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Fraser 1 of 16 Predatory Pricing as an Optimal Strategy in Technological Standards Wars Eric M. Fraser† 1. Introduction..............................................................................................................................1 2. Predatory Pricing History in Antitrust Law .........................................................................2 2.1. Economic skepticism toward predatory pricing.................................................................3 2.2. Supreme Court adoption of the economic literature and sentiment...................................4 3. Standards Wars........................................................................................................................5 4. Proposed Antitrust Analysis of Standards Wars ..................................................................7 4.1. Optimal Pricing Strategies: Wars of Attrition....................................................................7 4.2. Significance of Strategic Effects......................................................................................15 5. Conclusion ..............................................................................................................................16 Courts have adopted the views of prominent commentators that predatory pricing is irrational and rare. This paper argues that in technological standards wars, the general skepticism is misplaced. Standards wars follow the model of wars of attrition; in those games, manipulating a competitor’s assumptions, potentially through predatory pricing, is often an optimal strategy. 1. Introduction Predatory pricing describes the practice of a firm charging below-cost prices to drive out competitors. If successful, the predatory firm could then raise prices to supracompetitive levels. Such behavior falls under § 1 and § 2 of the Sherman Act, which forbid some forms of monopolization and attempted monopolization. Many prominent commentators have argued that predatory pricing is irrational and therefore should not receive much antitrust attention. While the first-order direct effects of predatory pricing generally render it irrational, second-order strategic effects in at least one domain paint another picture. Economic principles from competitive strategy and game theory reveal that predatory pricing might be an optimal strategy in technological standards wars. In standards wars, at least two firms compete to establish a product or platform as an industry standard. Many historical standards wars gained significant attention, including the wars between Thomas Edison and Nikola Tesla over alternating current versus direct current in electricity transmission, the Betamax versus VHS war, and the more recent Blu-ray versus HDDVD battle over high definition optical media. These wars often have a winner-take-all ending. † J.D. Candidate 2009 and John M. Olin Scholar in Law and Economics, The University of Chicago Law School; M.B.A. Candidate 2009, The University of Chicago Booth School of Business; B.A. in Physics 2005, Pomona College. Fraser 2 of 16 The characteristics of these wars often lead to an optimal strategy of behaving in ways that would appear irrational in a typical competitive environment, such as predatory pricing. Standards wars typically follow the model of wars of attrition, a game theory model that first emerged in evolutionary biology. In wars of attrition, two or more parties compete for a single resource but both incur increasing costs along the way. Evolutionary biologists predict that an optimal strategy is to give off the appearance of irrationality. Economists who borrowed the biological models reached similar conclusions. An optimal strategy in a business war of attrition is to introduce information asymmetries to shift the perceived value of winning the prize, sometimes in otherwise-irrational ways such as incurring a short-term loss. In the absence of antitrust restrictions, firms should generally engage in strategies that yield positive returns, appropriately discounted. Exploring how predatory pricing shifts the behavior of competitors reveals the expected present value of the future cash flows from a predatory pricing strategy. Comparing these cash flows with the expected cash flows from a nonpredatory strategy produces the conditions that must be satisfied for a predatory pricing strategy to have a positive expected value. High-profile standards wars emerge multiple times each decade and competitors battle over smaller, industry-specific standards much more often. In light of the frequency of these wars, and in light of the fact that predatory pricing might be an optimal strategy in this domain, antitrust law should discount the calls to ignore predatory pricing as a real, rational strategy, at least in the arena of technological standards. Courts should apply the test the Supreme Court established for predatory pricing without relying too much on the assumption that predatory pricing is rare and irrational. 2. Predatory Pricing History in Antitrust Law A predatory pricing firm charges below-cost prices to drive out competitors and, once the competitors exit, raises prices above the competitive price. This practice, therefore, requires an investment in below-cost pricing. For this investment to make a profit, the firm must push its competitors out of the market enough to gain enough market power to be able to raise its prices above the competitive level. If successful, the practice results in higher prices and reduced output. This monopolization, if successful, triggers the Sherman Act. Predatory pricing has been the focus of several high profile cases in the past few years. Most recently, the Supreme Court actually evaluated the inverse of predatory pricing. In Weyerhaeuser Co. v. Ross-Simmons Hardwood Lumber Co.,1 the Court evaluated predatory bidding. In predatory bidding, a firm overpays for inputs to drive up prices. The firm hopes that the artificially high prices will drive competitors out of business. In Weyerhaeuser, the Court held that “[p]redatory-pricing and predatory-bidding claims are analytically similar.”2 In holding that predatory bidding claims should be analyzed using the predatory pricing rules,3 the Court effectively reaffirmed its prior predatory pricing holdings. 1 549 U.S. __, 127 S.Ct. 1069 (2007). 127 S.Ct. at 1076. 3 Id. at 1077–78. 2 Fraser 3 of 16 While Supreme Court cases attract attention by default, one of the most well-known predatory pricing cases came from the case against Microsoft.4 Microsoft allegedly made an investment in sacrificing short-term profits by giving away its Internet Explorer browser and related software for free, or even at a negative price. But unlike traditional predatory pricing cases, Microsoft did not seek to raise the price of Internet Explorer to supracompetitive levels. Instead, it allegedly sought to use the enhanced market power to reinforce its monopoly in the Windows operating system.5 Microsoft fought in multiple technological standards wars. Most notably, it tried to establish Internet Explorer, Windows, and other products as the industry standards. Accordingly, the analysis developed here about predatory pricing in standards wars might shine light on Microsoft’s behavior. Current antitrust law tracks economic literature from the past several decades.6 Accordingly, this part describes the economic literature that influenced the Supreme Court in its modern predatory pricing cases. It then describes how the Court adopted the economic analysis of the time. 2.1. Economic skepticism toward predatory pricing A long line of economists, lawyers, and judges have asked whether predatory pricing can ever be successful. Two of the earliest and most well known answers came in the form of John McGee and Roland Koller’s empirical studies from 1958 and 1971.7 Using the 1911 Standard Oil case8 as a framework, McGee argued that a firm would already have to have a large market share to engage in predatory pricing. But then actually engaging in predatory pricing would require reducing the price over that large market share, which would involve very large costs. The smaller competitor would know that the larger competitor was incurring large costs and that it could not incur those costs forever. The smaller competitor would remain in the market, therefore, and the predatory strategy would fail. Even if the smaller firm exited the market in response to the predatory behavior, McGee argued that the large firm would still not recover its initial below-cost investment because after it raised its prices to supracompetitive levels, either the initial smaller firm or another firm would enter and compete with the predatory firm. The predator would then have to make another investment to drive out the entrant. If it again succeeded and raised its prices to recover the investment, the cycle would start again with new entry. Figure 1 illustrates this cycle of entry. Playing this game out reveals that the predatory firm could never expect to recover the investment so the net present value of the strategy is negative. The rational firm facing a negative expected value would never engage in predatory 4 See United States v. Microsoft Corp., 253 F.3d 34, 68 (D.C. Cir. 2001) (explaining the plaintiffs’ predatory pricing claims, which were ultimately rejected). 5 Id. 6 See RICHARD A. POSNER, ANTITRUST LAW vii–xi (2d ed., Chicago 2001) (explaining the modern consensus around applying economics principles to antitrust problems). 7 See John S. McGee, Predatory Price Cutting: The Standard Oil Case, 1 J.L. & ECON. 137 (1958); Roland H. Koller II, The Myth of Predatory Pricing: An Empirical Study, 4 ANTITRUST L. & ECON. REV. 105 (1971). 8 Standard Oil Co. v. United States, 221 U.S. 1 (1911). Fraser 4 of 16 behavior to begin with. Ultimately, McGee concluded that predatory pricing is generally irrational and rare.9 Figure 1: The cycle of entry in predatory pricing This early economic approach gained the attention of antitrust scholars such as thenProfessors Robert Bork and Frank Easterbrook, who used similar arguments to urge courts to effectively ignore predatory pricing claims.10 Bork relied in part on McGee and Koller to assert that “the theoretical argument . . . suggests that predatory price cutting is most unlikely to exist and that attempts to outlaw it are likely to harm consumers more than would abandoning the effort.”11 Easterbrook went further, discarding actual price predation into the mythical realm of dragons and claiming that “there is no sufficient reason for antitrust law or the courts to take predation seriously.”12 While courts did not completely ignore predatory pricing claims, they largely adopted the skeptical view of the literature at the time. 2.2. Supreme Court adoption of the economic literature and sentiment In Matsushita Electric Industrial Co., Ltd. v. Zenith Radio Corp.,13 just a few years after Bork and Easterbrook’s articles, the Supreme Court expressly embraced the economic literature by citing the work of McGee, Koller, Easterbrook, and others for the proposition that “there is a consensus among commentators that predatory pricing schemes are rarely tried, and even more rarely successful.”14 This statement began the Court’s skepticism toward predatory pricing claims. The Court ultimately reversed a grant of summary judgment against the alleged predatory firm. One of the two grounds for reversal was that “the [Court of Appeals] failed to consider the absence of a plausible motive to engage in predatory pricing.”15 Again citing the commentators, 9 See McGee, supra note 7. But consider that then-Professor Richard Posner apparently resisted this notion. For Posner’s updated discussion of the topic, see Posner, supra note 6, at 207–23. 11 ROBERT H. BORK, THE ANTITRUST PARADOX: A POLICY AT WAR WITH ITSELF 155 (Free Press 1978). 12 Frank H. Easterbrook, Predatory Strategies and Counterstrategies, 48 U. CHI. L. REV. 263, 264 (1981). 13 475 U.S. 574 (1986). 14 Id. at 589–90. 15 Id. at 595 10 Fraser 5 of 16 the Court concluded that “economic realities tend to make predatory pricing conspiracies selfdeterring.”16 Several years later, the Supreme Court revisited predatory pricing in Brooke Group Ltd. v. Brown & Williamson Tobacco Corp.17 In Brooke Group, the Court reiterated its stance on “the general implausibility of predatory pricing”18 from Matsushita. It then noted that while the plaintiffs alleged coordination in Matsushita, predatory pricing “is even less likely when . . . there is no express coordination.”19 If anything, the Court was starting to doubt the viability of predatory pricing claims even more. Brooke Group established a new standard for predatory pricing plaintiffs. After Brooke Group, plaintiffs must both “prove that the prices complained of are below an appropriate measure of its rival’s costs”20 and demonstrate “that the competitor had a reasonable prospect, or . . . a dangerous probability, of recouping its investment in below-cost prices.”21 Again revealing its general skepticism toward predatory pricing claims, the Court admitted that “[t]hese prerequisites to recovery are not easy to establish.”22 The Matsushita-Brooke Group progression of Supreme Court cases validated the emerging opinion that predatory pricing was irrational; indeed, no plaintiff has succeeded on a predatory pricing claim after Brooke Group. To have any chance at success in monopolizing a market through predatory pricing, the literature claimed, the firm engaging in predatory pricing would have to have large market share to begin with. That large market share would make below-cost pricing very expensive because selling a large number of units at a loss on each unit would yield a very large loss. Competitors would anticipate that the firm could not engage in such behavior forever, so the other firms would remain in the market, turning to the capital markets for additional funds to survive in the meantime, if necessary. Moreover, given the cycle of entry, no firm could sustain supracompetitive pricing long enough to recoup its initial investment in below-cost pricing because the high prices would provide an incentive for another firm to enter and start the cycle again. This analysis correctly explains the general first-order direct effects, but predatory pricing may actually be rational in at least one situation when second-order strategic effects might dominate. 3. Standards Wars Standards ensure that different products work together. Standards take many forms and economists have labored to develop a complete taxonomy of the different types of standards. One common system categorizes standards based on what types of products a standard links, whether the standard is open or closed, and how the standard emerged.23 16 Id. 509 U.S. 209 (1993). 18 Id. at 227. 19 Id. 20 Id. at 222. 21 Id. at 224. 22 Id. at 226. 23 For this standard framework adopted in the following paragraphs, see Victor Stango, The Economics of Standards Wars, REV. NETWORK ECON. 1, 3–4 (2004). 17 Fraser 6 of 16 Standards can link multiple devices of the same product type or they can link multiple types of products. For example, communications goods require standards to link two instances of the same good, such as two telephones or two webcams. System goods rely on standards for compatibility between different types of products, such as between a DVD and its player or a razor and its blade. This distinction affects the type and magnitude of the network effects the standards create. Communications goods rely on direct network effects: the usefulness of a product is a direct function of the number of compatible products. The fax machine provides the typical, but dated, example. A fax machine provides little value on its own, but additional fax machines create value by being able to send documents between the machines. Both system goods and communications goods rely on indirect network effects. For example, additional Bluray players do not make one player more valuable directly, but additional players increase the incentives for studios to release compatible content. The larger market may drive down prices or increase variety, so an owner of a Blu-ray player benefits indirectly from a larger numbers of players. Network effects create a powerful barrier to entry. Another type of categorization describes who can participate in the system. One type, a closed system or sponsored system, requires some kind of property right, such as patents, to exclude outsiders. Under this type of system, game developers must secure licenses from Nintendo to distribute games that work on Nintendo’s game systems. In contrast, other standards are open or unsponsored. Any paper company can cut 8 1/2-inch by 11-inch pages to ensure compatibility with most printers and copiers. Closed systems rely on barriers to entry so we should expect to see more successful predatory pricing in those systems.24 Finally, some standards emerge through competition; others through cooperation.25 Standards wars yield de facto standards such as the Blu-ray format instead of HD-DVD. In contrast, informal industry consensus or formal standards-setting organizations such as ANSI, IEEE, or even government agencies such as the FCC create de jure standards such as WiFi. The predatory pricing analysis that follows pertains to standards that follow from standards wars, including those wars that ultimately lead to de jure standards. These wars have several important characteristics. First, they often involve a winnertake-all ending. In winner-take-all games, at the end of the war one and only one standard will emerge as the winner and the other will die. For example, no studios produce consumer films for Betamax or HD-DVD players anymore. Some markets support multiple standards for a variety of reasons. Consumers know the hassle, however, of supporting both standard and metric wrenches, Mac and PC systems, and even A4 or legal-sized paper. Firms engaged in a standards war want to be the only supplier in a winner-take-all game in a market with only one victorious standard. Standards also exhibit lock-in or excess inertia. These characteristics describe the reluctance of the market to switch to a new standard, even a superior one. Both the winner-take-all nature of the wars and the lock-in effect make the rewards for winning the game very high. The winner-take-all ending guarantees monopoly profits for sponsored systems with property rights in the standard and lock-in makes these profits sustainable beyond what one would expect in a perfectly competitive market. 24 Though consider that the predatory bidding in Weyerhaeuser came from a paper company, my example of an open system. Weyerhaeuser Co. v. Ross-Simmons Hardwood Lumber Co., 549 U.S. __, 127 S.Ct. 1069 (2007). 25 Or coopetition. See generally ADAM M. BRANDENBURGER & BARRY J. NALEBUFF, CO-OPETITION (Doubleday 1997). Fraser 7 of 16 Many economists have proposed frameworks for predicting dominant standards. They have identified factors such as the technical superiority of a standard, the availability of complementary assets, the existing installed base, regulation, time of entry, marketing, and many others.26 The high definition optical media war provides a useful case study. Blu-ray and HDDVD both entered the market at about the same time, with startlingly similar technology, no installed base, and roughly equal marketing budgets. At best, they could try to line up complementary assets. Indeed, each struggled hard to secure a handful of deals from movie studios and both took the strategy of linking to a new game system (either the PlayStation 3 or the Xbox 360). Because of this level playing field, neither had many strategic options and technology pundits struggled to predict a winner. 4. Proposed Antitrust Analysis of Standards Wars 4.1. Optimal Pricing Strategies: Wars of Attrition Many of these categories from economics are useful for a manager to evaluate his firm’s chances for success, but few of them provide any levers to pull to make strategic decisions. When all else fails, managers often pull the price lever. In many cases, managers can engage in strategic price setting to affect the outcome of a standards war. This part develops the model of a simplified world. This simplified world excludes the possibility of cooperation between players—like Brooke Group, not Matsushita. Aside from antitrust concerns about collusion, the option to cooperate essentially ends the battle between the cooperating firms. At that stage, the cooperating firms either compete with the non-cooperating firms (as in the case of the alliances around Blu-ray and HD-DVD), in which case the strategies developed here remain unchanged other than being applied to an alliance instead of a single firm, or it ends the war altogether, as in the case of the (non-high-definition) DVD alliance. To simplify the analysis, this simplified world only contains two firms. Many highprofile standards wars, including nearly all of the real examples used in this paper, have only two dominant players. In this model both firms entered at the same time, have products that are roughly equal, have the same marginal cost, and are otherwise similar. To preserve the property rights that provide monopoly profits, this war takes place between dueling sponsored standards. Finally, the model also assumes that marginal cost does not vary with quantity. In a standards war, each firm has two options: fight or exit. Fighting involves incurring additional costs. Many of these costs, such as manufacturing plants and marketing expenditures, cannot be recovered if the firm subsequently exits the market. As in any strategic decision, the managers of a firm should consider the net present value of the discounted expected cash flows.27 Additionally, the firm should consider only the future cash flows; sunk costs spent in previous rounds should not affect the decisions of the current or future rounds. 26 See, e.g., Fernando F. Suarez, Battles for Technological Dominance: An Integrative Framework, 33 RSCH. POL’Y 271, 275 (2004). 27 See, e.g., Easterbrook, supra note 12, at 272 (“Money earned in the future, after the victim has collapsed, must be discounted to present value and compared with the present value of the income forgone during the predation.”); BORK, supra note 11, at 145 (“The future flow of profits, appropriately discounted, must then exceed the present value of the losses.”). Fraser 8 of 16 If both firms exit, all future cash flows for both firms are zero, assuming no exit costs. If one firm exits but the other fights, the fighting firm expects cash flows from monopoly pricing; the exiting firm expects zero cash flows. If both firms fight, then both firms expect cash flows associated with a duopoly. Table 1 illustrates this single-period payoff table, with M denoting the discounted expected cash flows for a monopoly and D denoting the discounted expected cash flows for each firm in a duopoly. Firm B Firm A Exit Fight Exit (0, 0) (0, M) Fight (M, 0) (D, D) Table 1: Payouts for standards war Future cashflows for a monopoly must be positive or no firm would try to compete. Duopoly cashflows could be positive or negative depending on whether the market can support two competing standards. Technological standards wars may yield negative duopoly profits for several reasons. First, the lower quantity produced by each firm compared to a single-firm monopoly might not allow each firm to reach an efficient manufacturing scale.28 Next, consumers will likely purchase fewer total devices in a duopoly world because of network effects. Network effects make a device exponentially more valuable as the number of compatible devices increases.29 A standard with 50 percent market share, therefore, will be significantly less valuable than 50 percent of its value as a monopoly. Finally, consumers may delay purchasing devices during a standards war out of fear of choosing the standard that ultimately fails.30 The negative-cashflow case simplifies the analysis, remains relatively common, and still supports the case that in some instances, predatory pricing might be the optimal strategy. Table 2 approximates this new single-period payoff strategy. The table uses dollar-sign notation where more dollar signs indicate larger cashflows. The absolute magnitude has no meaning, but intercell and intracell comparisons are appropriate. 28 See JEAN TIROLE, THE THEORY OF INDUSTRIAL ORGANIZATION 19 (“The average cost declines until it reaches the ‘most efficient scale,’ MES, where it intersects the marginal-cost curve.”) (MIT 1988). 29 See Christopher S. Yoo, Beyond Network Neutrality, 19 HARV. J. OF L. & TECH. 1, 21 (2005) (“[T]he number of possible connections increases exponentially with network size.”). 30 See Pai-Ling Yin, quoted in Stephen J. Dubner, What Are the Lessons of the Blu-Ray/HD-DVD Battle? A Freakonomics Quorum, N.Y. TIMES: FREAKONOMICS, http://freakonomics.blogs.nytimes.com/2008/03/04/what-are-the-lessons-of-the-blu-rayhd-dvd-battle-afreakonomics-quorum, Mar. 4, 2008 (“Consumers, worried about buying the losing technology (think Betamax vs. VHS), may delay adoption of both technologies until the battle is resolved.”). Fraser 9 of 16 Firm B Firm A Exit Fight Exit (0, 0) (0, $$$$) Fight ($$$$, 0) (–$$, –$$) Table 2: Revised payouts for standards war With these realistic assumptions, the game begins to look like a war of attrition.31 Wars of attrition model behavior of two or more players competing for a single prize (here, a monopoly in the standard) while continually incurring sunk costs in the process. The model first emerged in evolutionary biology before economists borrowed it to model auctions.32 In wars of attrition in biology, as well as the model developed for Table 1, no dominant strategy exists. The game has two Nash equilibria, (fight, exit) and (exit, fight). Solving, and therefore winning, the multi-period war of attrition requires asymmetric information about the other player’s expected actions. Strategic pricing decisions can inject uncertainty into the game by manipulating the expected payouts. Reducing prices below cost, or predatory pricing, has multiple effects that introduce this type of uncertainty. First, the direct effect of Firm A’s below-cost pricing is an increase in the costs to Firm B of staying in the war. If Firm B matches the below-cost prices, the expected cashflows from fighting decrease because of the loss it must incur. If Firm B does not match the prices, then it will lose customers and therefore its revenues will decrease. This direct effect represents the traditional antitrust harm expected from predatory pricing. Predatory pricing also has other, indirect, effects. Firm A’s low pricing signals to Firm B that A’s costs are lower than they really are. From Firm B’s perspective, then, not only are its own payouts lower for fighting, but Firm A’s payouts are greater if it fights because it has a lower cost structure. If the pricing does not fool Firm B about A’s cost structure, the strategy may at least cause Firm B to think that A is crazy and is willing to incur significant losses to 31 Bork noted that “[p]redation is a war of attrition,” but made more general assumptions to reach a contradictory result from the one developed here. BORK, supra note 11, at 147. 32 See J. Maynard Smith, The Theory of Games and the Evolution of Animal Conflicts, 47 J. THEOR. BIOL. 209 (1947) (first proposing the war of attrition moel); John G. Riley, Noncooperative Equilibrium and Market Signalling [sic], 69 AM. ECON. REV. 303 (1979) (applying the biological models to economics); see also Lewis Kornhauser, Ariel Rubinstein, & Charles Wilson, Reputation and Patience in the ‘War of Attrition,’ 56 ECONOMICA 15 (1989); Drew Fudenberg & Jean Tirole, A Theory of Exit in Duopoly, 54 ECONOMETRICA 943 (1986); John G. Riley, Strong Evolutionary Equilibrium and The War of Attrition, 82 J. THEOR. BIOL. 383 (1980); John G. Riley, Evolutionary Equilibrium Strategies, 76 J. THEOR. BIOL. 109 (1979); D.T. Bishop, C. Cannings, & J. Maynard Smith, The War of Attrition with Random Rewards, 74 J. THEOR. BIOL. 377 (1978); D.T. Bishop & C. Cannings, A Generalized War of Attrition, 70 J. THEOR. BIOL. 85 (1978); J. Maynard Smith & G.R. Price, The Logic of Animal Conflict, 246 NATURE 15 (1973). Fraser 10 of 16 fight.33 Firm A can make this commitment to craziness credible by accompanying it with other commitments such as building excess capacity.34 Introducing this uncertainty further reduces Firm B’s expected payoffs from fighting because it reduces the perceived probability that Firm A will exit. With these effects, Table 3 shows the expected payoff for the next round as Firm B sees the world after Firm A has dropped its prices. Of course, the payoffs do not reveal Firm A’s investment in below-cost pricing, both because the sequential nature of the game kicks that investment out of future cash flows and into the sunk cost category and because Firm A’s behavior obscured its true payoffs. The Table only shows what Firm B perceives Firm A’s payouts to be. If Firm A can credibly communicate that it will not exit the war (hence the greyed out column), then Firm B faces an expected cash flows of zero if it exits and negative cash flows if it fights. In that case, Firm B will exit and Firm A will win the war.35 Firm B Firm A Exit Fight Exit (0, 0) (0, $$$$$) Fight ($$$, 0) (–$$$$, –$) Table 3: Payoffs as seen by Firm B after Firm A announces price reductions Determining whether this strategy will pay off for Firm A requires modeling the present value of its expected cash flows with and without the predatory pricing strategy. The difference between the present values will yield the expected value from engaging in predatory pricing. To calculate the expected cash flows for both the predatory and non-predatory cases, assume Firm B makes a final decision at time T of whether to fight or exit. Before time T, Firm A makes duopoly profits (or losses). Because this period is finite, we model it as an annuity with discount rate r lasting T periods with coupon payments (Qd) (Pd – MC), where Qd represents 33 Cf. DREW FUDENBERG, JEAN TIROLE, GAME THEORY 387 (MIT 1991) (describing crazy reputational strategies); see also Fudenberg & Tirole, supra note 32, at 956 (describing “a ‘reputation’ for predation”). 34 See William M. Landes & Richard A. Posner, 94 HARV. L. REV. 937, 949 n.26 (1981) (“[The firm]’s excess capacity may make a threat to engage in predatory pricing to keep out new entrants more credible.”); see also TIROLE, INDUSTRIAL ORGANIZATION, supra note 28, at 255 (explaining strategic excess capacity in a war of attrition). But intentionally building excess capacity may have antitrust consequences. See In re E.I. Dupont de Nemours & Co., 96 F.T.C. 653 (1980) (dismissing antitrust complaint but exploring defendant’s alleged excess capacity). 35 Others have proposed models with different assumptions. One well-known study proposed that a perturbation in the certainty with which one firm view’s the other’s costs, or positive discounted expected cash flows from a duopoly, will also yield an equilibrium of exit. See Fudenberg & Tirole, supra note 32, at 943 (“[W]e argue that all equilibria but one disappear when the information structure is perturbed.”). Similarly, another study found that if one player has even a small probability of irrational behavior and will always fight, then the other player should “concede immediately.” Kornhauser, Rubinstein, & Wilson, supra note 32, at 18. This uncertainty is the hallmark of solving these modified war of attrition games. Fraser 11 of 16 duopoly quantity sold in each period, Pd the duopoly price, and MC marginal cost. After time T in the non-predatory case, Firm A either continues to make duopoly profits with probability p0B.fight, or makes monopoly profits with probability p0B.exit. We assume these cash flows continue forever, so we model them as a perpetuity starting at time t = T, discounted to t = 0.36 Coupon payments are either duopoly profits per period or monopoly profits per period. The equation below shows the expression. Figure 2 illustrates this sequence, with an arbitrary value of p0B.exit = p0B.fight = 0.5. PV0 = (Qd )(Pd − MC) 1− r 1 p0B.exit (Qm )( Pm − MC ) p0B.fight (Qd )( Pd − MC ) + T + T T r r (1+ r) (1+ r) (1+ r) € Figure 2: Firm A’s expected cash flows without predatory pricing If Firm A engages in predatory pricing, the cash flows are the same as before with a few differences. First, during the predatory period leading up to when Firm B makes its decision (at t = T),37 the cash flows will be the somewhat lower, below-cost predatory cash flows given by the familiar form (Qpp) (Ppp – MC). These cash flows will be negative because Ppp < MC for 36 In reality, a firm’s cashflows will not be perpetual, nor will they remain flat. As long as the time t = T is short relative to period during with Firm A operates, however, the perpetual model will have only a marginal effect. Similarly, incorporating growth into the analysis would add another assumption without much benefit. 37 For simplicity, assume that the predatory pricing strategy does not affect the timing of Firm B’s decision. Fraser 12 of 16 predatory pricing, by definition. 38 The only other difference is that the probabilities of Firm B fighting and exiting will change. Specifically, pppB.exit should be larger and pppB.fight should be smaller. Again, the period of t < T is modeled as an annuity; afterwards it is a perpetuity. The equation below shows these modified cash flows and Figure 3 illustrates the new sequence. PVpp (Q )( P = pp B.exit − MC ) Qm )( Pm − MC ) p B.fight 1 p pp ( (Q )( P − MC) 1− + pp T d d T + T r r r (1+ r) (1+ r) (1+ r) pp € Figure 3: Firm A’s expected cash flows with predatory pricing The analysis for the predatory pricing case assumes that Firm A will stay in the market no matter what firm B decides. Keeping this assumption preserves the symmetry between Firm A and Firm B except for the predatory pricing strategy. Relaxing the assumption actually simplifies the analysis. If Firm A knows that Firm B will fight, then Firm A will exit if it faces negative duopoly cashflows. The cashflows if Firm B exits remain the same, but now Firm A faces cashflows of zero with probability pppB.fight. Accordingly, the last term on the above equation goes to zero and the bold line segment in Figure 3 for t > T gets shifted up by (pppB.fight)(Pd). Eliminating the assumption that Firm A will stay to fight even if Firm B decides to fight, 38 Note, however, that some disagreement exists over whether which measure of cost is appropriate. See Cargill, Inc. v. Monfort of Colorado, Inc., 479 U.S. 104, 117-118 n.12 (1986) (explaining the different approaches, including marginal cost, average variable cost, and average total cost). Marginal cost is not only the preferred measurement for use in economic models, but it is also the lowest of the measurements so if anything using that measurement understates the likelihood of predatory pricing. Cf. U.S. v. AMR Corp., 335 F.3d 1109, 1115–16 (10th Cir. 2003) (“[M]arginal cost, an economic abstraction, is notoriously difficult to measure and cannot be determined from conventional accounting methods.”) (citations omitted). Fraser 13 of 16 therefore, increases the expected vaue of engaging in a predatory pricing strategy. While relaxing the assumption simplifies the calculations, the remaining analysis maintains the assumption that Firm A will fight no matter what because it preserves the information symmetries between the firms. When Firm A decides whether or not to engage in predatory pricing, it will consider the expected value of the decision. The expected value of invoking the predatory pricing strategy is given by the difference between the present value of the predatory and non-predatory strategies, or EV = PVpp – PV0. Figure 4 shows this graphically. The expected value of the predatory pricing strategy is the sum of the shaded regions, noting that one of the regions is negative. The time value of money prevents simple integrals from doing the trick, so we must preserve the discounting terms in the original expressions. Using the fact that pB.fight + pB.exit = 1 and defining (pppB.exit – p0B.exit) as ΔpB.exit simplifies the expression: EV = € B.exit B.exit Qpp ( Ppp − MC ) − Qd ( Pd − MC ) Qm ( Pm − MC ) −Δp Qd ( Pd − MC ) 1 Δp 1− + + T T T r r r (1+ r) (1+ r) (1+ r) Using the known relationships between some of those variables helps to make sense of the equation. The first expression, which represents the investment in below-cost pricing, must be negative. The relationships between the variables confirm this fact. Ppp < MC because by definition predatory pricing involves below-cost pricing. Additionally, Ppp < Pd unless the natural duopoly price is a predatory pricing world. Assuming a standard downward-sloping demand curve, that pricing relationship implies that Qpp > Qd, making the first term negative. The second two terms, which represent the effects of the predatory pricing decision after Firm B makes a decision, must together be positive. This section explained that ΔpB.exit > 0. Pm > MC or no one would enter the market. Additionally, downward sloping demand curves imply that the monopoly price exceeds the duopoly price while the monopoly quantity supplied falls short of the duopoly quantity (absent coordination). Symbolically, Pm > Pd and Qm < Qd.. Fraser 14 of 16 Figure 4: Difference in strategies Naming some of the terms in that expression helps to link the expected value equation to the rest of the analysis: Qpp ( Ppp − MC ) − Qd ( Pd − MC ) 1 Investment ≡ 1− 1+ r T r ) ( Monopoly profits ≡ € Duopoly profits ≡ € 1 Qm ( Pm − MC ) T r (1+ r) 1 Qd ( Pd − MC ) T r (1+ r) ∴ EV = −Investment + Δp B.exit ( Monopoly profits) − Δp B.exit ( Duopoly profits) € That simplified expression maps nicely onto the shaded regions in Figure 4. The important question for antitrust analysis is when this strategy will pay off. That is, when the € expected value will be positive. That question involves an inequality. Predatory pricing is an optimal strategy in a technological standards war when it satisfies the following inequality: EV > 0 ⇒ Investment < Δp B.exit ( Monopoly profits − Duopoly profits) € Fraser 15 of 16 4.2. Significance of Strategic Effects If monopoly profits far exceed duopoly profits, a firm may behave strategically to increase the probability that the competing firm will exit. This second-order strategic behavior represents the rent-seeking behavior with which antitrust law should concern itself because it results in the standard anticompetitive effect of reduced output. The analysis does not stop there, however. Courts weigh the anticompetitive effect of a practice against the procompetitive effects.39 Procompetitive effects abound in standards. Fundamentally, standards facilitate valuable coordination.40 This coordination increases as the number of competing standards decreases. Consider the costs of supporting both Macs and PCs, analog and digital television signals, and foreign electrical outlets and voltages standards. The analysis earlier explored the network effects of a single standard. In the short-term, at least, consumers are often better off when a standard dominates the market because of direct and indirect network effects. Direct network effects increase the value of some types of devices by increasing the number of other users with which any user can communicate. Indirect network effects increase the value of other types of devices through increased variety and lower-priced complementary goods. Additionally, consumers who want to adopt a new technology often inefficiently delay purchase during a standards war for fear of choosing the losing standard.41 A quick resolution to a standards war can reduce the deadweight loss associated with consumers who want to purchase at the prevailing price but instead wait until a winning standard emerges.42 On the other hand, standards also create anticompetitive effects. Standards constrain the market in addition to coordinating it. Standards exhibit lock-in, path dependency, and other forms of excess inertia. Consider the deadweight loss incurred in advertising alone for the transition from analog to digital television broadcasts. A single dominant standard maximizes switching costs when new, superior standards emerge. Most applicable to antitrust analysis however, the excess inertia in standards erects strong barriers to entry. These barriers to entry break the cycle described by McGee and illustrated in Figure 1. Once a firm forces out a competing firm, neither that firm nor a new firm can reenter the market without incurring considerable costs. The inertia-created barriers cause the very “dangerous probability, of recouping  investment in below-cost prices” the Brooke Group test requires.43 It is impossible to determine generally whether the pro-competitive effects of settling on a standard outweigh the anticompetitive effects of artificially settling on the standard through 39 See California Dental Ass'n v. F.T.C., 526 U.S. 756, 788–89 (1999) (explaining that “the defendant bears the burden of establishing a procompetitive justification”). 40 See generally Shane Greenstein, Markets, Standards, and the Information Infrastructure, 13 IEEE MICRO 36 (1993). 41 See note 30, supra. 42 Note that the analysis here assumed that the time of decision, T, remained unchanged. Also consider that settling on a standard too soon can lead to the dominance of an inferior standard. See the discussion of “Social optimality of standards selection and timing” in Paul A. David & Shane Greenstein, The Economics Of Compatibility Standards: An Introduction To Recent Research, 1 ECON. OF INNOVATION & NEW TECH. 3, 11–12 (1990). 43 Brooke Group Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209, 226 (1993). Fraser 16 of 16 predatory pricing. The Brooke Group test, then, should continue to shape the predatory pricing antitrust analysis. But the analysis here demonstrates that at least in technological standards wars, predatory pricing is not as unlikely and irrational as courts and commentators suggest. Accordingly, courts should conduct a thorough analysis of each predatory pricing case, at least in the technological standards arena, before discounting a claim because of its supposed unlikelihood. 5. Conclusion Commentators and courts generally agree that predatory pricing is irrational and rare. Indeed, in many industries the direct effects of predatory pricing dominate and make it an unlikely option for a profit-maximizing firm. But such rent-seeking behavior might be an optimal strategy for situations in which second-order strategic effects yield a positive expected value for a predatory pricing strategy. Technological standards wars provide one example of such a situation. Standards wars often take the form of a war of attrition from evolutionary biology. In both battles, two or more players compete for a single prize while incurring more and more unrecoverable costs along the way. In these battles between evenly matched competitors, an optimal strategy involves shifting a competitor’s assumptions. Introducing information asymmetries into the game increases the probability that the competitor will exit. In standards wars, predatory pricing can serve as the assumption-shifting information asymmetry. Its many effects include shifting a competitor’s assumptions about the firm’s costs and making a commitment to behave in ways that appear irrational, including remaining in an unprofitable game. If these forces cause the competitor to exit, the firm will reap the enormous rewards of positive monopoly cashflows from owning the winning standard. Unlike many other industries, technological standards exhibit patterns of excess inertia that serve as barriers to entry. These barriers to entry break the cycle of reentry that commentators rely on to predict extremely low levels of rational predation. In some cases, a profit-maximizing firm would engage in rent-seeking predatory pricing behavior. Courts should therefore disregard the calls to ignore predatory pricing and instead rely on the test expressed in Brooke Group. If a firm engages in below-cost pricing with “a reasonable prospect, or . . . a dangerous probability, of recouping its investment in below-cost prices,”44 a court should acknowledge the predatory behavior. At that point, it should weigh the precompetitive benefits against the anticompetitive costs. That analysis must be case-by-case, but in standards wars several characteristics will occur frequently. In an industry that can support only one standard, settling on a standard—any standard—sometimes benefits the market because it settles consumer uncertainty and enhances value through network effects. On the other hand, prematurely settling on a standard invokes the costs of monopoly pricing and excess inertia without reaping the benefits of a good standard. Moreover, if the market can support multiple standards, predatory pricing might simply result in the kind of deadweight loss that antitrust law seeks to prohibit. 44 Brooke Group Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209, 226 (1993).