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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.
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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
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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).
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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
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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
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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).
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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.”).
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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.”).
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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.
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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).