 5 igure A in the aendix shows an advertisement for Hewlett-Packard CD-Writers ublished in local Israeli newsaers. As it turns out, the camaign was shared by icrosoft Cor. 6 The advertisement shows a large hoto of an original box that contains icrosoft Office000 and, next to it, a irated coy of the software with the statement: Warning! Coying software, games, or music rotected by coyright is strictly forbidden and constitutes a serious criminal offense. Violators are subject to a maximum of 3 years imrisonment and a fine of NIS,000,000 (equivalent to aroximately $0,000). Beneath the hotos, the ad continues in highlighted letters: Nonetheless, if you do have something to coy, let us offer you the best CD-Writers in the world Hewlett-Packard. Undoubtedly, the involvement of icrosoft Cor. in roducing this advertisement casts susicion that icrosoft Cor. is, in effect, engaged in romoting the violation of its own coyrights in some segments of the market. 7 The Netscae case rovides another examle of alleged selective coyright enforcement. 8 or some time, Netscae distributed its software free of charge (while dominating more than 80% of the browser market). Then, at some oint, Netscae divided the market into commercial and non-commercial segments, and while maintaining its free-distribution olicy for non-commercial customers, it began charging commercial users 40 to 00 dollars for its software. Although there is no clear evidence of a direct selective enforcement strategy in Netscae s behavior, Netscae olicy could be interreted as designed to crowd rivals out of the browser market. That is, by giving u some rofits that could have been roduced under cometition in the non-commercial market, Netscae maintained its monoolistic control of the commercial market. 9 The basic intuition runs as follows: consider a market that consists of a single firm with a unique roduct. Potential cometitors threaten to develo a substitute roduct and enter the market. We claim that equilibrium is sustained when the monooly intentionally slits the market into, say, two sub-markets with 5 In general, the romotion of coyright violation within the software industry might be carried out in various ways, both actively (by not using the enforcement mechanisms available to the firm) and assively (by not using rotective measures and anti-coying devices). 6 See further discussion on this matter in Kasi (000) 7 This susicion is corroborated by the fact that BSA, which is the main civil enforcement authority of icrosoft Cor. in Israel, tends to overlook non-commercial users in its advertisements in the local media and mainly focuses on commercial users. Also, Kasi (000) oints out that icrosoft s comliance with resenting the software Office000 in an advertisement for Hewlett-Packard CD-writers is arguably designed to imlicitly encourage readers to coy its software. 8 or further discussion of the Netscae case, see, for examle, Karinski (995). 9 In site of Netscae s evidential failure, its strategy, ex ante, may have indeed been rational. To Netscae s misfortune, however, its rival was icrosoft Cor., which was later indicted for an antitrust violation for distributing its browser gratuitously in all sub-markets. htt://

5 Ben-Shahar and Jacob: Selective Enforcement of Coyright unambiguous boundaries. 0 In one sub-market, the monooly enforces its coyright and thereby reserves its monoolistic ower. In the other, coyright is not enforced and the rice, in effect, dros to zero. or a new firm to enter the market, it must generate a rofit at least sufficient to justify the initial fixed entry cost. By slitting the market so that in one segment the roduct is, in effect, marketed at a rice of zero, the monooly considerably reduces the rosective cometitor s otential rofit. If accurately executed, this strategy eliminates any incentive for rosective cometitors to enter the market: one sub-market will roduce no rofits, while limiting sales to the other sub-market and cometing there with the existing monooly may not comensate the cometitors for the high fixed entry cost. This selective coyright enforcement strategy may considerably reduce social welfare. The described equilibrium relies on the fact that otential rofits are insufficient to comensate rivals for the fixed cost of entering the market. If those rofits, combined with the consumer surlus net of the monooly s reduction in rofits, exceed the fixed entry cost, then an exogenous intervention by enforcing coyrights may become socially beneficial. We identify conditions under which such intervention may increase social welfare. inally, we discuss ossible rocedures within the legal system that might enhance cometition by eliminating strategic selective enforcement of coyrights and increasing efficiency. These can be adoted by both rivate and ublic entities. We should note that in addition to the analysis of andes and Posner (989), several studies in the coyright law literature examine the incentives for the creator and their effect on social welfare. iebowitz (985), for examle, identifies market conditions in which some level of coyright infringement leads to increased social welfare. Besen and Kirby (989) argue that in some cases, where it is less costly to distribute a coy by sharing than by roducing an additional original unit, coyright holders might rationally seek a certain level of 0 or examle, in the context of the software industry, it is likely that the two sub-markets are the commercial and rivate segments (which are ossibly differentiated by the elasticity of the demand functions). One may also think, for examle, of two geograhical sub-markets in the international context. We ignore here the ossibilities of imitation and licensing between cometitors. As examined, for examle, by Katz and Shairo (987), imitation and licensing may alter the leader s strategy with resect to innovation. Ignoring these ossibilities, however, allows us to focus on the main idea raised in our analysis, namely, the otential indirect maniulation of rices by means of selective enforcement of coyright. Another strategy that the monooly may adot is to interchangeably allow coyright violation in the market in one eriod and enforce coyright in the next eriod. This olicy, however, may not only be technically difficult to imlement (that is, selling a roduct in a market where it has reviously become a norm to coy), but it may not suort a erfect Nash equilibrium under a finite time horizon. or more on this strategy, see, for instance, Kres (990:468). See also the discussion following Proosition. Published by The Berkeley Electronic Press, 004 3

6 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 infringement. The underlying intuition is that while sharing via coying reduces the number of original sales, it also enhances consumers willingness to ay because they can share and trade the goods with others. Bakos et al. (999) identify the aggregation effect associated with rofitable coyright violation. They show that in some cases a grou valuation of a roduct might have a robability distribution with lower variance than that of an individual member of the grou, which allows the roducer to extract more from the consumer surlus. 3 In the following section we briefly discuss legal considerations of redatory ricing and outline our aroach in this context. In Section 3 we construct the model. In Section 4 we derive a erfect Nash equilibrium in which a leading firm adots a selective enforcement strategy to maximize rofits under the threat of a ossible rival entering the market. We further demonstrate, in Section 5, the ossible increase in social welfare that may follow an exogenous intervention in the monooly s selective coyright-enforcement strategy. In Section 6 we discuss ossible legal imlementation of an exogenous intervention. We summarize in Section 7.. Predatory Pricing Antitrust regulations might revent a monooly from simly setting a redatory rice. Exosure to a criminal suit, however, deends on the authorities enforcement olicy and the interretation of redatory ricing by the courts. This interretation is articularly imortant in cases dealing with intellectual roerty, where costs are incurred mainly at the research and develoment hase, while subsequent marginal costs are esecially low. In such cases, it may be argued that no rice is redatory because one cannot sell below a zero cost. 4 oreover, in the traditional view of redatory ricing, the redator is likely to face difficulties maintaining its redation olicy over extended eriods. This is because it is comelled not only to sell at a lower rice, but also to roduce more units to match the greater demand that follows the rice cut. 5 Nevertheless, as argued by Posner (000, age 3): Intellectual roerty is characterized by heavy fixed costs relative to marginal costs dramatically so in the case of software, where it is only a slight overstatement to seak of marginal cost as zero. urthermore, deterring entry by means of redatory ricing is not always an irrational strategy. In the new technology it is lausible that the rofit 3 or further economic analysis of coyright law see, for examle, Benjamin and Kormendi (974), Ordover and Willig (978), Novos and Waldman (984), Johnson (985), Besen (986), Nascimento and VanHonacker (988), Conner and Rumelt (99), Takeyama (994), unney (996), Goal and Sanders (997), iu (00) and Hui and Png (003). 4 or further discussion of such cases, see, for examle, Watson (998). 5 See, for examle, cgee (958) and Edlin (00). htt:// 4

7 Ben-Shahar and Jacob: Selective Enforcement of Coyright from extending the monooly another year or two will exceed the cost of the exclusionary ractices required to achieve the extension [Posner (000, age 7)]. The Sureme Court of the United States argues that a threshold to a redatory ricing claim is the cost. 6 However, as construed by many legal scholars, 7 the Sureme Court limits redation claims to those cases where rices are below average total cost (that is, not necessarily below marginal cost). The Court does not embrace a articular cost test such as the Areeda-Turner average variable cost rule. oreover, since the Brooke decision and due to dynamic develoments in the economic environment, courts and lawmakers have sought to re-evaluate and exand the traditional view of redatory ricing. Their basic argument is that, frequently, a rice higher than short-run marginal cost is redatory because it can be aimed at both excluding an equally efficient rival and allowing the redator to engage in rolonged eriods of monoolistic ricing. 8 urthermore, Edlin (00) argues that, in effect, there is no comelling reason to restrict redation cases to below-cost ricing because above-cost ricing can also limit cometition and thus harm consumers. 9 egislators and courts worldwide have further exanded the redatory ricing framework. or examle, under the legal systems of Canada, England, and the EEC, arguing for a redatory ricing strategy is ossible if rices are below average total cost. 0 As noted by Elhauge (003), cases also tend to suggest that Euroean doctrine may be interreted such that any rice cut made by the monooly in resonse to a rival s entry is illegal, whether the new rice is above or below cost. The emhasis is on the monoolist s intention to drive the rival out of the market. According to Elhauge (003), under EC law, redation may be established when the resulting rice fails to maximize the monoolist short-run rofits. We argue that, in comarison with traditional redatory ricing schemes, the redation strategy discussed here may revail because the additional demand 6 See Brooke Grou td. v. Brown & Williamson Tobacco Cor., 509 U.S. 09, (993). 7 See, for examle, Hovenkam (994), ccall (997), and Bolton et al. (000). 8 or further discussion, see also Bolton et al. (00), Watson (998), Sector (00), and Edlin (00). 9 In articular, Edlin (00) exlores a strategy in which the monooly, in resonse to the rival s entry, sets a rice above its own cost but below the entry s cost. This ractice is redatory because it may be maintained for extended eriods and thus forces the rival out of the market. 0 or these ractices, see, for examle, Section 50()(c) of the Cometition Act R.S.C. 985, C- 34 in Canada, Section 8() of the Cometition Act 998 in England, and AKZO Chemie BV. v. Commission of Euroean Communities, 99 ECJ CEEX EXIS 5086 and Cie maritime Belge Transorts Sa and others V. Euroean Commission and others [000] All E.R. (EC) 385 in the EEC. Also, see ang (997). Elhauge (003) further discusses the imortance of EC law for the U.S. in the era of global markets. Published by The Berkeley Electronic Press, 004 5

8 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 that follows redation is filled by the ublic, which simly roduces more irated coies. oreover, the monooly in our case recous the losses generated in one sub-market by maintaining its monoolistic rice in the other sub-market, thus enjoying immediate rofits in lace of uncertain future ones. Nonetheless, the authorities might find it difficult to rove that the monooly is violating antitrust laws in the case resented here, since the burden on cometitors is not imosed directly by the firm but merely indirectly the users are, in effect, resonsible for this henomenon by transgressing the law. The monooly s omission is in choosing not to exercise its rights to a civil action 3 or to start a criminal action. 4 Also, because redatory ricing is difficult to rove, using masquerading techniques in ractice immunizes the redator. Because it might be difficult to distinguish between exclusionary ractices and ordinary commercial ractices in which a firm chooses to omit enforcement, we roose in Section 6 reliminary guidelines for examining whether the monooly is, in fact, allegedly engaged in a wrongful act. 3. The odel Consider two otentially roducing firms in the market: a leader and a follower. Though one firm s roduct is unique, it may be a erfect substitute for that of the other firm. or simlicity, let us assume that the firms roduction functions are identical and their marginal costs of roduction are zero. 5 et us denote the leader by and the follower by. Consumers can costlessly reroduce the roduct if coyright is not enforced by the firm. Therefore, the roducing firm must decide on the quantity it intends to roduce and its intended level of coyright enforcement. We assume, without loss of generality, that the firm s decision on the level of enforcement, e, is binary. That is, e={0,}, where e=0 (e=) reresents no enforcement (erfect enforcement). Suose that both firms exhibit a constant marginal enforcement cost denoted by mc. 6 This also forces the rival, which wishes to recou its initial investment, to invest in enforcing both the monooly s and its own coyrights. 3 See Section 50 (b) of the 976 Coyright Act. 4 See Section 506 (a) of the 976 Coyright Act. 5 While, for simlicity, we model the marginal roduction cost to equal zero, the intuition resented here also maintains under a ositive marginal roduction cost. 6 odeling two distinct roduction functions with increasing marginal costs imlies that the firms should otimally balance roduction and enforcement. Our assumtion about the cost of roduction and enforcement allows us to overlook this issue and focus on the main insight of the model. Also, one may argue that the marginal cost of enforcement might even dro with quantity since the latter is associated with a lower rice for the roduct, which in turn decreases the incentive for coyright infringement. htt:// 6

9 Ben-Shahar and Jacob: Selective Enforcement of Coyright In addition, suose that there are two sub-markets with distinct demands for the substitute roducts and that boundaries between the sub-markets are maintained. Particularly, let us assume that market s i, i={,}, demand function for the roduct is a biqi if e =, () i =, 0 if e = 0, where i and q i are the rice of the roduct and the demanded quantity in submarket i, and a and b i are ositive constants, where we assume that b >b. 7 The number of consumers in a sub-market i is n i, and each consumer requires no more than one unit of the roduct. In order to assure non-negative rices for all q, we assume that b i a/n i. We osit that if the leader alone is to revail in the market, it will either charge a monoolistic rice in sub-market i and enforce its coyright, or not enforce its coyright and thereby ermit rices to dro to zero. 8 If the leader and the follower are to coexist in the market, then we assume that they comete in a Stackelberg-tye cometition and enforce coyrights in either both or one of the sub-markets. 9 Particularly, we osit two ossible ricing schedules for each of the monooly and duooly market states: a monooly rice with coyright enforcement in each of the sub-markets (denoted by ); a monooly rice with coyright enforcement in sub-market and no coyright enforcement (leading to a zero rice) in sub-market (); a Stackelberg cometition rice with coyright enforcement in each sub-market (); and a Stackelberg cometition rice with coyright enforcement in sub-market and no coyright enforcement (leading to a zero rice) in sub-market (S). One should note that given the described monooly and duooly set-u, any ricing and enforcement strategy other than,, S, and is necessarily dominated. This stems from the fact that, indeendent of whether the market exeriences full or zero enforcement, the best a monooly (Stackelberg cometitor) can do in equilibrium is to set the monooly (Stackelberg) rice. 7 The assumtion that b >b is not essential. The results may, qualitatively, also obtain if b b. 8 Notice that if coyright is not enforced, it is irrelevant whether the charged rice is ositive or zero, since all consumers are assumed to costlessly coy the roduct, which in effect sets the rice to zero. 9 We should note that our results do not articularly rely on the Stackelberg set-u assumtion. One can, similarly, construct a setting with, for examle, either a Cournot-tye oligooly (where the rofits of the cometitors are identical) or erfect cometition, which will also generate no entry on the art of the follower(s). Hence, the intuition resented in the model does not deend on the secific set-u. Published by The Berkeley Electronic Press, 004 7

10 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 Now, following Equation () and given the four otential market rice schedules, it is a straightforward matter to derive the rofit generated by the firms under each scenario. This art of the analysis follows ordinary derivation of monooly and Stackelberg quantities and rices, which are shown in the aendix. The otential rofits are then ( b + b )( a mc) () π =, 4b b (3) (4) (5) (6) and (7) ( a mc) π =, 4b ( b + b )( a mc) π =, 8bb ( b + b )( a mc) π =, 6bb S ( a mc) π =, 8b S ( a mc) π =, 6b where π and π are the monooly s rofit when coyright is enforced in both sub-markets and in sub-market only, resectively; π and π are the leader s and follower s rofits, resectively, when a Stackelberg cometition with S S coyright enforcement ersists in both sub-markets; and, finally, π and π are the leader s and follower s rofits, resectively, when a Stackelberg cometition with coyright enforcement revails in sub-market, while no coyright enforcement revails in sub-market. Next we demonstrate a erfect Nash equilibrium under which a monooly otimally adots a strategy of selective coyright enforcement. htt:// 8

11 Ben-Shahar and Jacob: Selective Enforcement of Coyright 4. Selective Coyright Enforcement Denote the monoolistic (Stackelberg) rice in each sub-market if one firm only revails (two firms revail) and coyrights are fully enforced by P (P ). ikewise, denote the monoolistic (Stackelberg) rice if one firm only revails (two firms revail) and coyrights are enforced in sub-market only by P (P S ). Now, given the rofit functions in Equations ()-(7) derived under the described four market conditions, consider the following extensive form game layed by the leader and the follower as deicted in igure. igure : The interaction between the leader and the follower as an extensive form game feasible actions resulted rices outcomes end-node number =, e = =, e = enter, e= =, = ( π, π AC ) I not =, = (π, 0) II =, e = enter, e= = S S, =0 ( π, π S AC ) III =, e =0 not =, =0 (π, 0) IV In the first stage of the game, the leader selects the rices to revail in each sub-market. As a sole roducer at that stage, the leader can select either = with e = and = with e = (where i and e i, i={,}, are the rice and enforcement level, resectively, in sub-market i) or, alternatively, = with e = and = with e = 0. In the second stage of the game, the follower chooses whether to enter or not enter the market. Entry is accomanied by a fixed cost of magnitude AC. 30 The equilibrium rices in each sub-market after the follower s decision in stage two, contingent uon the leader s action in stage one, aear next to the end nodes in igure. 3 ost imortant, notice that in the strategies leading to node IV, the 30 In fact, AC is the average fixed entry cost er eriod. Hence, when entering the market the follower considers the rofits er eriod vis-à-vis the corresonding average fixed cost. 3 The rationale for =0 under end node III is discussed following Proosition. Published by The Berkeley Electronic Press, 004 9

12 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 leader sets identical monoolistic rices in both sub-markets but enforces coyright only in sub-market. ollowing Equation (), the non-enforcement in sub-market leads to a zero rice in that market. inally, the term to the left (right) of the comma in the arenthesis in igure reresents the rofits of the leader (follower), deending on the revailing rices in each sub-market, which follow the reviously chosen actions. Under the above set-u, we claim that S Proosition : If π < AC < π, then the unique erfect Nash equilibrium (PNE) of the described extensive form game leads to an outcome where the incumbent sets rices = with enforcement e = and = with enforcement e =0, and the follower ots not to enter. Corollary : The condition, which yields the unique PNE in Proosition, is b 6b AC equivalent to 0 < [ ] <. b ( a mc) Proof: The strategies that suort the outcome described in Proosition are eader: Set = with e = and = with e = if the follower does not enter thereafter; otherwise, set = with e = and = with e = 0.3 ollower: Enter and set e = and e = if leader sets = with e = and = with e = ; otherwise, do not enter. ocusing on the sub-game, which follows the incumbent s roosed rices = with e = and = with e =, note that the follower s otimal resonse is to enter and set e= (an action accomanied by an average fixed cost of entry, AC, and a marginal cost of enforcement, mc), if this action generates greater rofits than not enter. That is, enter and set e= is a strategy suorting a sub-game Nash equilibrium if (8) π AC > 0. 3 Note from Equation () that, rovided that e =0, then setting 0 is redundant since rices will, in effect, dro to zero due to coyright infringements. Equivalently, given that e i =, the monooly is always better off setting the monoolistic rice. htt:// 0

13 Ben-Shahar and Jacob: Selective Enforcement of Coyright ikewise, if the leader chooses = with e = and = with e = 0, then the sub-game Nash equilibrium is suorted by a follower s not enter strategy if S (9) π AC < 0. (0) rom inequalities (8) and (9) we get S π < AC < π. Now, given the follower s otimal resonse strategy, the leader anticiates that ricing = with e = and = with e = will generate a rofit of magnitude π, while ricing = with e = and = with = 0 e will eventually roduce π. Consequently, the leader s choice of = with e = and = with e = 0 suorts a sub-game Nash equilibrium if () π > π. (a) ollowing Equations (3) and (4), the condition in () may be resented as ( a mc) ( b + b )( a mc) π = > = π. 4b 8b b However, given that b >b, it follows after a reduction that Condition (a) sustains for all a, b >b, and mc. inally, note that the Nash equilibrium in each sub-game is unique. This rovides the uniqueness of the soken PNE (end of roof of Proosition ). Given the exressions for the rofit functions in (5) and (7), the condition in (8) may be written as ( b + b )( a mc) (8a) π AC = AC > 0, 6b b and the condition in (9) may be exressed as S ( a mc) (9a) π AC = AC < 0. 6b Published by The Berkeley Electronic Press, 004

14 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 However, conditions (8a) and (9a) imly that AC is such that S ( a mc) ( b + b )( a mc) π = < AC < = π, which after a reduction leads 6b 6bb to the condition aearing in Corollary. Note that the game described in igure is a two-stage interaction, where the leader makes the first move simultaneously committing to certain rice and enforcement levels and the follower resonds by either entering or not entering the market. One may argue that, realistically, there could be a third stage in the game, where if the follower chooses to enter the market, the leader should be able to change her initial no-enforcement olicy in sub-market and otimally shift to an enforcement regime. Indeed, conditional on the follower entering the market, the leader would be better off by now enforcing a Stackelberg equilibrium rice in sub-market than by attaining zero rofits from that sub-market, if she continues the no-enforcement olicy. This would, of course, lead to a different equilibrium than that stated in Proosition. In fact, the outcome of this equilibrium would be identical to that obtained under end-node I in igure. While the three-stage-game argument is valid under some circumstances, there are also real-world situations in which the leader may commit to the noenforcement olicy so that it is either comletely irreversible or requires excessive effort to reverse. These situations are in line with the two-stage framework of the model. The leader is better off with the irreversible commitment because she then obtains the outcome of end node IV as oosed to that of end node I. The software industry is an examle of a market in which the leader can credibly commit to a olicy of no coyright enforcement: if no enforcement involves, for examle, the failure to act on coyright rotection measures generally inherent in the software, then the olicy cannot be reversed with resect to roducts already sold. oreover, enforcing coyright in a market where infringement has already become a norm might consume both time and cash. 33 Hence, for ractical matters, the no-enforcement decision may be considered irreversible. In other words, in situations in which the leader adots measures that ersuade the follower that she is, in fact, committed to no enforcement, then the resented model is valid and the derived outcome sustains erfect Nash equilibrium The revailing norms among eer-to-eer users and the use of software like Naster and Kazaa show how difficult it is to change these norms. 34 Additional arguments that substantiate the credibility of a monooly s threat of redatory ricing can be found, for examle, in Salo and Romaine (999) and Goldsmith and Posner (999). htt://

15 Ben-Shahar and Jacob: Selective Enforcement of Coyright Intuitively, there are two crucial elements leading to the attained PNE. The S first is that π < AC < π, which imlies that the follower merely ots to enter the market when rofits may be extracted from both cometitive sub-markets. The other condition is π < π, which imlies that the leader is better off generating a monoolistic rofit from one sub-market than cometing in both submarkets. 35,36 Also, consistent with Edlin (00), one might argue that contrary to the strategy adoted under Proosition, the monooly would, in fact, be better off enforcing its coyright until the moment that entry actually occurs, and utilizing its selective enforcement olicy only subsequent to the aearance of a rival firm. This argument is undoubtedly valid in circumstances where the variable costs in the industry are not insignificant, such that the rival firm faces not only a fixed cost hurdle in entering the market, but also an ongoing variable cost obstacle once oerating in the market [see, for examle, the case of the airline industry suggested by Edlin (00)]. In contrast, we roose a situation (tyical to the software industry) in which the otential rival s variable cost is relatively trivial while the bulk of its cost is concentrated in research and develoment of the initial roduct (rior to entering the market). In this case, the monooly redicts that once the rival enters the market it will be articularly difficult to drive it back out (due to its low variable costs). In other words, the monooly s alternative, of crowding the rival out once it is in the market, is imractical. This, combined with 35 As one can see from the roof, π < π does not exlicitly aear in Proosition since it holds for all a, b >b, and mc, given the setting of the model. 36 S Note that π < AC < π and π < π imly that it is necessary for attaining the PNE that S the AC exerienced by the follower sustains π < AC < π. In other words, AC must fall between the monooly s rofit in sub-market and that of the follower if it enters that market. S One might argue, however, that, realistically, if AC is greater than π it is likely to also be greater than π, which imlies that the monooly should not have entered the market in the first lace. The resonse to this claim is twofold: first notice that although the model demonstrates a duooly situation, one can more generally think of the alternative full cometition framework, where the cometitor s rofit is substantially lower than that of a monooly. That is, our duooly framework may also be extended to a cometitive market where the difference between followers and monooly s rofits is more significant. urthermore, under some circumstances it is likely that the AC exerienced by the leader is lower than that incurred by the follower. This may be true for several reasons: frequently, in order to comete, the follower must launch a better roduct. oreover, the monooly s dominance in the market is already established and the cometitor is thus often required to devote substantial resources to establishing its market share. In the software industry, the major reason corresonds to the network effect: in order to comete with the monooly the sueriority of the roduct resented by the follower should be such that it not only comensates the customers in terms of technical qualities, but also dominates network effect advantages such as comatibility, switching costs etc. Published by The Berkeley Electronic Press, 004 3

16 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 the monooly s commitment to selective enforcement, drives the monooly to conduct its redatory strategy rior to the entrance of the rival. This effectively substantiates the incumbent s choice between those strategies leading to endnodes I and IV in igure. inally, consistent with clean and Riordan (989) and Waldman (99), it may be argued that our model would collase once an oligooly is introduced, because of free riding by the incumbent firms. Note, however, that investing in entry deterrence by an oligoolistic firm in the general case [such as discussed in clean and Riordan (989) and Waldman (99)] translates to a lack of investment in coyright enforcement in our framework. That is, while underinvestment generally romotes the entry of rivals in the ordinary case, it is underinvestment in enforcement that raises the barrier to entry in our model. This, in turn, imlies that, in the resence of an oligooly, free riding would only further encourage this under-investment in enforcement that makes entry more difficult. Under the equilibrium roosed in Proositions, the monooly allegedly conducts an illegal ricing olicy. However, the olicy is sohisticatedly hidden. Although rices are seemingly identical everywhere, the selective coyright enforcement indirectly and intentionally functions as a mechanism that, in effect, achieves the same objective raising barriers to entry by means of a redatory ricing olicy. Next, we show that the ricing and enforcement strategy conducted by the monooly might lead to economic inefficiencies. 5. Efficient Exogenous Intervention We argue that Proosition : If the condition for the described PNE is satisfied and, further, if 3b ( a mc) b ( a + 30amc 5mc ) AC <, then an exogenous intervention 3bb in enforcing coyrights is otimal. Corollary : If the condition for the described PNE is satisfied and, further, if b 3a + 6amc 3mc >, then an exogenous intervention in enforcing b ( a mc) coyrights is otimal. Proof: Recall that under the described PNE, the leader sets = with e = and = with e =0 and the follower does not enter the market. The follower enters the market only if, at the minimum, = and = are to revail in the htt:// 4

17 Ben-Shahar and Jacob: Selective Enforcement of Coyright resective sub-markets together with coyright enforcement. We therefore comare the social welfare attained under the PNE state, (that is, without exogenous intervention) with that obtained under (that is, with exogenous coyright enforcement). Denote the monoolistic (Stackelberg) sulied quantity in sub-market i, i={,}, if one firm only revails (two firms revail) in the market by q ( q ). Now, igures and 3 deict the social loss in the market under and, resectively, excluding fixed costs. igure : Social loss under (without exogenous coyright enforcement) i i igure a: Sub-market igure b: Sub-market mc D q q D mc q q igure 3: Social loss under (with exogenous coyright enforcement) igure 3a: Sub-market igure 3b: Sub-market mc mc D D q q q q Published by The Berkeley Electronic Press, 004 5

18 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 The shaded areas indicate the dead-weight loss. The stried areas deict the loss of consumer surlus due to intervention. Summing u the shaded areas in igures a and b, we find that the total social loss (dead-weight loss) under, denoted by S, is ( a mc) () S =. 8b Similarly, comuting the sum of the shaded and stried areas in igures 3a and 3b, we find that the total social loss (dead-weight lus loss of consumer surlus) under, denoted by S, is b ( a mc) + b ( a + 3mc) + 4bmc( a mc) (3) S =. 3b b If the value obtained from subtracting the right-hand side of Equation () from the right-hand side of Equation (3) is greater than the fixed costs associated with the follower s entry, then exogenous intervention is socially beneficial. That is, exogenous intervention in enforcing coyrights is otimal if (4) AC < S S. Substituting the right-hand side of Equations () and (3) with the exressions in (4) yields 3b ( a mc) b ( a + 30amc 5mc ) (5) AC <. 3b b However, given Proosition, we know that the condition in (0) is sufficient for the PNE. Thus, combining the conditions in (0) and (5) roduces the requested result (end of roof of Proosition ). Provided that the conditions for PNE in (0) are achieved, the condition for intervention resented in Inequality (5) is redundant if and only if the righthand side of Inequality (5) is greater than π in Equation (5). That is, if (6) 3b ( a mc) b ( a + 30amc 5mc 3b b ) ( b > + b )( a mc) 6b b then attaining the PNE conditions is sufficient for an intervention to become efficient. However, Inequality (6) reduces to b 3a + 6amc 3mc (7) >, b ( a mc), htt:// 6

19 Ben-Shahar and Jacob: Selective Enforcement of Coyright which is the condition rovided in the Corollary (end of roof of Corollary ). Proosition argues that there may be market conditions that require regulators intervention to imrove efficiency. Such intervention is required when the follower s rofit combined with the accomanying consumer surlus are greater than the combination of the entry fixed costs and the reduction in the monooly s rofit. If this is indeed the case, then exogenous enforcement of coyright becomes socially beneficial. 37 We should emhasize that the identified condition for exogenous intervention in coyright enforcement, resented in Proosition, is secific to the assumed Stackelberg cometition. Put differently, if the alternative to the above PNE were a cometitive equilibrium, the secific condition for intervention would change. oreover, there could also be cases in which exogenous intervention may not benefit social welfare. 38 The basic insight is that under certain market conditions, regulators should evaluate the effect of intervention in enforcing coyright law in order to maximize social welfare. Concetually, this result is analogous to the well-acceted motivation of antitrust authorities for restricting the abuse of monoolistic ower: namely, the otential reduction in social welfare. Here the monoolistic abuse is conducted via selective coyright enforcement as oosed to more conventional ways, such as direct redatory ricing. We further conduct a comarative statics analysis for the intervention conditions, which yields the following: Corollary 3: Given that the condition for the PNE is satisfied, then the greater b is, the more likely is the otimality of the exogenous intervention in enforcing coyright. Corollary 4: Given that the condition for the PNE is satisfied, then the smaller b is, the more likely is the otimality of the exogenous intervention in enforcing coyright. 37 In fact, for a comlete analysis of the efficiency asect, we also require that from the monooly s ex ante ersective, the rofit generated under coyright enforcement in both submarkets,, is greater than the fixed cost associated with entering the market. Otherwise, given π the exected intervention olicy, the monooly would fail to enter the market in the first lace and society would lose the otential welfare. Note, however, that the latter requirement holds, in general, for many antitrust cases where intervention is advocated and is not restricted to the articular aradigm resented in our model. 38 or examle, if a Cournot equilibrium relaces the resented Stackelberg equilibrium, then an exogenous intervention would not benefit social welfare under our assumed setting. Published by The Berkeley Electronic Press, 004 7

20 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 Proof: The roof of both Corollaries 3 and 4 is immediate following the condition in Corollary. Observing igures and 3 immediately clarifies the intuition. Given that the PNE, as resented in igure, is attained, then one may notice from igures b and 3b that a greater b corresonds to a steeer demand curve (that is, a more inelastic demand function) in sub-market. This, in turn, decreases the shaded and the stried area of social loss under (igure 3b). It thus follows that a greater level of b, ceteris aribus, is associated with a diminishing social loss when intervention occurs. urther, notice that any increase in the level of b sharens the sloe of the demand function in sub-market. This, in turn, decreases the dead-weight loss in both igures a and 3a. Nevertheless, the dro in the dead-weight loss due to a rise in b is greater under (see igure a) than it is under (see igure 3a). It therefore follows that if the condition for the PNE is satisfied, then an increase in the level of b, ceteris aribus, reduces the likelihood that exogenous intervention will imrove efficiency. inally, we claim that Corollary 5: Given that the condition for the PNE is satisfied, then the smaller the marginal enforcement cost mc is, the more likely is the otimality of the exogenous intervention in enforcing coyright. Proof: Differentiating the right-hand side of the condition for an otimal exogenous intervention resented in Inequality (7) yields [(3a + 6amc 3mc ) /( a mc) ] (8) > 0, mc which imlies that the likelihood that an exogenous intervention in enforcing coyright imroves efficiency rises as the level of mc falls. The intuition here is obvious: the smaller the marginal cost of coyright enforcement, the more robable it is that the additional coyright enforcement imosed on the market by regulators will indeed benefit social welfare. 6. Exogenous Intervention: egal Imlementation In the revious section, we identify the conditions under which selective enforcement of coyright yields inefficiency that may require exogenous intervention. Before we turn to the legal mechanisms that might imrove efficiency, a crucial reliminary roblem must be addressed: namely, how antitrust authorities can determine whether any given case of non-enforcement is an innocent resonse to high enforcement costs, or is, in fact, a strategy wrongfully adoted to deter the entry of rivals. htt:// 8

21 Ben-Shahar and Jacob: Selective Enforcement of Coyright Our analysis suggests the following questions as guidelines: ) Is there sufficient cometition in the market? ) Does the coyright holder hold market ower? 3) Are different levels of coyright enforcement being observed in different segments of the market? 4) Is coyright enforcement articularly costly? 39 5) Do other firms in equivalent situations enforce their coyrights? Of course, these are only reliminary guidelines to which more arameters could be added. Other elements to be considered include a rima facie redatory ricing scheme and the firm s ossible use of business justification and the efficiencies defense as suggested and alied by Bolton et al. (000) (see ages 74-78). If the answers to the questions above suggest that the firm oerates in a non-cometitive market in which it alies, aarently without justification, different levels of enforcement in different sub-markets; and if, in articular, the firm fails to emloy any non-costly rotective measures against infringement in some or all segments of the market, then the susicion that the firm is violating antitrust laws aears justified. In this case, we may consider two tyes of legal intervention: rivate and ublic. Under a rivate enforcement regime, a cometitor is given tools with which to contest the leading firm s wrongful acts. The State does not directly intervene in the market, but it allows a cometitor to act uon its interest. 40 Thus, for examle, once the veil covering the monooly s wrongful activity is ierced and the firm s strategic enforcement is revealed as redatory ricing, a cometitor may file an antitrust suit for violation of both Section of the Sherman Act 4 and Section 4 of the Clayton Act. 4 urthermore, Section 6 of the Clayton Act 43 allows rivate injunctive relief. 39 Although some means of enforcement (courts, for examle) are costly, there are many less costly measures against infringements such as anti-coying devices embedded in software. ailure to use inexensive rotective measures, given all other circumstances, can thus be held against the coyright owner. 40 One can argue that cometitors might not sue or, as we later claim, ask the government to sue, but only threaten the monooly that they will do so. This would allow the cometitors to reach a Coasian deal with the leader under the threat of cometition. While this argument is indeed valid, it only alies to certain market conditions. The effectiveness of such a threat deends on several factors such as how credible it is; the number of cometitors willing to enter the market or willing to make a credible threat; the chances for detection, etc. The higher the transaction costs and the need for coordination, the less likely that such a threat can succeed. oreover, if the motivation for an anti-trust olicy is to maximize consumer surlus, then one should consider acting even rior to the cometitor s comlaint or formal filing of a suit. In criminal law the state often acts even against the will of the involved arties. 4 5 U.S.C.A U.S.C.A U.S.C.A. 6. Published by The Berkeley Electronic Press, 004 9

22 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 Antitrust laws are not alone in roviding cometitors with remedies. Other areas of law can be used as well. 44 One examle is the doctrine of coyright misuse. 45 The rationale underlying the coyright misuse doctrine is the following: while authors have by law certain monoolistic rights, which often equi them with market ower, society seeks to limit the extension of owners coyrights beyond the boundaries drawn by the law. 46 Since the doctrine was first imlemented in 990, the courts have been divided in their views. Some regard the doctrine as a branch of antitrust law, emhasizing the fact that without antitrust rinciles the courts have no clear guidelines by which to determine whether a firm is indeed misusing its rights. 47 Others, however, emhasize a more general ublic welfare aroach for assessing misuses, stressing the indeendent character of the coyright misuse doctrine. 48 Under either interretation, however, the strategic enforcement adoted by the monooly in our model is recognizable as coyright misuse. Two obstacles must be resolved in alying the coyright misuse doctrine to strategic enforcement. The first is that the doctrine is, by and large, used as a shield and not as a sword. Defendants raise a coyright infringement suit in order to revent the enforcement of coyrights uon them. The other obstacle lies in the class of circumstances in which the doctrine is generally imlemented. 49 In our case, counter to the ordinary alication, it is the cometitor who seeks a more intensive enforcement of coyright by the monooly. Nevertheless, if the legal system aims to restrain the monooly ower generated by rivileges rovided to the firm by society, these differences are insignificant and the coyright misuse doctrine may be alied. or examle, if the leading firm sues for a breach of its coyright in the future, the court may refuse to rovide it with any remedies. The sanction for recurring strategic 44 The alied doctrines used for enforcement are either art of the ositive law or to be develoed over time by future courts decisions. 45 While less develoed, the coyright misuse doctrine has the same roots as the atent misuse doctrine. 46 Thus, for examle, this doctrine was imlemented in a case where a firm, in order to extend its rights, had used anticometitive clauses in its standard software licensing agreement and was, therefore, found by the court to have racticed coyright misuse. See asercomb Am., Inc. v. Reynolds, 9. d 970 (4 th Cir.990) (hereafter referred to as the asercomb decision). 47 See, for examle Judge Posner in Saturday Evening Post Co. v. Rumbleseat Press, Inc., 86. d 9 (7 th Cir. 987), 48 See, for examle, the asercomb decision. 49 Paradigmatically, the misuse doctrines (in atent and coyright law) were designed to revent the extension of the monooly ower granted by the legislator through unlawful means. The underlying motivation is that the realm of coyright and atent law is not wrongfully extended, for examle, by a tying arrangement, draconian anticometitive licensing, etc. Instead, in our case, monooly ower is extended by narrowing the realm of coyrights via selective enforcement. htt:// 0

23 Ben-Shahar and Jacob: Selective Enforcement of Coyright behavior may be the ractical withdrawal of rights granted by the State. 50 The risk of losing its rights in all sub-markets should rovide the monooly with sufficient motivation to enforce them. oreover, the law may be amended along these lines to allow cometitors new and more flexible remedies under the doctrine of coyright misuse or other doctrines. 5 In general, the cometitor would have an incentive to sue, under either antitrust or coyright law, if its exected comensation (as ruled by the courts) exceeded the cost of bringing the suit. urthermore, the monooly might refrain from its strategy if courts imosed exected costs greater than the benefit derived from the monooly s olicy. In the sirit of igure in Section 3, the court should imose on the monooly exected costs greater than π π, which, in turn, will shift the equilibrium from end node IV to end node I (see igure ). This may be achieved, for examle, if the sanction for the monooly s strategic behavior is a comlete withdrawal of the rights given by the State or even unitive damages. 5 The other mechanism the legal system might rovide is ublic enforcement. This framework includes two major means: first, the State, like the rivate entities, may enforce antitrust law uon the leading firm. The State can file a criminal suit for antitrust violations through either the TC or the DOJ. Note that from a ublic welfare ersective, the likelihood that the overall ublic interest is maintained is greater here than under a rivate suit initiated by a cometitor. This is because the State might consider the requirements of the individual firm as well as those of the consumers. 53 inally, the State may use criminal law by ursuing the breaching ublic. Indeed, the U.S. Coyright Act includes a criminal rocedure that allows the government to imose a fine or even incarceration when a arty commits willful infringement. 54 By adoting the role of the coyright owner, the government can 50 A rationale for comlete withdrawal of coyright is that by failing to attemt to enforce its coyright in one sub-market, the monooly roves an intention to transfer its rights to the ublic domain; therefore, it should comletely lose its coyright in both sub-markets. 5 Note that, consistent with our framework, a broader interretation of the fair use doctrine (i.e. allowing more fair use) may benefit coyright holders but, concurrently, might reduce overall efficiency. 5 Note that the threat to remove all coyrights granted by the State is weakly credible because under either alternative (with or without coyright withdrawal), the cometitor remains out of the market while the monooly suffers a substantial loss if the threat is exercised. Hence, the cometitor might gain a market share if, in fact, the monooly internalizes the threat ex ante. 53 This claim ignores the otential greater transaction cost involved when the initiative for enforcement is ublic rather than rivate. Yet we argue that this ossible greater cost may lose significance in relation to the broader reach of the State vis-à-vis the individual cometing firm. 54 See section 506 and 506(a) of the Coyright Act and section 39 of title 8, United States Code. Published by The Berkeley Electronic Press, 004

24 Contributions to Economic Analysis & Policy, Vol. 3 [004], Iss., Art. 8 enforce coyright through criminal rocedure. This will roduce a deterring effect because it will raise the costs of coying. Raising these costs will, in turn, oen the door for cometitors to enter the market and will enhance overall efficiency. In the sirit of Corollary 5 in the revious section, this ublic olicy is more likely to reserve otimality as the marginal enforcement cost becomes smaller. Note that by adoting the role of coyright enforcer, the State, while enhancing cometition, might also increase the rofit of the monooly. In light of igure 3b, the monooly, in effect, rolls the enforcement costs under the mc curve onto the taxayer. While this roduces a wealth distribution effect, efficiency is still enhanced. Indeed, it may be argued that the monooly should be charged by law for the State s enforcement costs. 7. Summary According to conventional law and economic analysis, two major economic forces determine the otimal level of coyright enforcement. One, which suorts comlete enforcement, is designed to motivate creators, ex ante, by assuring a maximum return for their efforts. The other, which suorts no enforcement, is aimed ex ost at both maximizing the number of consumers for the work, and facilitating the creation rocess by allowing a creator to draw uon works created by others. Comleting the ex ost argument, we claim in this study that a creator may use the violation of her coyright as a mechanism to effectively induce a rice break in a subset of the market, which, given sufficiently high entry costs, deters cometitors from entering the market. The creator may, in fact, maximize longterm rofits by strategically romoting an otimal level of coyright infringement. htt://

25 Ben-Shahar and Jacob: Selective Enforcement of Coyright Aendix igure A: An advertisement for Hewlett-Packard CD-Writers ublished in local Israeli newsaers. As it turns out, the camaign was shared with icrosoft Cor. Published by The Berkeley Electronic Press, 004 3