Impossibility of Collusion under Imperfect Monitoring with Flexible Production By Yuliy Sannikov and Andrzej Skrzypacz* We show that it is impossible to achieve collusion in a duopoly when (a) goods are homogenous and firms compete in quantities; (b) new, noisy information arrives continuously, without sudden events; and (c) firms are able to respond to new information quickly. The result holds even if we allow for asymmetric equilibria or monetary transfers. The intuition is that the flexibility to respond quickly to new information unravels any collusive scheme. Our result applies to both a simple sta- tionary model and a more complicated one, with prices following a mean-reverting Markov process, as well as to models of dynamic cooperation in many other set- tings. (JEL D43, L2, L3) Collusion is a major problem in many mar- We study the scope of collusion in a quan- kets and has been an important topic of study tity-setting duopoly with homogenous goods in both applied and theoretical economics. From and flexible production—that is, if firms can exposed collusive cases, we know how numer- change output flow frequently.2 As in Green and ous real-life cartels have been organized and Porter (984), in our model firms cannot observe what kinds of agreements (either implicit or each other’s production decisions directly. They explicit) are likely to be successful in obtain- observe only noisy market prices/signals that ing collusive profits. At least since George J. depend on the total market supply. We show that Stigler (964), economists have recognized that collusion is impossible to achieve if: imperfect monitoring may destabilize cartels. Nevertheless, the seminal paper of Edward J. 1. New, noisy information arrives continu- Green and Robert H. Porter (984) has shown ously, without sudden events; that, even with imperfect monitoring, firms can create collusive incentives by allowing price 2. The firms have flexible production technol- wars to break out with positive probability. ogies and can thus react to new information quickly; and * Sannikov: Department of Economics, 549 Evans Hall, 3. Public signals depend on total market sup- University of California, Berkeley, CA 94720 (e-mail: [email protected]); Skrzypacz: Stanford Grad- ply only, and not on individual decisions. uate School of Business, 58 Memorial Way, Stanford, CA 94305 (e-mail: [email protected]). We thank Jeremy There are many markets that fit the general Bulow, Kyna Fong, Drew Fudenberg, Joseph Harrington, features of our model. For example, in markets Ichiro Obara, Yuval Salant, Robert Wilson, and seminar participants at the SED 2004, IIOC 2005, Midwest Macro with homogenous goods, e.g., chemicals, firms 2005, SITE 2005, Arizona State University, UC Berkeley, are selling both to a spot market and to clients, Columbia University, University of Chicago, University with client deals being private but affecting the of Illinois in Urbana Champaign, University of Iowa, New York University, Penn State University, University of Pennsylvania, Princeton University, Rutgers Univer- 2 The term flexible production is usually understood sity, Stanford University, University of Texas in Austin, as describing low costs of changing the amount and the and Washington University for useful comments and variety of output. In this paper, we use this term in a nar- suggestions. rower sense, having firms face low costs of changing flow There are many papers describing explicit and tacit but restricting them to produce only one type of output. collusion among firms. For comprehensive studies, see, Flexibility on the variety dimension has separate effects for example, George A. Hay and Daniel Kelley (974), on the scope of collusion: increased product differentiation Margaret C. Levenstein and Valerie Y. Suslow (2006), or may improve collusion, but increased complexity of moni- Joseph E. Harrington (2006). toring may destabilize cartels. 1794 VOL. 97 NO. 5 SAnnIKov AND SKRZYPACZ: ImPossIBILITY OF CollUSIon 1795 .POPQPMZTVQQMZ $PVSOPUTVQQMZ F D J 1S 5JNF Figure spot market. The spot price can be used to moni- collecting individual company data and aggre- tor the success of collusion. One example that gating that data over monthly periods, breaking received a lot of attention was the cartel produc- conditions and 3. ing lysine, an amino acid.3 This cartel tried to The practice of collecting data on market collude by setting and monitoring a target price shares has been especially common among car- at first. However, those early attempts failed. tels.5 Even the Joint Executive Committee rail- Quoting from Cabral (2005, 20): road cartel, the motivation for the Green and Porter (984) model of equilibrium price wars,6 The topic of lysine prices came up at a collected data on individual members’ market dinner meeting in Chicago between ADM shares. Other cartels have also limited the flexi- and European executives. The latter com- bility of its members to respond to new informa- plained about low prices and accused tion by setting strict rules regarding acceptable ADM of being responsible for it. ADM’s Whitacre responded that “one can point a forms of contracts with customers and by col- lot of fingers,” and that the best thing to do lecting data about suspected deviations through was to find a solution to the problem. secret investigations (e.g., see the sugar trust cartel described in David Genesove and Wallace P. Mullin 200). The cartel has encountered the difficulty The failure of the lysine cartel to collude by related to condition 3: they could not identify the setting a target price at the beginning of its oper- deviator.4 What solution did they agree upon? ation illustrates how the provision of incentives Along the lines of Green and Porter (984), they can break down under flexible production, even could have agreed upon a new target price, com- when firms have very clear information about the mitting to go to a price war if the price fell below success of collusion. Figure illustrates this sur- the new target. However, that would repeat the prising fact using a theoretical model presented old story: as our results suggest, that would not in Section VI. In this example, spot prices are have worked. Instead, the solution was to let correlated over time and have an unconditional output figures “be collected every month by the mean of 2 Q, where Q is the total quantity. trade association … . If one company sold more Figure shows two sample paths of prices when than it was allotted, it would be forced to pur- the firms produce Cournot Nash quantities and chase lysine from companies lagging behind” when they split the monopoly quantity.7 Just by (Eichenwald 2000, 205). Thus, the cartel began 5 For a comprehensive list of such arrangements, see Harrington (2006). 3 The lysine cartel has received a lot of attention thanks 6 See Thomas Ulen (983) and Porter (983) for a to the abundance of detailed information available on its detailed study of this cartel. inner workings, including FBI videotapes of cartel mem- 7 In this nonstationary setting, the absence of collusion bers’ meetings. The cartel was described in detail by Kurt is characterized by a Markov perfect equilibrium (MPE), Eichenwald (2000) in a 600-page book, and discussed fur- and the first-best collusion is similarly a state-dependent ther by Luis M. B. Cabral (2005) and Harrington (2006). strategy. However, the Nash equilibrium and monopoly 4 The problems were real—ADM was indeed over- quantity of a one-shot analogue of this game (with constant producing. demand – Q) serve well for illustration. 1796 THE AMERICAN ECONOMIC REVIEW DECEMBER 2007 looking at the price level at any moment of time, 1SJDFJOQFSJPE it is obvious whether the firms are colluding or not. Yet, despite this apparent transparency, collusion is impossible when firms see prices 1SJDFJOQFSJPE continuously and act sufficiently frequently, and when prices depend only on the total supply. Why? A first guess may be that fast arrival of 3FHJPO information and the flexibility to respond to it 3FHJPO facilitate collusion, as firms can punish poten- tial deviators more quickly. However, although Figure 2 this intuition is true in games with perfect mon- itoring, it does not always hold in games with imperfect monitoring, as demonstrated for the price) for one period of length D, and the verti- first time in the classic paper of Dilip Abreu, cal axis illustrates the summary statistic in the Paul Milgrom, and David Pearce (99) (here- next period of length D. In an optimal symmet- after AMP).8 Let us see why collusion is impos- ric equilibrium, at the end of each period firms sible under the wide range of conditions we test the summary statistic against a cutoff level study. to decide whether to trigger a price war. Figure 2 First, let us consider the classic case of a illustrates the critical regions and 2 that trig- stationary repeated game with a strongly sym- ger a price war in a game with period length D. metric collusive scheme, in which firms behave If the time period between moves increases to identically after all histories. Following Abreu, 2D, two forces influence the scope of collusion. Pearce, and Ennio Stacchetti (986) (hereaf- First, firms learn more information per period, ter APS’86), an optimal symmetric equilib- which helps collusion. Second, the gain from rium has two regimes: a collusive regime and a deviation in a given period increases, which price war–punishment regime. In the collusive hurts collusion.9 From Figure 2, we learn that regime, firms produce less than the static Nash the first effect is stronger when D is small, i.e., equilibrium quantities. If the price drops below collusion is more difficult with smaller time a critical level, this arouses enough suspicion of periods between moves.