«Abstract Although economists have made substantial progress toward formulating theories of collusion in industrial cartels that account for a variety ...»
Price cutting and business stealing in imperfect cartels
B. Douglas Bernheim Erik Madsen
Stanford University Stanford GSB
Although economists have made substantial progress toward formulating theories
of collusion in industrial cartels that account for a variety of fact patterns, important
puzzles remain. Standard models of repeated interaction formalize the observation
that cartels keep participants in line through the threat of punishment, but they fail to explain two important factual observations: ﬁrst, apparently deliberate cheating actually occurs; second, it frequently goes unpunished even when it is detected. We propose a theory of equilibrium price cutting and business stealing in cartels to bridge this gap between theory and observation.
1 Introduction An important objective of theoretical research in Industrial Organization is to achieve a conceptual understanding of the mechanisms through which actual price-ﬁxing cartels ar- rive at collusive outcomes. Analyses of strategic models involving repeated interaction have ∗ We would like to thank Susan Athey, Kyle Bagwell, Lanier Benkard, Jeremy Bulow, Ben Golub, Leslie Marx, David McAdams, Andy Skrzypacz, Takuo Sugaya, Robert Wilson, Alex Wolitsky, and three anony- mous referees for valuable comments and discussions. We are especially indebted to Jonathan Levin for in- sightful guidance that helped to shape the project at critical stages. We are also grateful for comments by sem- inar participants at Stanford University, Stanford GSB, and the 12th Columbia/Duke/MIT/Northwestern IO theory conference. Both authors acknowledge ﬁnancial support from the National Science Foundation.
1 yielded important insights but also leave signiﬁcant gaps.1 Our object in this paper is to pro- vide a theoretical account of two important but thus far unexplained empirical regularities.
First, cartel members sometimes deliberately cheat on price-ﬁxing agreements. Second, when cheating is detected, punishment does not always follow. Instead, cartel members often urge each other to recall their common interests and let cooler heads prevail. See Section 2 for a discussion of historical examples of this pattern.
Existing theories of collusion cannot account adequately for these observations. Theories with imperfect monitoring, such as Green and Porter (1984), were originally formulated to explain why cartels tend to break down, giving way to price wars and retaliatory business stealing.2 Signiﬁcantly, they attribute the collapse of price ﬁxing solely to events beyond the control of the cartel members, rather than to their intentional choices. Thus they imply that cartel members never deliberately cheat on collusive agreements.3 In addition, according to these theories, if cheating did occur and was detected, it would deﬁnitely trigger punishment.4 This gap in the literature has important practical implications. Attorneys for companies accused of collusion often point to evidence of price cuts and business stealing, and to a purported lack of retaliation, as “proof” that a cartel is ineﬀective (see Section 2). Though 1 Leading theories of collusion in price-ﬁxing cartels include Green and Porter (1984), Rotemberg and Saloner (1986), Abreu et al. (1986), Abreu (1988), Bernheim and Whinston (1990), Athey and Bagwell (2001), Athey et al. (2004), Athey and Bagwell (2008), and Harrington and Skrzypacz (2011).
2 This tendency has been widely discussed in the literature; see, e.g., Porter (1983), Green and Porter (1984), Genesove and Mullin (1998, 2001), Harrington (2006), and Marshall et al. (2015), as well as Section
2. Standard models with perfect monitoring cannot account for such breakdowns because they imply that neither cheating nor punishment occurs in equilibrium.
3 To be clear, the theory of imperfect monitoring can in principle account for unintended cheating, such as apparent defections from collusive agreements attributable to “rogue employees” who are not involved in the conspiracy. In particular, one could construct a model with imperfectly controlled sales personnel whom, in equilibrium, each ﬁrm would instruct to quote some collusive prices (which means deliberate cheating would not occur). However, analogously to Green and Porter (1984), “rogue” salespeople would periodically grant price concessions (e.g., with the object of enhancing their own compensation given their false understanding of their employer’s objectives). Because other ﬁrms would be unable to distinguish between actual and rogue defections, all defections would have to occasionally trigger punishments.
4 To be sure, the Folk Theorem tells us that just about anything can happen in standard repeated oligopoly games. Using this ambiguity to contrive an equilibrium that sustains a particular price-quantity sequence – for example, one in which ﬁrms occasionally disrupt a stable market allocation without triggering punishment – does not provide a legitimate theoretical explanation for the characteristics of that sequence. By way of analogy, there are also equililibria with alternating periods of high and low prices, but one cannot reasonably characterize that observation as a theory of price wars. Given the vast multiplicity of equilibria, one must impose discipline on the process of equilibrium selection, for example by insisting on optimality within some appropriate class. Generally, the most proﬁtable equilibria consistently allocate production among ﬁrms according to some principle such as comparative advantage, and therefore do not exhibit patterns interpretable as deliberate business stealing. Similarly, one can construct equilibria in which defections trigger punishments probabilistically rather than with certainty, but that does not explain why cartels would adopt such arrangements. The theory of optimal penal codes in repeated games shows that such arrangements are not generally desirable.
2 intuitively plausible, the possibility that an imperfect but nevertheless eﬀective real-world cartel might exhibit some degree of deliberate price cutting and business stealing, and that such behavior might sometimes go unpunished despite detection, has as yet found no rigorous theoretical articulation.
In this paper, we attempt to bridge this important gap between theory and observation by constructing a theory of equilibrium price cuts and business stealing in imperfectly eﬀective cartels. We formulate a model in which ﬁrms have natural advantages with respect to serving particular market segments and must incur sunk costs (associated with investments required for supplier prequaliﬁcation and bid preparation) before attempting to do business with any speciﬁc customer (or group of customers). For intermediate discount factors, some collusion is feasible but perfect collusion is not. Our agenda is to study the properties of imperfectly collusive equilibria in those settings.
Our main result demonstrates that, under reasonably general conditions, the best collusive equilibria within an important class have several key properties. First, the cartel in eﬀect attempts to divide the market according to the ﬁrms’ relative advantages. Second, while the cartel may establish an aspirational price (in our model, the monopoly price), it recognizes that perfect collusion is unsustainable, and consequently also explicitly or implicitly establishes a price ﬂoor, at which each ﬁrm can be assured of locking up its “home market.” Third, each ﬁrm often charges the aspirational price in its home market, but also sometimes cuts its price in an attempt to defend market share against anticipated “raids” by competitors. Fourth, ﬁrms sometimes attempt to raid each others’ markets, in all such cases setting prices above the ﬂoor, so as to avoid stealing business if the home ﬁrm has made the “safe” choice. If, however, the home ﬁrm has also set a price above the ﬂoor, the rival may successfully steal business. Fifth, whenever such price cuts or business stealing occur, they go unpunished. However, the cartel would punish business stealing by “away” ﬁrms at or below the ﬂoor. Thus, we demonstrate that deliberate and unpunished price cuts and business stealing (which would appear to observers as “cheating”) can be critical to the healthy functioning of a cartel.5 Our theory has implications for the relationship between conduct and patience that contrast markedly with conventional accounts. In an ideal world, cartels would like to divide the market among their members at the monopoly price. However, sustaining this division requires a certain degree of patience, as in a standard Folk Theorem. In classical cartel models, insuﬃciently patient ﬁrms adapt by lowering the collusive price, without any 5 For a complementary perspective on these issues, see the recent work of Rahman (2015).
3 Figure 1: The nature of collusion
further modiﬁcation to the collusive structure; see Figure 1, Panel A.6 Our analysis points to an alternative mode of conduct: rather than coordinate on a lower price, the cartel (optimally) attempts to divide the market at the aspirational monopoly price, but succeeds only imperfectly. Cartel members occasionally “cheat” by raiding their competitors’ markets and cutting prices in their own markets, down to a ﬂoor price below which raids are unacceptable (and punished harshly). This ﬂoor price reﬂects the level of collusion achieved by the cartel, and is increasing in the discount factor; see Figure 1, Panel B.7 The theory thus predicts that, instead of (or possibly in addition to) lowering the aspirational price (which in our particular model is always the monopoly price), impatience may result in greater apparent discord and price-cutting relative to that price, without entirely undermining the eﬃcacy of the cartel.
This theory also has potentially testable implications, for example, that unpunished business stealing occurs at prices above the cartel’s ﬂoor, whereas all business stealing at prices below that ﬂoor triggers punishment.8 In practice, this implication may prove diﬃcult 6 For standard models of Bertrand competition with homogeneous products (which we assume in this paper), the curve in Panel A would exhibit a discontinuous jump from the competitive price level to the monopoly price level at a threshold discount factor.
7 For the particular Bertrand-style model we examine, the aspirational price is always the monopoly price, as shown in the ﬁgure. However, with other models of competition, both the aspirational price and the price ﬂoor might be increasing in δ.
8 Technically, in our model, business stealing below the price ﬂoor never occurs on the equilibrium path.
However, in a more general model it could occur for unrelated reasons, such as imperfect control over “rogue” 4 to test because a cartel’s price ﬂoor may not be known with precision (indeed, in practice, price agreements can appear somewhat fuzzy, and understandings concerning the ﬂoors may be implicit rather than explicit). For this purpose, one cannot use the average price as a proxy for the ﬂoor, because the theory implies that some business stealing will occur at below-average prices. A more robust testable implication of the theory is that, the higher the price at which business is stolen, the lower the likelihood that apparent “cheating” will trigger punishment. Testing this implication falls outside the scope of our current theoretical inquiry.
The rest of this paper is organized as follows. Section 2 reviews historical evidence of deliberate unpunished cheating by members of industrial price-ﬁxing cartels. We present a simple model of industrial competition in section 3. Section 4 characterizes the properties of non-collusive equilibria (i.e., equilibria in one-shot play). Section 5 presents our main results, while section 6 describes an important extension. Some brief concluding remarks appear in section 7. Additional extensions, as well as all proofs, appear in the Appendix.
2 Deliberate cheating in the historical record Instances of cheating on cartel agreements, such as undercutting agreed-upon price targets to steal customers allocated to competitors, appear in the records of many price-ﬁxing cases.
Marshall et al. (2015) provide an excellent survey derived from European Commission decisions on major industrial cartels from 2000 to 2005. Of 22 rulings over that period, they classify nine as “discordant,” a designation indicating “evidence of frequent bargaining problems and deviations by cartel members, occurring throughout the cartel period.” The classify only six as fully concordant, meaning the cartel functioned smoothly throughout the collusive period. These ﬁgures likely understate the proportion of discordant cartels, because their sample is inherently selected to include only those price-ﬁxing conspiracies eﬀective enough to draw antitrust scrutiny; see, for example, the discussion of selection issues in Levenstein and Suslow (2006).9 Remarkably, observed price cutting and business stealing often appears to go unpunished, with cartel members instead reminding each other that “our competitors are our friends and our customers are our enemies,”10 and urging one another to recall their common interests salespeople who have no knowledge of the cartel; see footnote 3.
9 Harrington (2006) provides further discussion EC cartel decisions from the early 2000s.
10 This statement was made by Archer Daniels Midland president James Randall in an April 30, 1993 meeting with executives of a Japanese lysine producer. http://www.nytimes.com/1998/08/04/business/ videotapes-take-star-role-at-archer-daniels-trial.html 5 and let cooler heads prevail. Examples of such forbearance litter the record of the discordant cartels surveyed by Marshall et al. (2015).11 For instance, the global lysine cartel, which operated at least from 1992 through 1995, discussed a persistent and substantial gap between target and actual prices in its European markets at cartel meetings throughout 1993 and