Explicit Collusion and Market Share Allocations
Robert C. Marshall

Leslie M. Marx

Penn State University

Duke University

August 9, 2008

Abstract
We show that explicit cartels can implement market share allocations using a reporting framework that is considered to be legally acceptable for trade associations.
This simple resolution of the market share cartel’s monitoring problem provides an explanation for the apparent prevalence of market share allocations relative to customer
or geographic allocations by explicit cartels.
Keywords: explicit collusion, tacit collusion, price …xing, antitrust, trade associations
JEL Classi…cations: C72, L13, L41

The authors thank the Human Capital Foundation (http://www.hcfoundation.ru) for support. We are
grateful to Scott Lobel, Chip Miller, Matthew Rai¤, and Steven Schulenberg for helpful comments. Allerrors are our own. The authors can be reached at Department of Economics, 613 Kern Graduate Bldg.,
University Park, PA 16802, rcm10@psu.edu, and Fuqua School of Business, Duke University, Durham, NC
27708, marx@duke.edu.

1Introduction“Fixing market shares is probably the most e¢ cient of all methods of combating secret price reductions. No one can pro…t from price-cutting if he is moving
along the industry demand curve, once a maximum pro…t price has been chosen.
With inspection of output and an appropriate formula for redistribution of gains
and losses from departures from quotas, the incentive to secret price-cutting iseliminated. Unless inspection of output is costly or ine¤ective (as with services),
this is the ideal method of enforcement ....” (Stigler, 1964, p.46)

Stigler (1964), with its numerous themes and messages, is one of the most important
papers in the …eld of industrial organization. Green and Porter (1984), which is also seminal,
is a derivative of Stigler (1964). Yet, many of the messages of Stigler’s groundbreaking work
have faded because they have not been su¢ ciently developed. This paper is an attempt tofollow up on one remarkable but underdeveloped theme in Stigler’s paper, the prevalence ofmarket share allocations among explicit cartels.
Although market share allocations are prevalent among explicit cartels, geographic allocations and customer allocations, as well as combinations of these with market share allocations, are observed in practice.1 These cartel organizations have di¤erent properties whenit comes to the ease of monitoring compliance, the need for updates to the agreement overtime, the susceptibility of the cartel’s sustainability to outside entry, and the variabilityof the share of cartel surplus captured by various cartel members over time. We argue inthe next section of this paper that a market share allocation may be a superior choice as
1

For legal opinion related to these cartel organizations, see paragraph 9 of United States v. Suntar Roo…ng,
Inc., 897 F.2d 469 (10th Cir. 1990), which states: “Consistent with the analysis of the Supreme Court andprevious holdings of this court and of other circuits, we concur with the determination of the trial court andhold that the activity alleged in the indictment in this case, an agreement to allocate or divide customers
between competitors within the same horizontal market, constitutes a per se violation of Sec. 1 of theSherman Act. See United States v. Topco Assocs., Inc., 405 U.S. 596, 608, 92 S.Ct. 1126, 1133, 31 L.Ed.2d515 (1972) (“[o]ne of the classic examples of a per se violation of Sec. 1 is an agreement between competitors
at the same level of the market structure to allocate territories in order to minimize competition"); UnitedStates v. Goodman, 850 F.2d 1473, 1476 (11th Cir.1988) (“customer allocation agreement alone is a per seviolation of 15 U.S.C. Sec. 1”) (citing United States v. Cadillac Overall Supply Co., 568 F.2d 1078, 1090
(5th Cir.), cert. denied, 437 U.S. 903, 98 S.Ct. 3088, 57 L.Ed.2d 1133 (1978)); United States v. Cooperative
Theatres of Ohio, Inc., 845 F.2d 1367, 1372 (6th Cir.1988) (“customer allocation ... is the type of ‘naked
restraint’ which triggers application of the per se rule of illegality”); Mid-West Underground Storage, Inc.
v. Porter, 717 F.2d 493, 497-98 n. 2 (10th Cir.1983) (“[t]he essence of a market allocation violation ... isthat competitors apportion the market among themselves and cease competing in another’s territory or for
another’s customers”); United States v. Koppers Co., 652 F.2d 290, 293 (2d Cir.), cert. denied, 454 U.S.
1083, 102 S.Ct. 639, 70 L.Ed.2d 617 (1981).”1

long as compliance with the agreement can be monitored. We examine the question of themonitoring of a market share allocation and show that in some environments the necessary
monitoring can be accomplished through the “legal” assistance of a trade association. According to Burns (1936, p.58), “One important further consequence of providing statistics
of total production at very short intervals is that each member is enabled to calculate theextent to which changes in his volume of business are paralleled by changes in the total
volume, i.e., whether his share of the total is changing or not; the Department of Commerce
approved of this use of the statistics.”2 Thus, the legal facilitation by a trade association …llsin the last piece of the puzzle for a market share cartel.
We reviewed the twenty major industrial-product cartel decisions of the European Commission between 2000 and 2005.3 For nine of these cartels the authors of the EC decisions
report that a trade association (or a technical standards committee, or a “consulting …rm”)
played an important role in providing information for cartel members.4 The nine decisions
reporting a role for a trade association are Amino Acids, Carbonless Paper, Citric Acid, Copper Plumbing Tubes, Electrical and Mechanical Carbon and Graphite Products, Industrial
and Medical Gases, Industrial Tubes, Organic Peroxides, and Zinc Phosphate. In all but
one of these cases (Industrial and Medical Gases), the cartel organization involved a market
share allocation. Viewed another way, of the …fteen cases where a market share allocation2

On the legality of a trade association providing such information, Sullivan and Harrison (1988) stateat p.98 that: “A review of the important Supreme Court cases on data dissemination indicates that the
Court is inclined to approve an exchange of past data in summary or aggregate form which do not disclose
individual transactions or customers, (1) where there is no disclosure of present or future information, (2)where there are no enforcement or coercive mechanisms that pressure the membership, (3) where the data
are available to nonmembers for reasonable fees, or at least to those that have a ‘commercial need to know’or would be at a competitive disadvantage without the information, and (4) where the market structure of
the industry suggests that it is not highly concentrated or tending towards collusion.”
For additional commentary, see Henry (1994). The rule-of-reason applies for information-pooling agreements. The exchange of information is not illegal per se (American Column, 1921; Linseed Oil, 1923; Maple
Flooring, 1928; First Cement, 1925). To be challenged, it must restrict competition or help …rms to reachagreements on prices. However, sharing of …rm-speci…c data is suspicious (American Column, 1921; Linseed Oil, 1923). Sharing of aggregate, anonymous, and historical data does not necessarily raise objections,even though it may bring about a certain uniformity of action in the industry (Maple Flooring, 1928; First
Cement, 1925).
The parties to the EC decision in Organic Peroxides argued that the legality of a trade association providing
aggregate statistics extends to private consulting …rms hired by industry members (EC decision at footnote
49).
3
The twenty cases are detailed in the Appendix. Complete references for the EC decisions cited in thispaper are given in Table A.1.
4
The lack of mention of a trade association in an EC decision does not imply that the cartel did not use or
rely on one to conduct its business. The authors of the EC decision may have provided a narrow descriptionof the cartel’s conduct.

2was a component of the cartel’s organization, eight mention a role for a trade association.
Our model begins with an oligopoly framework not unlike Green and Porter (1984), but
is based on price competition. Stochastic demand shocks can occur each period. As in Greenand Porter, there is no way for the …rms to avoid equilibrium-path punishment phases undertacit collusion. As in Porter (1983), the optimal tacitly collusive trigger-strategy equilibrium
may not achieve the monopoly outcome, even during periods of cooperation.
To model explicit collusion, we begin by assuming …rms can credibly communicate theirmarket outcome to a single …rm that acts as a clearinghouse for such information. We showthat the collusive outcome can be sustained in this environment if the …rms use transfers.
We then increase the degree of information sharing by assuming that all …rms can credibly
communicate their market outcomes to one another. In this case, the monopoly outcome
can be sustained even without the use of transfers. Finally, we assume that communicationis restricted to ‡ow through a trade association, which can only report industry aggregates.
We give conditions under which this is su¢ cient to sustain the monopoly outcome.
In our model, a market share allocation arises naturally since, with the report from thetrade association, cartel members can detect whether their own market shares have changed,
and thus whether there was cheating on the collusive agreement. Therefore, with this limited
information exchange and a market share allocation, the …rms are able to eliminate allpunishment periods associated with tacit collusion and increase payo¤s in cooperative periods
to the monopoly outcome.
Other authors considering collusion in an environment with repeated price competition
include Tirole (1988), Athey and Bagwell (2001), Bagwell and Wolinsky (2002), Athey,
Bagwell, and Sanchirico (2004), and Harrington and Skrzypacz (2007).5 Tirole (1988) andBagwell and Wolinsky (2002) consider models of tacit collusion based on Bertrand price competition, where …rms’ prices and quantities are private information. As in our benchmark
model of tacit collusion, under certain conditions trigger strategies can be used to support
behavior in non-punishment periods that maximizes the expected joint stage-game payo¤s.6Harrington and Skrzypacz (2007) consider a model of explicit collusion in which …rms’prices
are private information, but quantities are public information, and total demand is …xed.
5Blume and Heidhues (2008) and Skrzypacz and Hopenhayn (2004) focus on collusion in repeated singleunit auctions. For an example of a bidding cartel operating in a repeated auction context, see Asker (2007).
On the problem of identifying and testing for bid rigging, see Bajari and Summers (2002) and Bajari andYe (2003).
6
The underlying logic is that of the Folk Theorem (see Friedman, 1971; and Fudenberg and Maskin,1986).

3

Their results highlight di¤erences between environments with symmetric versus asymmetriccartel punishments. Athey and Bagwell (2001) and Athey, Bagwell, and Sanchirico (2004)
assume perfect monitoring of prices and quantities and consider a range of collusive environments, including environments with and without communication and with and withouttransfer payments among …rms. They allow individual cost shocks that are private information and provide results on the e¢ ciency and payo¤ properties of equilibrium outcomes.
The paper proceeds as follows. We begin by discussing the prevalent use by explicit
cartels of market share allocations in Section 2. Section 3 describes the basic componentsof the model and develops the benchmark case of tacit collusion. In Section 4, we moveto an environment of explicit collusion, which involves information sharing and transfers
among the colluding …rms. Section 5 focuses on the role of a market share allocation as acomponent of an explicitly collusive equilibrium. Section 6 concludes with a discussion of
longer-run e¤ects of an explicit cartel’s ability to share information and make transfers. In
particular, these arrangements may allow the cartel …rms to undertake projects that increase
the cartel’s pro…tability that no individual …rm would undertake on its own.

2

Cartel organization

We focus on three cartel organizations: a customer allocation, a geographic allocation,
and a market share allocation. These three cartel organizations are highlighted in Posner(1976, p.62), where he states,“If the major …rms in a market have maintained identical or nearly identicalmarket shares relative to each other for a substantial period of time, there isgood reason to believe that they have divided the market (whether by …xing
geographical zones or sales quotas or by an assignment of customers), and thereby
eliminated competition, among themselves.”
A customer allocation within an explicit cartel assigns speci…c customers to speci…c cartel
members. A geographic allocation within an explicit cartel speci…es geographic areas where
speci…c cartel members can and cannot sell product.7 A market share allocation among
members of an explicit cartel speci…es the maximum shares of within-cartel sales that eachcartel member is allowed in the market for a given time period. Combinations of these cartel
7

On geographic patterns of trade and home bias in a non-collusive setting, see Hortaçsu, Martinez-Jerez,
and Douglas (2006).

4

allocations are possible and observed. For example, explicit cartels often allocate a country
where a member has production facilities exclusively to that producer (geographic allocation)
but apply a market share allocation in regions where there is no cartel production.
Table 1 contrasts these three cartel allocation schemes in terms of their ease of monitoring
compliance, the need for updates to the agreement over time, the susceptibility of cartel
sustainability to outside entry, and the variability of the share of cartel surplus captured byvarious cartel members over time.
As shown in the table, a market share allocation may be a superior choice as long ascompliance with the agreement can be monitored.

Table 1: Comparison of Cartel Organizations
Organization Requirements Monitoring

Disruptions*Customerallocation

Customers
known inadvance

Easy

Changes incustomer
identities

Geographic
allocation

Sales areassociatedwith locations

VariesMarket shareallocation-?

OutsideEntry

Share of Cartel
Surplus**Affected by
Causeschanges in relative
reallocation
sizes of customers

Changes in trade
Affected by
Causesregulations andchanges in relative
reallocation
boundaries
growth of areas-

No withincartel
reallocation

Stable*In all cases, the cartel is affected by changes in the membership of the cartel itself. We focus on external factors
causing disruptions.
**In all cases, a cartel may choose to change cartel members' relative shares. We focus on external factors forcing
such a change.

In what follows, we discuss aspects of each cell in this table. The requirements column isfairly straightforward. A cartel cannot allocate customers if the identities of the customers
are not known in advance of the sales, and it is not meaningful for a cartel to allocate
geographic areas if individual sales cannot be associated with a particular geographic area.
No special requirements are necessary for a cartel to agree to …xed within-cartel market
shares.
The remaining four columns deserve more detailed discussion. We address these in turnin the following four subsections. We summarize in Section 2.5.
5

2.1

Monitoring

With a customer allocation, if each customer single sources, each …rm need only observethat it is selling to the customers allocated to it. If a customer multiple sources, then it
may be necessary to verify …rms’shares of a customer’s purchases.8 A buyer may have an
incentive to allow a supplier to audit its purchases if the audit is required in order for thebuyer to obtain rebates based on the share it purchases from the supplier.
With a geographic allocation, if each producer is in a separate country and import/export
statistics and other information about cross-border trade is readily available or if there are
restrictions on cross-border trade, then monitoring can be straightforward.9 If it is known
which customers are in which geographic areas and if customers single source, then each …rmneed only observe that it is selling to the customers in the geographic area allocated to it.
Monitoring is more di¢ cult if customers are not …xed and/or it is di¢ cult to monitor the‡ow of goods across geographic boundaries.
With a market share allocation monitoring might appear to be a daunting task. If producers are located in the same country, and that country is a large market, then cross-border
trade will not provide su¢ cient information to enforce a global market share allocation.
Monitoring may also be encumbered if customers multiple source. A global market shareallocation requires that the cartel’s total market size be assessed and communicated to cartel
members so each cartel member can ascertain whether it has achieved its agreed-to market
share.
In this paper, we examine explicit collusion based on a market share allocation under
three di¤erent monitoring regimes.10 We …rst assume …rms can credibly communicate their
8

One possibility is to use …delity rebates based on market shares, with associated audits, to verify shares.
The EC decision in Copper Plumbing Tubes at paragraph 622 states, “However, for certain durations
and countries, control was facilitated by export statistics.” The same decision at paragraph 144 states, “At
least until 1995, monitoring was facilitated by national certi…cation procedures. Copper plumbing tubes
had to be certi…ed in each Member State. Each Member State had its own certi…cation label. Certi…cation
organisations ... prohibited producers at least until 1995 to indicate di¤erent national certi…cations onplumbing tubes.”
Patent licensing agreements can also facilitate monitoring. As stated in the Temporary National Economic
Committee (TNEC), Hearings, Part 25, Cartels, Washington, DC: U.S. Government Printing O¢ ce, 1941,
at p.13341: “In the incandescent electric lamp industry, ... the Westinghouse Electric Co. pays the General
Electric Co. a royalty of 1 percent on sales of lamps which do not exceed 25.4 percent of the combined lamp
sales of the two concerns. It pays a royalty of 30 percent on sales made in excess of this. ... The …ve otherlicensed assemblers are prohibited from making and selling lamps for export. They pay a royalty of 3 1/3
percent on lamp sales which do not exceed a certain percentage of General Electric sales. They are required
to pay an additional royalty of 20 percent on sales made in excess of their stipulated shares.”10
Cartels have often found ways to monitor members. In discussing the International Steel Cartel ofthe late 1930’s, Hexner (1943, p.95) states, “One should realize that violations which occurred sometimes
96

market outcome to a single …rm that acts as a clearinghouse for such information.11 For
example, the EC decision in Amino Acids at paragraph 122 states, “ADM named Ajinomoto
as the o¢ ce to which each lysine producer would provide monthly sales …gures.”12
Second, we increase the degree of information sharing by assuming that all …rms can credibly communicate their market outcomes to on another. For example, Stocking and Watkins(1991, p.335) state that in the Incandescent Lamp Cartel, “Each member was required tothrow open his plants and research laboratories to the inspection of any member.”13
Third, we assume that communication is restricted to ‡ow through a trade association,
which can only report industry aggregates.14 For example, the EC decision in Zinc Phosphate at paragraph 35 states, “Over the time period considered in this Decision, the …ve
main European producers of zinc phosphate exchanged information and met within trade associations. These trade associations collected and compiled the sales data of each individualcompany and informed them in return about the size of the market.”15
To ensure the accuracy of the statistics it reports, some trade associations audit the …rms’
reported information.16 For example, The EC decision in Amino Acids at paragraph 100
happened many thousands of miles from the centers of cartel activities. However, more often than one might
suppose, infringements of cartel regulations were reported by competing distributors within a few hours,
even if they occurred in the most remote regions of the world.”
11
Hay (1982, p.454) describes the possibility of e¤ective collusion with asymmetric information sharing:“For purposes of accomplishing the oligopoly tasks, the exchange of information need not be symmetrical.
That is, the oligopolists may bene…t as a group even if only some …rms unilaterally provide information
about their own activities.”
12
In other examples, the EC decision in Organic Peroxides at paragraph 128 states, “Shortly before eachquarterly meeting, one of the participants on a rotating basis would receive the date [sic] from the twoother participants.” In addition, the EC decision in Citric Acid at paragraph 85 states, “each company
would report its monthly sales …gures to [a Roche executive’s] secretary in Basel, who would then contact
the companies and provide each company’s sale …gures for the corresponding month. ... since the sales ofthe four companies made up a signi…cant part of total ECAMA sales, the regular report of which provided
aggregate sale …gures, this could be used to identify any company that gave incorrect data.”
13
In another example, the EC decision in Specialty Graphite at paragraph 101 states, “In addition, thefrequent exchanges of shipment records among competitors [cartel members] allowed a detailed monitoringof sales and the detection of possible deviations to the cartel instructions.”
14
Exhibit No. 2176 of the TNEC (1941) Hearings on cartels (pp.13573–13574) is a public statement fromthe Department of Justice Division for Enforcement of Antitrust Laws released June 27, 1939. It states,“The Department’s preliminary investigation indicates that certain trade associations not only disseminate
production statistics but take steps to see that their members produce no more of the total supply thanthese statistics indicate has been their proportionate share.”15
In another example, the EC decision in Organic Peroxides at paragraph 92 describes the Zurich-based…rm AC Treuhand as performing the following functions (among others): “organised the auditing of the datasubmitted by the parties” and “collected data on OP sales and provided the participants with the relevant
statistics.”
16
According to Clark (1983, p.927), “In the typical case, an industry trade association is authorized tocollect detailed information on the transactions executed by each member. To ensure full compliance, the7states, “ADM stated that the way for them to communicate is through a trade association.
ADM explained by way of example that ADM reported its citric acid sales every month to a
trade association, and every year, Swiss accountants audited those …gures.”Alternatively, theassociation might require …rms to post bonds that are forfeit if the …rm is caught not reporting
truthfully.17 Stocking and Watkins (1991) describe the use of bonds in the “common fund”
of the Steel Cartel (p.183), the “guarantee deposits”of the Aluminum Alliance (p.232), andthe “indemnity funds”deposited at a Swiss corporation by the Incandescent Electric Lamp
Cartel (p.337).
Henry (1994, p.503) suggests that there may even be antitrust bene…ts associated withusing a trade association: “Employing an independent third party to undertake data collection, compilation, and dissemination can signi…cantly decrease the antitrust risk. Third
parties eliminate the need for direct contact between the information providers and, thus,
reduce the risk of collusion. Moreover, third parties can aggregate the data so that particular information providers are not identi…able.” We show that, although it may be legallypermissible for a trade association to report data in aggregate form, the fact that data isaggregated is not su¢ cient to prevent that information exchange from being an importantfacilitator of collusion.
We do not mean to suggest that the exchange of any information through a trade association is legal, nor are we arguing that because the exchange and dissemination of certain
information through a trade association is legal, it could not be part of an illegal collusive
mechanism. It has long been recognized the practices of a trade association may lead to the
suppression of competition and that any such practices would be considered a violation of
the antitrust laws.18
association or an independent auditing …rm is sometimes empowered to audit company records, and …nes
may be levied for failure to report sales quickly or accurately.”
17
Commenting on cartels’use of bonds, Hexner (1943, p.102) states, “According to the EIA [continental
European steel cartel] agreement, the management committee …xed rather high deposits, placed in thecustody of the EIA business agency in Luxemburg, which were intended to insure the orderly ful…llment of
obligations assumed with membership in the EIA and in the comptoirs closely connected with it.”18
See, e.g., the 1922 letter from Attorney General H. M. Daugherty to Secretary of Commerce Herbert
Hoover stating, “Therefore the expression of the view that the [trade association practices] enumerated byyou, with the exceptions stated, may be done lawfully is only tentative; and if in the actual practice of anyof them it shall develop that competition is suppressed or prices are materially enhanced, this Department
must treat such a practice as it treats any other one which is violative of the Anti-Trust Act.”(Jones, 1922,
p.333)

8

2.2

Disruptions

A customer allocation must specify individual customers. However, customers can comeand go. Entry, exit, mergers, and divestitures can change the set of existing customers.
These changes create a need for updates to an explicit cartel’s customer allocation.
Updates to a geographic allocation may also be called for if changes in the regulatory or
political environment, e.g., boycotts, wars, tari¤s, etc., make it di¢ cult or costly for a particular cartel member to serve a particular geographic area. Although relatively uncommon,changes in national boundaries can create a need for updates of geographic allocations.
A market share allocation need not be invalidated by changes in the environment.

2.3

Outside entry

For a cartel operating under a customer allocation, outside entry causes a reallocation ofcartel surplus among the cartel members unless non-cartel entrants serve customers allocatedto the various cartel members in equal proportion. For a geographic allocation, outside entry
causes a reallocation of cartel surplus among the cartel members unless outside entrants serve
the same proportion of each cartel member’s geographic area.
For a cartel operating under a market share allocation, non-cartel entry need not cause areallocation. Outside entry reduces the overall surplus available to the cartel members but
does not require a reallocation of the within-cartel market shares.

2.4

Share of cartel surplus

The smooth function of a cartel can be disrupted if a cartel member believes that itis being relatively disadvantaged by an exogenous shift in the marketplace or economic
environment. Thus, it can be important for the sustainability of a cartel that the cartel
members’relative shares of the collusive surplus remain equitable.
In a dynamic environment, one would not expect customers’demands to vary in exact
proportion to one another, so the share of cartel surplus captured by the various cartel
members under a customer allocation would be expected to change over time. Similarly,
in a dynamic environment, one would not expect the demand in various geographic areas
to vary in exact proportion to one another, so the share of cartel surplus captured by thevarious cartel members under a geographic allocation would be expected to change over time.
However, with a market share allocation, cartel members’shares of the cartel surplus remain

9constant over time.

2.5

Summary

To summarize, if we return to Table 1, we see that a customer allocation, when it isfeasible, may be desirable because of the ease of monitoring. However, a customer allocation
has a number of undesirable properties when the set of customers or their relative sizeschange over time or if cartel price increases induce non-cartel entry.
In some cases, monitoring can also be straightforward for a geographic allocation, so thatorganization may be desirable as well. However, a geographic allocation can fare poorly insome political environments or when the relative purchases of di¤erent geographic areas varyover time or there is non-cartel entry.
Because both customer allocations and geographic allocations have desirable properties
for a cartel in certain environments, we might expect to observe these organization in use. For
example, a customer allocation was a component of the cartel agreement in several EC cases(see Table A.2 in the Appendix). A geographic allocation was also a component of several EC
cases and was used in Tuscaloosa v. Harcros 158 F.3d 548 (11th Cir. 1998), where providersof repackaged chlorine were alleged to have allocated contracts in geographic markets, and in
U.S. v. Koppers, where two road construction …rms divided the state of Connecticut between
them:“Arthur Schuck, Koppers’manager of its eastern road materials district, madea proposal to Dosch-King in 1967 that the two …rms divide the state between themso that Dosch-King would be the low bidder in the western part of Connecticut,
where its activities were concentrated, and Koppers would be the low bidder inthe eastern part, where its storage facility and distribution point were located.”19
As shown in Table 1, as long as a cartel can e¤ectively monitor a market share allocation,
it appears to dominate the other cartel organizations considered there. As we show in theremainder of this paper, e¤ective monitoring is possible if the cartel can enlist a tradeassociation to collect data on cartel output and disseminate aggregate information to thecartel members.20
19

United States v. Koppers Co., 652 F.2d 290 (2d Cir. 1981) at paragraph 4.
Before continuing to the next section, however, it may be useful to be clear about some things we are notarguing in this paper. We are not arguing that collusion cannot be e¤ective without a market share allocation.
As described above and in the Appendix, e¤ective cartels have used other organizations, including, but not
20

10

3

Benchmark— Tacit collusion

We consider a model with n …rms that interact repeatedly over an in…nite time horizon,t 2 f0; 1; :::g. We assume the …rms have a common discount factor 2 (0; 1). Firm i’s
strategy set in the stage game is Si , which is constant over time. The stage game payo¤ for…rm i in period t is i (s; "t ); where i : j2N Sj! R; s is the pro…le of strategy choices
in period t; and "t 2
is a random variable that is i.i.d. across time and common to all…rms. We assume is a closed, bounded interval in R and that the distribution of "t has
positive density on the interior of .
In each period t, the …rms’ strategies, together with the shock "t ; generate a “market
outcome” for …rm i of mi : j2N Sj! M . We assume that …rm i’s market outcome
captures the e¤ect on …rm i’s payo¤ of both the shock "t and the rival …rms’ strategies.
Thus, there exist functions ^ i : Si M such that if m
^ i = mi (s; "t ); then ^ i (si ; m^ i ) = i (s; "t ).
Our main application is to an environment with price competition. In this application,a …rm’s strategy is its price, and a …rm’s market outcome is the quantity it sells, which
depends on …rm i’s price and its rivals’prices, as well as the shock. Thus, even though a…rm’s market outcome depends on the other …rms’strategies, its payo¤ depends only on its
own strategy and its market outcome. In Section 5, we expand the …rms’strategy spaces toinclude sales e¤ort.
The timing within each period is as follows: (i) …rms simultaneously choose strategies,(ii) each …rm observes its own payo¤ and its own market outcome.
We let strategy pro…le se be an equilibrium of the stage game, with expected stage
Pgame payo¤s E"t [ i (se ; "t )]. De…ne (s) E"t [ ni=1 i (s; "t )] ; which is the expected joint
stage-game payo¤ of the n …rms given their strategies.
Let s 2 arg maxs (s) be the optimal cartel strategies, which we assume are unique.
We assume that for each …rm i; E"t [ i (s ; "t )] > E"t [ i (se ; "t )] so that each …rm’s expectedstage-game payo¤ increases if the …rms choose “collusive” strategies s rather than the“noncooperative strategies”se .
We assume that for each …rm i there exists sdi such that E"t i (sdi ; s i ; "t ) > E"t [ i (s ; "t )] ;so that a one-shot deviation by …rm i from an agreement to play s increases …rm i’s expected stage-game payo¤. We also assume that for all sdi such that E"t i (sdi ; s i ; "t ) >limited to, customer and geographic allocations. We are also not arguing that collusion cannot be e¤ectivein the absence of a trade association. Clearly it can— see the EC decision in Vitamins and other cases listed
in the Appendix. The analysis of a particular cartel must take into account the speci…cs of the particularmechanism used by that cartel.

11

E"t [ i (s ; "t )], and all "t 2 ; there exists "0t 2ddi (si ; s i ; "t ); m i (si ; s i ; "t )such that=(00i (s ; "t ); m i (s ; "t )) :(1)

Thus, the pro…t and market outcome observed by …rms other than i is the same when …rm
i deviates by choosing sdi and the shock is "t ; as it is when …rm i does not deviate, but
the shock is "0t . In the case of price competition, this assumption says that a …rm cannot
distinguish the undercutting of its price by a rival …rm from a negative demand shock.21
Now suppose that there is a tacitly collusive equilibrium of the in…nitely repeated game inwhich the …rms choose strategies s in all periods on the equilibrium path for all realizationsof the shock.22 This implies that for all "t 2 ; if …rm j 6= i observes ( j (s ; "t ); mj (s ; "t )) ;then …rm j chooses strategy sj in the next period. But then, …rm i can pro…tably deviate
by choosing strategy sdi since it increases its expected payo¤ and, using (1), does not triggera response by the other …rm. This proves the following result.
Proposition 1 There is no tacitly collusive equilibrium in which …rms maximize their expected joint stage-game payo¤ in every period on the equilibrium path.
Proposition 1 implies that under a tacitly collusive agreement, there must be punishments on the equilibrium path, and so the cartel’s discounted expected payo¤ is less than1(s ). In particular, with positive probability there must be some periods in which …rms
1
use strategies other than s .

3.1

Trigger strategies under price competition

Possible tacitly collusive equilibria include equilibria in which certain market outcomestrigger a Nash-reversion punishment phase as in Porter (1983) and Green and Porter (1984),23
21

In Green and Porter’s (1984) model, a low market price can be the result of a deviation by another …rm
or a negative demand shock.
22
We de…ne tacit collusion to be non-cooperative in…nitely repeated play. However, Green and Porter(1984) note in their footnote 5, “It is logically possible for this agreement to be a tacit one which arises spontaneously. Nevertheless, in view of the relative complexity of the conduct to be speci…ed by this particularequilibrium and of the need for close coordination among its participants, it seems natural to assume herethat the equilibrium arises from an explicit agreement.”
23
The use of reversion to pre-collusive play as a punishment for deviations from collusion is explicitly mentioned in Congressional testimony involving dyestu¤s manufacturers (Patents: Hearings before the Committee
on Patents, United States Senate, Seventy-Seventh Congress, Second Session, on S. 2303 and S. 2491, Part
5, May 13 and 16, 1942, United States Government Printing O¢ ce, 1942, p.2424). The testimony includes
a letter from a foreign sales manager of a dyestu¤s manufacturer stating: “You and your contemporaries

12and other equilibria involve more sophisticated stick-and-carrot strategies as in Abreu (1986)
and Abreu, Pearce, Stacchetti (1986, 1990).
Depending on the discount factor and other parameters, there may exist tacitly collusive
equilibria in which …rms choose strategy pro…le s in some periods on the equilibrium path.
However, as discussed in Green and Porter (1984), there may not exist a Nash reversion,
trigger-strategy equilibrium in which …rms play s in the non-punishment periods. Furthermore, even if such equilibria exist, as shown in Porter (1983), the joint-payo¤-maximizing
equilibrium of that type may require that …rms use strategies other than s in the nonpunishment periods.
To provide a simple formalization of these ideas, we consider an environment with symmetric …rms, homogeneous products price competition, and constant marginal cost. Under
these assumptions, the Nash equilibrium of the stage game is for all …rms to choose priceequal to marginal cost, and so i (se ; "t ) = 0.
In order for each …rm to have positive sales under collusion, it must be that all …rms
choose the same price, i.e., si = s1 for all i. A …rm deviating to a price above s1 has zeropayo¤, and a …rm deviating to a price below s1 captures all the sales and so has payo¤bounded above by n 1 (s ; "t ). We assume the shock "t a¤ects the …rms symmetrically, so if
the shock is su¢ cient to drive sales to zero for one …rm, it also drives sales to zero for theother …rms.
Consider a tacitly collusive Nash-reversion, trigger-strategy equilibrium as in Green andPorter (1984). Classify periods as either punishment periods or non-punishment periods. To
begin, assume the punishment continues inde…nitely once it is triggered.
If a …rm deviates by charging price below s1 ; all other …rms will have zero sales. So any
trigger-strategy equilibrium in this environment must involve punishment periods following
any period in which at least one …rm observes zero sales. If a …rm observes zero sales, it
knows that either there was a su¢ ciently negative demand shock and all …rms had zero sales,or one or more of the other …rms deviated and undercut the collusive price, in which case all
non-deviating …rms observe zero sales. In either case, following such a period, it is common
knowledge that the next period is a punishment period.
Thus, the …rst period, t = 0; is a non-punishment period, and for t
1 period t is apunishment period if in any period prior to t; any …rm has a market outcome of zero.
should be in a position to establish market prices based upon de…nite strength determination of color, which
prices should be followed by you if such an understanding is reached. But, if you have any indication thata contemporary is not adhering to such prices, then immediately revert to the prices prevailing before any
arrangements were established.”

13

Consider whether a …rm can pro…tably deviate from strategies specifying that they choose
the expected joint-payo¤ maximizing strategy pro…le s in non-punishment periods and thestage-game Nash equilibrium se in punishment periods. Let (si ) Pr[minj6=i mj (si ; s i ; "t )= 0] be the probability that a punishment phase is triggered when …rm i chooses si and…rms other than i choose s i . Note that (si ) = 1 for si < si since a deviation triggers
a punishment phase with certainty, but we assume (si ) 2 (0; 1) so that there is positive
probability that a punishment is triggered even when …rms choose s .
Assuming no deviations, …rm i’s expected payo¤ is
E"t [ i (s ; "t )] + 1
V ( )
1
(1
E"t [ i (s ; "t )]=:1(1(si ))(si )E"t [ i (se ; "t )](si ))

Firm i’s expected payo¤ from choosing si < si in one period and then returning to equilibrium play in the ensuing punishment phase is
V (si ; )E"ti (si ; s i ; "t )= E"ti (si ; s i ; "t )+1

E"t [ i (se ; "t )]< nE"t [ 1 (s ; "t )] :Since lim !1 V ( ) = (s1 ) E"t [ 1 (s ; "t )] ; the deviation is not pro…table as long as1su¢ ciently large and (s1 ) < n1 ; giving us the following result.

is

Proposition 2 Assuming homogeneous products price competition with symmetric …rms
with constant marginal cost, there exists a tacitly collusive equilibrium in which …rms maximize their expected joint stage-game payo¤ in some periods on the equilibrium path if andonly if is su¢ ciently close to one and (s1 ) < n1 .
Proof. The proof of su¢ ciency follows from the discussion in the text. For the proof ofnecessity, note that for su¢ ciently low, the incentives for short-run deviations dominate,
regardless of the punishment strategy employed, since in a tacitly collusive equilibrium,
punishment payo¤s are bounded below. If (s1 ) is su¢ ciently large, then punishments are
triggered with su¢ ciently high probability that again incentives for short-run deviations
dominate. Q.E.D.

14

3.2

Optimal trigger strategies under price competition

Although Proposition 2 shows that the strategies that maximize the expected joint payo¤ in the stage game can be achieved in some periods (non-punishment periods) in tacitly
collusive equilibria, such equilibria may not be optimal for the tacitly colluding …rms. It
may be that the optimal tacitly collusive agreement requires that …rms choose strategies
in non-punishment periods other than those that maximize their expected joint stage-gamepayo¤. By choosing strategies with a lower joint payo¤, it may be possible to reduce the
incentive for …rms to deviate, thereby allowing the …rms to sustain cooperation with lesssevere punishments. In a model with quantity competition, Porter (1983) shows that whenever the optimal trigger-price mechanism in his model involves interior values for the trigger
price and length of punishment, then it involves using strategies in non-punishment periods
that result in an expected joint payo¤ that is less than its maximum. Our analysis withprice competition is similar to the analysis of Tirole (1988, Section 6.7.1.1).
Since we focus on symmetric equilibria, we can simplify notation by letting ~ (si )E"t [ i (si ; :::; si ; "t )] and ~(si ) Pr [mi (si ; :::; si ; "t ) = 0].
We now allow …nite punishment lengths. If the punishment phase lasts for only T 1
periods, then a …rm’s expected payo¤ when …rms choose si is

1(1~ (si )~(si ))~(si ) T:

The optimal symmetric tacitly collusive equilibrium of this type is de…ned by s~i and T~ thatsolve
~ (si )(~
si ; T~) 2 arg max(2)
si ;T 1(1 ~(si ))~(si ) T
subject to the incentive compatibility constraint that
~ (~
si )
1

(1

~(~
si ))

~ (~
si )

~

~(~
si )

T~

n~ (~
si ) + T

1

(1

~(~
si ))

~

~(~
si ) T;or equivalently,
T~

n

1

n(1
n~(~
si )

~(~
si ))
:
1

(3)

Note that (3) must bind because otherwise the punishment length could be shortened.
Using (3) to substitute into the maximand in (2), we can …nd the optimal collusive price by15

solving
s~i 2 arg max
si

11

1 n~(si )~ (si ):
1 ~(si )(4)

It is clear from this expression that the optimal price does not depend on the discountfactor. Also, this expression is positive as long as ~(si ) 2 [0; n1 ); i.e., for an equilibrium pricesu¢ ciently small.
For example, if we assume zero marginal cost and linear demand D(p) = max f0; 1 p "t g ;where "t is uniformly distributed on [0; 1]; then~ i (p) =

Z 1 p
0

1
(1
n

p

")pd" =

1
p(1
2n

p)2 ;

~(p) = Pr(1 p "t 0) = p; and the expected joint-payo¤ maximizing price is p = 13 .
p
2
Solving (4), we get p~ = 1+n 3n1 n+n ; which one can show is less than p for all n 2.
Thus, in the optimal tacitly collusive equilibrium, even in non-punishment periods, …rms do
not choose the strategies that maximize their expected joint stage-game payo¤.
In general, if we assume ~ and ~ are continuously di¤erentiable and that the maximandin (4) is concave, then taking the derivative with respect to si and evaluating it at si = si ;the optimal collusive price is less than si if@ ~ (si )
<
@si
(1

n 1
@~(si )~ (si ):~(si )) (1 n~(si )) @si(5)This proves the following proposition.
Proposition 3 In an environment with symmetric …rms with constant marginal cost engaged in homogeneous products price competition, assuming di¤erentiability and concavity,
if (5) holds, then in the optimal tacitly collusive trigger-strategy equilibrium, …rms neverchoose the strategies that maximize their expected joint stage-game payo¤.
To summarize, in this section we show that there are a number of reasons why expectedjoint pro…ts are not maximized under tacit collusion. First, Proposition 1 shows that …rms
cannot sustain the optimal stage-game strategies without having punishment periods onthe equilibrium path that reduce …rms’ payo¤s. Second, by Proposition 2, even in nonpunishment periods the discount factor may prevent there from being any tacitly collusive
equilibrium that supports the optimal stage-game strategies. Finally, by Proposition 3,
even if the discount factor is su¢ ciently large that the optimal stage-game strategies can
16be supported in a tacitly collusive equilibrium, such an equilibrium may not be the optimal
tacitly collusive equilibrium because of the severity of punishments required to support suchstrategies.

4

Explicit collusion

In this section, we consider explicitly collusive agreements between the …rms. Explicit
collusion occurs when …rms exchange information and/or resources for the purposes of increasing pro…ts through the suppression of inter…rm rivalry. Collusion is also explicit if …rms
formally agree to the strategies they will employ. For example, collusion is explicit if …rms
communicate an agreement to participate in an otherwise tacitly collusive equilibrium.
We consider di¤erent possibilities for the information exchange between explicitly colluding …rms. Speci…cally, we consider di¤erent possibilities for …rms’ abilities to monitor themarket outcomes of their rivals.

4.1

One-sided monitoring

In this section, we assume that …rm 1 can observe the market outcome of the other …rms,
but not vice versa; we refer to this environment as one with one-sided monitoring. For
example, a …rm in country 1 might be able to monitor imports to country 1 and so be able
to observe the quantity sold in country 1 by foreign …rms, but the foreign …rms might not
be able to observe how much the domestic …rm sells. Or …rm 1 might play the role of aring leader for the cartel and as part of the cartel agreement have the authority to audit themarket outcomes of the other …rms. Or …rm 1 might be a large …rm that sells at least someproduct to each customer and so through …delity rebates or other contractual agreements
have the right to audit the various customers’purchases. See Section 2 for speci…c examples.
In environments with one-sided monitoring, we show that by using transfers, the …rms
can achieve the optimal cartel outcome, maximizing the expected joint stage-game payo¤ inevery period on the equilibrium path.
The timing within each period is as follows: (i) …rms simultaneously choose strategies,(ii) each …rm observes its own payo¤ and its own market outcome, (iii) …rm 1 observes themarket outcome of the other …rms, and (iv) …rms make transfers. Related to (iv); we assume…rms can observe whether any …rm failed to make a required transfer.
The following condition says that deviations for a given strategy pro…le are detectable17

by …rm i if …rm i can calculate a statistic based on its strategy and market outcome and themarkets outcome of the other …rms whose value identi…es deviations by the other …rms.
De…nition 1 Pro…table deviations from strategy pro…le s^ are detectable by …rm i if there
exists statistic i : Si M n ! R and ^ i 2 R such that for all "t 2 ; j 6= i; and sj 2 Sj ;^ j ; "t ) > j (^s; "t ) implies
j (sj ; ssi ; m(sj ; s^ j ; "t )) 6=i (^si ; m(^s; "t )) = ^ i :i (^This de…nition says that pro…table deviations by …rm j are detectable by …rm i if there
is some statistic that …rm i can calculate given its information, such that if …rm i does notdeviate, then the value of the statistic di¤ers from the value ^ i if and only if …rm j deviates.
Deviations that are not pro…table need not be detected. For example, a su¢ ciently large
negative shock might reduce all …rms’ quantities to zero, in which case a deviation might
not be detectable, but it would also not be pro…table.
Note that the de…nition requires that, when no …rm deviates, the value of …rm i’s statistic
is independent of the shock "t . For example, in an environment with heterogeneous products
price competition and a common, multiplicative shock, deviations are detectable using as
the statistic a …rm’s market share, i (si ; m) = Pnmi mj .
j=1
We now construct an explicitly collusive equilibrium with one-sided monitoring in which
the …rms choose strategies that maximize the expected joint stage-game payo¤ in every
period on the equilibrium path. In the equilibrium we construct, …rm 1 uses its information
to determine transfer payments between it and the other …rms. In period t, …rm 1 makes apayment to …rm j offj (mj ) E"t [ j (s ; "t )] ^ j (sj ; mj ):Expected transfers are zero, but if …rm j’s pro…t is less than its expected value, then…rm 1 makes a payment to …rm j. If …rm j’s pro…t is greater than its expected value, thenfj (mj ) is negative and …rm j makes a payment to …rm 1. Thus, …rm j’s per-period payo¤
is constant at E"t [ j (s ; "t )] ; and …rm 1 absorbs all the uncertainty generated by the shock"t . If either …rm fails to make the required payment, then in the next period …rms begin apunishment phase in which …rms choose their Nash equilibrium strategies. For the results
below it is su¢ cient to assume that the punishment phase is in…nitely long.
We show that there exists 0 < 1 such that for all > 0 ; these strategies form anequilibrium. First, note that each …rm’s strategy is feasible in that it depends only on
variables that it can observe. Second, we show that …rm 1 has no pro…table deviation. To
18see this, note that for any price, …rm 1 prefers to make the payments required of it rather
than trigger a punishment phase.
Lemma 1 For su¢ ciently large, for any s1 ; for all j such that fj (mj ) > 0; it is a best
reply for …rm 1 to make the transfer payment fj (mj ) to …rm j.
P
Proof. If …rm 1’s does not make its required payments, it saves j6=i max ffj (mj ); 0g ; whichPis bounded above by
j6=i E"t [ j (s ; "t )] ; but the punishment phase begins in the nexteperiod, so …rm 1’s looses 1 E"t [ 1 (s ; "t )1 (s ; "t )] in the continuation game. Thus, forsu¢ ciently close to 1, it is a best reply for …rm 1 to make the payments. Q.E.D.
Using Lemma 1, we can complete the demonstration that …rm 1 has no pro…table deviation. By Lemma 1, it is su¢ cient to show that for any s1 ; …rm 1’s expected payo¤ in period
t if it chooses s1 and makes the required transfers is less than or equal to its expected payo¤
in period t if it chooses s1 and makes the required transfers.
Firm 1’s expected payo¤ hin period t if it chooses s1 and makes thei required transfers isPbounded above by maxs1 E"t 1 (s1 ; s 1 ; "t )j6=i fj (mj (s1 ; s 1 ; "t )) . Using the de…nitionof fj (mj ); we can rewrite this expression as
max E"ts1= max E"t
s1

=

(s )

"

"

1 (s1 ; s 1 ; "t ) +X^ j (sj ; mj (s1 ; s 1 ; "t ))j6=i

1 (s1 ; s 1 ; "t ) +

X

X

#

#

j (s1 ; s 1 ; "t ))

j6=i

X

X

E"t [ j (s ; "t )]j6=i

E"t [ j (s ; "t )]j6=i

E"t [ j (s ; "t )] ;j6=iwhich is equal to …rm 1’s expected payo¤ in period t if it does not deviate. Thus, a deviationfrom s1 is not pro…table. The intuition is that the transfer payments …x the amount of thejoint surplus captured by …rms other than 1, so it is in …rm 1’s incentive to maximize thatjoint surplus.
Finally, to complete the proof that our strategies form an equilibrium, we must verify
that …rm j 6= 1 has no incentive to deviate. If …rm j deviates by choosing a price di¤erent
from sj , this either does not a¤ect …rm j’s period t payo¤, for example if "t is such that all…rms sell zero, or is detected by …rm 1 with probability one (by assumption) and so triggers
the punishment phase. This implies that for su¢ ciently close to one, …rm j prefers not to19deviate in this way. If …rm j deviates by not making a required transfer to …rm 1, then thisis detected and triggers the punishment phase, so again, for su¢ ciently close to one, …rm
j prefers not to deviate.
Proposition 4 If pro…table deviations from s are detectable by …rm 1, then for su¢ ciently
large, there exists an explicitly collusive equilibrium with one-sided monitoring in which s isplayed in every period on the equilibrium path if and only if transfers are allowed.
Proof. It remains to be shown that s cannot be supported without transfers. To see this,note that in the absence of transfers the logic of Proposition 1 applies: Suppose there is anequilibrium in which the …rms choose s in all periods on the equilibrium path. Then for all"t 2 ; if …rm j observes ( j (s ; "t ); mj (s ; "t )) ; then …rm j chooses strategy sj in the next
period. But then, …rm 1 can pro…tably deviate and, using (1), not trigger a response by theother …rms. Q.E.D.
In the equilibrium described above, one …rm can observe pro…table deviations by theothers, which prevents the less informed …rms from having an incentive to deviate. The
required transfers prevent the more informed …rm from having an incentive to deviate. As
shown in Proposition 4, these transfers allow …rms to sustain the overall joint-payo¤ maximizing strategies in equilibrium.

4.2

Complete monitoring

In the explicitly collusive equilibrium of the previous section, …rms must regularly maketransfers to each other. In this section, we show that increased information sharing between
the …rms allows them to maximize their joint payo¤ in every period in an explicitly collusive
equilibrium without using transfers. Thus, increased information sharing eliminates the needfor transfers.
In this section, we assume each …rm can observe the market outcome of every other …rm.
We refer to this environment as one with complete monitoring. The timing in each period is
as follows: (i) …rms simultaneously choose strategies, (ii) each …rm observes its own payo¤
and own market outcome and the market outcome of its rivals.
Proposition 5 If pro…table deviations from strategy pro…le s are detectable by all …rms,
then for su¢ ciently large, there exists an explicitly collusive equilibrium with complete

20monitoring and no transfers in which …rms maximize their expected joint stage-game payo¤in every period on the equilibrium path.
Proof. The proof is by construction. Let be the values of the detection statistics associatedwith s . Consider the following strategies: For …rm i: If (i) t = 0 or (ii) t > 0 and for
all < t; i (si ; m ) = i ; then choose sit = si ; otherwise choose sit = sei . Since any
pro…table deviation by …rm i is detected by the other …rms, then by the usual arguments,
for su¢ ciently close to 1, deviations are not pro…table. Q.E.D.
Using Proposition 5, if pro…table deviations from strategy pro…le s are detectable, thenthere exists an equilibrium of the in…nitely repeated game in which the …rms maximize
their expected joint stage-game payo¤ in all periods. This contrasts with our results fortacit collusion. As …rms move from the optimal tacitly collusive equilibrium to the optimal
explicitly collusive equilibrium, …rms not only eliminate the need for equilibrium-path punishment periods, but also potentially increase the stage-game payo¤s relative to those of the
non-punishment periods under tacit collusion. The result of Proposition 5 also di¤ers fromour results for the case of one-sided monitoring in that no transfers are needed, on or o¤ theequilibrium path, to support the optimal collusive outcome.
If pro…table deviations from strategy pro…le s are detectable by all …rms, then forsu¢ ciently large, in the price competition environment of Proposition 3, in the optimal
explicitly collusive equilibrium with complete monitoring, expected prices and joint stagegame payo¤s are higher in every period than in the optimal tacitly collusive trigger-strategy
equilibrium.
These results show that when each …rm can monitor the market outcome of the other,…rms can achieve the optimal cartel outcome without the use of transfers.
In Section 5 we show that, although the equilibrium described above does not requiretransfers, if we extend the model to allow small idiosyncratic shocks to market outcomes,
then transfers can play a useful role since transfers that compensate for deviations in thevalue of the detection statistic i (si ; m) from its cooperative value i can be used to eliminate
pro…table deviations.

4.3

Centralized monitoring

In this section, we allow the …rms to communicate via a third party, which we refer to as
the center. For example, an industry association or trade association might play the role of21

the center. We assume that …rms report their market outcomes to the center and that thecenter can detect deviations from truthful reporting. The center then makes a public report,
observable by the …rms. We refer to this environment as one with centralized monitoring.
Our assumption that the center can detect deviations from truthful reporting can bebased on several things. For example, a trade association may have the ability to audit…rms’ reports, or an association might require …rms to post bonds that are forfeit if they
are caught not reporting truthfully. Or a trade association might be able to observe …rms’
market outcomes directly, for example through publicly available import/export statistics.
See Section 2 for speci…c examples.
We assume that the center reports a summary statistic based on the reports of the …rms.
We show that it is su¢ cient for the center to report the total quantity sold by the …rms.
The timing within each period is as follows: (i) …rms simultaneously choose strategies,(ii) each …rm observes its own payo¤ and own market outcome, (iii) …rms (truthfully) reporttheir market outcomes to the center, and (iv) the center makes a public report.
Proposition 6 If pro…table deviations from strategy pro…le s are detectable by all …rms,
then for su¢ ciently large, there exists an explicitly collusive equilibrium with centralized
monitoring and no transfers in which …rms maximize their expected joint stage-game payo¤in every period on the equilibrium path.
Proof. The proof follows trivially from the proof of Proposition 5 if the center reports the…rms’market outcomes. Q.E.D.
For environments with price competition and multiplicative demand shocks, the center
need only report the sum of the reported market outcomes. In this case, each …rm can use
the center’s report to calculate its own market share, which is su¢ cient to detect deviations
by its rival. With more than two …rms, we assume it is a probability zero event that apro…table deviation by one …rm a¤ects the market shares of some, but not all, of its rivals.
Proposition 7 In environments with price competition and multiplicative demand shocks(or additive demand shocks and equal shares), then for su¢ ciently large, there exists an
explicitly collusive equilibrium with centralized monitoring and no transfers in which thecenter reports the total quantity sold and …rms maximize their expected joint stage-gamepayo¤ in every period on the equilibrium path.

22

Proposition 7 shows that the existence of a trade association that reports only the total production in the industry is su¢ cient to support strategies that maximize the …rms’
expected joint payo¤s. See footnote 2 on the legality of such reports.
Although it may be legally permissible for a trade association to report data in aggregate
form, Proposition 7 suggests that the fact that data is aggregated is not su¢ cient to preventthat information exchange from being an important facilitator of collusion.
We have focused on the case of all-inclusive cartels. If a cartel is not all-inclusive, in orderfor the trade association to play the same role as described above in facilitating collusion it
must report production numbers in a su¢ ciently disaggregated way that the cartel members
can calculate the total production of the cartel …rms. Henry (1994, 86) describes a DOJ
Business Review Letter from 1992 that suggests approval for a trade association to reportaggregate statistics for “relevant peer groups,”creating room for the “legal”reporting by atrade association of aggregate statistics for a non-all-inclusive cartel.
Exhibit No. 2173 of the TNEC (1941) Hearings on cartels gives a “List of industries
involved in cases brought before the FTC and/or the courts over the last ten years in which
the members of any industry employed a trade association or other common agency todeprive individual sellers of their freedom to determine their own output and/or the prices
at which they may sell, or to exclude other sellers from the trade.” In those same hearings,
Clair Wilcox testi…es (p.13316) that, “It would seem to me that the only way to obtaincomplete assurance that the merriment, diversion, and conversation of which Adam Smith
speaks do not lead to the conspiracies or contrivances to raise prices, which he fears, would
be to place an agent of the Federal Government in every trade association o¢ ce to readall correspondence, memoranda and reports, attend all meetings, listen to all conversations,and participate in all the merriment and diversion, and issue periodic reports thereon to theTrade Commission or the Department of Justice or to some other agency of the Government.”

5

Market share allocations

In this section we focus on our main application of price competition and discuss market
share allocations in more detail. Market share allocations play an important role in many
known cartels (see the Appendix for some examples). The …xing of market shares eliminates
the incentive to cut prices since a deviating …rm “is moving along a demand curve which is a…xed share of the industry demand, and hence has the same elasticity as the industry curveat every price”(Stigler, 1964, p.46).
23

In this section, we let n = 2, and we assume …rms choose prices and that the quantity
demanded from …rm i in period t when prices are s = (s1 ; s2 ) is mi (s; "t ) = Di (s)"t ; where"t0; with E ["t ] = 1. We assume no capacity constraints,24 but our results continue tohold if we allow …rms to choose a sales cap as part of their strategy.25
For homogeneous products, when …rms choose the same price, assume that the share ofdemand captured by …rm i; i (e); depends on the unobservable sales e¤orts of the …rms,e = (e1 ; e2 ). We assume sales e¤ort is costly, and we assume i (e) 2 (0; 1); 1 + 2 = 1; andi (0; 0)i . By allowing the case in which i (e) is a constant, we include the possibility
that sales e¤ort has no e¤ect and that market shares are exogenously given when …rms choose
equal prices. Thus, in this application, a …rm’s strategy consists of a price and a level ofsales e¤ort.
As noted by Posner (1976, p.52),“Setting the price above a seller’s costs will induce him to expend resources
on upgrading his output in the consumer’s eyes so as to take sales away from hiscompetitors and thereby engross a larger share of the pro…ts generated by thehigher than competitive price. ... Thus it may be necessary to agree to limit not
only price competition but the important forms of nonprice competition as well,a di¢ cult thing to do since there are so many ways in which sellers can vie forthe buyer’s patronage.”In this application, deviations are detectable by letting
market shares as the detection statistic,i (si ; m)(mi;
m1 +m2i;ii (s )
and using= D1 (sD)+D
2 (s )

if m1 + m2 > 0otherwise.

As suggested by Green and Porter (1984), because …rms can rely on calculations of market
shares to detect deviations, this environment re‡ects Stigler’s (1964) ideas about the role ofinformation sharing in supporting collusion.
Note that in this application, sales e¤ort is wasteful. However, in a tacitly collusive
equilibrium with homogeneous products there may be no equilibrium in which sales e¤ort
24

As shown in Benoit and Krishna (1987), if …rms choose their capacities prior to playing an in…nitely repeated price setting game, then collusive equilibria involve excess capacity, and the most collusive equilibrium
may involve a joint payo¤ for the …rms that is less than what could be achieved by a monopolist.
25
Imposing a sales cap might allow a …rm to limit how much price undercutting reduces its rivals’ sales
and so might reduce the probability of detection.

24

is zero. But in an explicitly collusive equilibrium with one-sided monitoring or completemonitoring, the sales e¤ort can be held down to its e¢ cient level of zero.
Using the detection statistic described above, explicit collusion with complete monitoring
does not require transfers; however, if we extend the model to allow small idiosyncratic shocks
to market outcomes, then transfers can play a useful role since transfers that compensate
for deviations in the value of the detection statistic i (si ; m) from its cooperative value i
can be used to eliminate pro…table deviations.
For example, suppose that when …rms choose s; market outcomes are m1 (s; "t ) + andm2 (s; "t ); where is a “small” shock with mean zero. We can view these shocks as
exogenous shocks to the …rms or as mistakes by the …rm. As noted in Posner (1976, p.53),“Even so, the cartel price might be undercut inadvertently, because of a computational mistake or a failure of communication either of the agreed price orof a change in it. Mistakes of this sort must be common when coordination ise¤ected, as it must be in industries subject to the Sherman Act, by clandestinemeans. Yet competing sellers will not know that the ‘cheating’was inadvertent,
and may retaliate; in this way a mistake can easily trigger a general round of
price cutting.”
Consider an explicitly collusive equilibrium with complete monitoring in which, aftermarket outcomes m^ 1 and m^ 2 are observed, …rm 1 makes a transfer to …rm 2 of x, wherex ^ 1 (s1 ; m^ 1 ) ^ 1 (s1 ; m~ 1 ) and m~1^ 1 +m^ 2 ). In this case, letting m~2^1 +m^ 2) ;1 (m2 (m^ 2) + x
2 (s2 ; m=

^ 2 ) + p(s ; "t )(m^1
2 (s2 ; m

m
~ 1)

=

^ 2 ) + p(s ; "t )(m^1
2 (s2 ; m

^1 +m
^ 2 ))1 (m=^ 2 ) + p(s ; "t )(m^1
2 (s2 ; m

(1

=

^ 2)
2 (s2 ; m

m
~ 2)

=

~ 2 ):2 (s2 ; mp(s ; "t )(m
^2

^1 +m
^ 2 ))
2 )(mThus, this transfer payment …xes the …rms’payo¤s at what they would be in the absence ofthe shock . Given this, the outcome of the explicitly collusive equilibrium with completemonitoring described in Proposition 5 can still be sustained if …rms make transfers. To see
this, note that as long as is su¢ ciently small and is su¢ ciently large, then for all market
outcomes, each …rm prefers to incur cost to avoid triggering a punishment phase.

25

6Discussion

In Section 2, we argue that once a cartel resolves the issue of monitoring, there areadvantages to a market share allocation as a basis for suppressing inter…rm rivalry. In
Sections 3–5, we show that the e¤ective monitoring of a market share allocation can beaccomplished through the standard and legally accepted practices of a trade association.
In the paper, we focus on the ability of various cartel organizations to enhance the pro…tof cartel members through the suppression of within-cartel rivalry. In this concluding discussion, we consider cartel activities that go beyond the suppression of within-cartel rivalry. Ina tacitly collusive equilibrium, where there is no inter…rm communication, it could be di¢ cult for …rms to recognize and coordinate upon conduct beyond the suppression of inter…rm
rivalry. In contrast, the history of explicit cartels as analyzed in Heeb et al. (2006) suggeststhat colluding …rms often coordinate e¤orts to engage in monopolization-like conduct and/or
shift out the demand curve for the cartel members’products, causing the maximal expectedjoint stage-game payo¤ to increase.26 As described in Jones (1922, pp.261–274), trade associations may coordinate activities typically associated with a dominant …rm in order todisadvantage non-member …rms, including: controlling channels of distribution, organizing
boycotts, establishing blacklists or whitelists, cutting non-members’supply, interfering with
non-members’labor supply or procurement of storage facilities, predatory pricing, malicious
litigation, espionage, intimidation and coercion, and misuse of governmental agencies.27 Although Jones’(1922) focus is on trade associations, the examples of activities he provides
apply equally well to cartels, regardless of whether a trade association is involved. Examplesof activities designed to shift demand for cartel members’products include promotional andinformational campaigns.
With a market share allocation, if cartel members share in the cost of monopolization
or demand-enhancing activities according to their market shares, their costs are then inproportion to their bene…ts. Because the bene…ts of such activities will often extend beyond
a given set of customers or beyond a given region, it may be more di¢ cult to align costs
and bene…ts when a cartel uses a customer or geographic allocation. Thus, these kinds ofpro…t-enhancing cartel activities may be encumbered by a customer or geographic allocation
26

The Department of Justice public statement described in footnote 14 states, “Another device is thecreation of a fund among a small group to buy competing plants which are troublesome competitors. Upon
acquisition, such plants are often shut down and dismantled. Thus, the socially desirable small independent
operation is eliminated from the …eld of competition.”
27
See Jones (1922, pp.261–274) for discussion, examples, and cites to cases related to each of these.

26relative to a market share allocation.
As a cartel undertakes monopolization or demand-enhancing conduct, pro…ts may increase beyond what is expected from the mere suppression of within-cartel rivalry. To theextent that the identi…cation and implementation of pro…table monopolization and demandenhancing activities requires information sharing among the …rms, the information sharingof explicit collusion, perhaps through an industry association, can facilitate this.
In the Vitamins Cartel, although the cartel used market share allocations to deter secretprice cutting, the EC decision in Vitamins indicates that the cartel also used market shareallocations to allocate the cost of investments that provided cartel-wide bene…ts.28 In general,in the absence of collusion, there are many actions that a …rm in a homogenous good oligopoly
could take that would bene…t the multiple …rms in the industry, but that would not providesu¢ cient bene…t to the individual …rm taking the action to justify the cost.
In conclusion, the sequence of models in this paper produce the ascending price path thatis typically associated with collusion.29 Prices are lowest with non-cooperative play. Prices
ascend with tacit collusion but do not reach the level attained with explicit collusion. Explicit
collusion prices are higher, but they increase even further when we allow for monopolizationand demand-enhancing activities by a cartel.

28

For an example from the Vitamins Cartel of an investment that provided industry-wide bene…ts andwhose cost was shared among the cartel …rms according to their market share allocations, see the EC decisionin Vitamins at 287: “In 1993 the parties [Roche and BASF] realised that a U.S. producer [of vitamin B2],
Coors, had a larger production capacity for vitamin B2 than they had estimated in 1991. In order to prevent
Coors from disrupting their arrangements by the export of its production surplus, Roche and BASF agreed
that the former would contract to purchase 155 tonnes of vitamin B2 (representing half of Coor’s capacity)in 1993. BASF in turn would purchase 43 tonnes from Roche: the burden was thus to be shared in the same
62:38 proportion as their quotas.”
In another example, the following quotation is Article XX of the International Merchant Bar Agreement,
1933: “The Management Committee shall, whenever it deems necessary, call upon groups for contributions
proportional to their quotas, to provide for or participate in the general expenses or other funds disbursedin the common interest.” (Hexner, 1943, p.317)
As described in Stocking and Watkins (1991, p.160), the International Nitrogen Cartel collected paymentsfrom its members in proportion to their sales to compensate Belgian producers for restricting their output.
As described in Stocking and Watkins (1991, p.160), the International Nitrogen Cartel collected paymentsfrom its members in proportion to their sales to compensate Belgian producers for restricting their output.
Also described in Stocking and Watkins (1991, p.447), DuPont and ICI contributed in proportion to theirshares in the cooperative arrangement Explosives Industries, Ltd. to the compensation made to WestfalischeAnhaltische Sprengsto¤ A. G. (Coswig) for restricting its exports.
29
Our model is a repeated game, but is not fully dynamic. In more dynamic environments, a cartel’s
success may be measured by the extent to which it prevents, minimizes, or delays a decline in prices, rather
than its e¤ectiveness at increasing prices.

27Appendix
We reviewed the twenty major industrial-product cartel decisions of the European Commission between 2000 and 2005. Table A.1 lists these twenty cases in order by the decision
date.

Table A.1: European Commission major industrial product cartel decisions (2000–2005)
Case name

Relevant products

Decision date1 Amino Acids

Lysine7-Jun-00

OJ L 152, 07/06/2001 p.24-72

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2001/l_152/l_15220010607en00240072.pdf

2 Soda-ash - Solvay, CFK

Soda-ash13-Dec-00

OJ L 10, 15/01/2003 p.1-9

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2003/l_010/l_01020030115en00100032.pdf

3 Graphite electrodes

Graphite electrodes

18-Jul-01

OJ L 100, 16/04/2002 p.1-42

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2002/l_100/l_10020020416en00010042.pdf

4 Vitamins

Vitamins

21-Nov-01

OJ L 006, 10/01/2003 p.1-89

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2003/l_006/l_00620030110en00010089.pdf

5 Citric Acid

Citric Acid

5-Dec-01

OJ L 239, 06/09/2002 p.18-65

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2002/l_239/l_23920020906en00180065.pdf

6 Zinc phosphate

Zinc phosphate11-Dec-01

OJ L 153, 20/06/2003 p.1-39

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2003/l_153/l_15320030620en00010039.pdf

7 Carbonless paper

Carbonless paper

20-Dec-01

OJ L 115, 21/04/2004 p.1-88

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2004/l_115/l_11520040421en00010088.pdf

8 Methionine

Methionine

2-Jul-02

OJ L 255, 08/10/2003 p.1-32

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2003/l_255/l_25520031008en00010032.pdf

24-Jul-02

OJ L 084, 01/04/2003 p.1-55

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2003/l_084/l_08420030401en00010055.pdf

9-Apr-03

OJ L 123, 17/05/2003 p.49-50

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2003/l_123/l_12320030517en00490050.pdf

9 Industrial and medical gases

Industrial and medical
gases(amended EC decision)

EC Journal citation

Location on the EU website

10 Methylglucamine

Methylglucamine

27-Nov-02

OJ L 038, 10/02/2004 p.18-46

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2004/l_038/l_03820040210en00180046.pdf

11 Plasterboard

Plasterboard

27-Nov-02

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/37152/en.pdf

12 Food flavour enhancers*

Nucleotides

17-Dec-02

OJ L 075, 12/03/2004 p.1-31

http://eur-lex.europa.eu/LexUriServ/site/en/oj/2004/l_075/l_07520040312en00010031.pdf

13 Specialty Graphite

Specialty graphite

17-Dec-02

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/37667/en.pdf

14 Sorbates

Sorbates

1-Oct-03

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/37370/en.pdf

Electrical and mechanical
15
Carbon brushes
carbon and graphite products

3-Dec-03

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/38359/en.pdf

16 Organic peroxides

Organic peroxides

10-Dec-03

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/37857/en.pdf

17 Industrial tubes

Copper tubing

16-Dec-03

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/38240/en.pdf

18 Copper plumbing tubes

Copper tubing

3-Sep-04

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/38069/en.pdf

19 Choline Chloride

Choline Chloride

9-Dec-04

OJ L 190, 22/07/2005 p.22-26

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/37533/en.pdf

20 Rubber chemicals

Rubber chemicals

21-Dec-05

Not published in Official Journal

http://ec.europa.eu/comm/competition/antitrust/cases/decisions/38443/en.pdf*Note that most documents related to this case require you to search for "flood [sic] flavour enhancers"

For each of these 20 cartel cases, we use the EC decision to classify the cartel’s organization as involving one or more of a customer allocation, geographic allocation, market shareagreement, or some other organization. These are shown in Table A.2. Also shown in Table
A.2, we indicate whether the EC decision mentions the involvement of a trade associationor other outside organization in the cartel’s activities. Note that the write-ups of the EC
decisions are idiosyncratic and do not purport to expose all information regarding a cartel’s28

organization. So the absence of mention of a trade association in an EC decision does notnecessarily mean that none was involved in facilitating cartel activities.
The EC decision paragraphs listed in Table A.2 are reproduced in the online appendix
associated with this paper.30
Table A.2: Paragraph numbers associated with discussions in the EC decisions
indicating features of cartel organization and a role for a trade association
Case name

Customerallocation

Geographic
allocation

Market shareagreement

Other

Trade association

211

211 (output
quotas)100, 113, 122, 253

81

81 (output
quotas)83

Amino Acids
Carbonless paper
Choline Chloride

99

64

64, 99Citric Acid81

87, 100

Copper plumbing tubes

137

239 (home mkt)

210, 239, 350

240Electrical and mechanicalcarbon and graphite products

128

131

128

82, 177

Food flavour enhancers

65, 68172

Graphite electrodes
Industrial and medical gases
Industrial tubes

50 (home mkt)

71

101
2, 79, 106, 107

105
2, 79, 103, 104

Methionine
Methylglucamine

64 (target prices)46, 9843, 46

Organic peroxides

85

92
429 (priceincreases)

Plasterboard
Rubber chemicals

66

Soda-ash - Solvay

58
281 (output
quotas)SorbatesSpecialty Graphite

147

Vitamins

2, 169

Zinc phosphate

2, 6, 113

2, 68

2 , 21435, 69, 254

As shown in Table A.2, for nine of these cartels, a trade association (or a technical standards committee or “consulting …rm”) is mentioned in the EC decision. The nine are Amino
Acids, Carbonless Paper, Citric Acid, Copper Plumbing Tubes, Electrical and Mechanical
Carbon and Graphite Products, Industrial and Medical Gases, Industrial Tubes, Organic
Peroxides, and Zinc Phosphate. In some cases, the association is described as playing a30

Available at http://faculty.fuqua.duke.edu/~marx/bio/papers/OnlineAppendixMS.pdf.

29

role by providing information to cartel members, in others a “consulting …rm” audits data
provided by cartel members, and in others an association is mentioned as providing coverfor gatherings of cartel members.
In eight of the nine cases mentioning a trade association (all except for Industrial andMedical Gases), a market share agreement was a key component of the cartel’s organization.
Viewed another way, of the …fteen cases where a market share agreement was a componentof the cartel’s organization, eight mention a role for a trade association.

30

References
Abreu, Dilip (1986), “Extremal Equilibria of Oligopolistic Supergames,” Journal of Economic Theory 39, 191-225.
Abreu, Dilip, Prajit K. Dutta, and Lones Smith (1994), “The Folk Theorem for RepeatedGames: A NEU Condition,”Econometrica 62, 939–948.
Abreu, Dilip, David Pearce, and Ennio Stacchetti (1986), “Optimal Cartel Equilibria with
Imperfect Monitoring,”Journal of Economic Theory 39(1), 251-69.
Abreu, Dilip, David Pearce, and Ennio Stacchetti (1990), “Toward a Theory of Discounted
Repeated Games with Imperfect Monitoring,”Econometrica 58, 1041–1063.
Asker, John (2007), “A Study of the Internal Organisation of a Bidding Cartel,” Working
Paper, New York University.
Athey, Susan and Kyle Bagwell (2001), “Optimal Collusion with Private Information,”
RAND Journal of Economics 32, 428–465.
Athey, Susan, Kyle Bagwell, and Chris Sanchirico (2004), “Collusion and Price Rigidity,”
Review of Economic Studies 71, 317–349.
Ayres, Ian (1987), “How Cartels Punish: A Structural Theory of Self-Enforcing Collusion,”
Columbia Law Review 87, 295.
Bagwell, Kyle and Asher Wolinsky (2002), “Game Theory and Industrial Organization,”in Handbook of Game Theory with Economics Applications, Vol. 3, edited by R. J.
Aumann and S. Hart, Amsterdam: Elsevier.
Bajari, Patrick L. and Garrett Summers (2002), “Detecting Collusion in Procurement Auctions,”Antitrust Law Journal 70(1), 143–170.
Bajari, Patrick L. and Lixin Ye (2003), “Deciding Between Competition and Collusion,”
Review of Economics and Statistics, 85(4), 971–989.
Benoit, Jean-Pierre and Vijay Krishna (1987), “Dynamic Duopoly: Prices and Quantities,”
Review of Economic Studies 54, 23–35.
Blume, Andreas and Paul Heidhues (2003), “Modeling Tacit Collusion in Auctions,”Journalof Institutional and Theoretical Economics, 164 (2008), 163–184.
Burns, Arthur Robert (1936), The Decline of Competition: A Study of the Evolution ofAmerican Industry, New York: McGraw-Hill Book Company, Inc.
Clark, Donald S. (1983), “Price-Fixing Without Collusion: An Antitrust Analysis of Facilitating Practices After Ethyl Corp.,”Wisconsin Law Review, 887.
31

Cramton, Peter C. and Thomas R. Palfrey (1990), “Cartel Enforcement with Uncertainty
about Costs,”International Economic Review 31(1), 17–47.
European Commission, 2003, “The Commission of the European Communities Decisionof 21 November 2001, Case COMP/E-1/37.512— Vitamins,” O¢ cial Journal of theEuropean Communities, October 1, 2003.
Friedman, James W. (1971), “A Non-cooperative Equilibrium for Supergames,” Review of
Economic Studies, 28, 1–12.
Fudenberg, Drew and Eric Maskin (1986), “The Folk Theorem in Repeated Games with
Discounting or with Incomplete Information,”Econometrica, 54(3), 533–554.
Graham, Daniel A. and Robert C. Marshall (1987), “Collusive Bidder Behavior at SingleObject Second Price and English Auctions,” Journal of Political Economy 95, 1217–
1239.
Graham, Daniel A., Robert C. Marshall, and Jean-Francois Richard (1990), “Di¤erential
Payments Within a Bidder Coalition and the Shapley Value,” American Economic
Review, 80(3), 493–510.
Green, Edward J. and Robert H. Porter (1984), “Noncooperative Collusion under Imperfect
Price Information,”Econometrica 52, 87–100.
Harrington, Joseph E., Jr. and Andrzej Skrzypacz (2007), “Collusion Under Monitoring ofSales,”RAND Journal of Economics 38(2), 314–331.
Hay, George A. (1982), “Oligopoly, Shared Monopoly, and Antitrust Law,” Cornell Law
Review 67, 439–481.
Heeb, Randal, William E. Kovacic, Robert C. Marshall, and Leslie M. Marx (2006), “Illuminating Section 2 Through Cartels,” Penn State University Center for the Study ofAuctions, Procurements, and Competition Policy (CAPCP) Working Paper.
Henry, Brian R. (1994), “Benchmarking and Antitrust,”Antitrust Law Journal 62, 483–512.
Hexner, Ervin (1943), The International Steel Cartel, Chapel Hill, NC: University of North
Carolina Press.
Hortaçsu, Ali, Asis Martinez-Jerez, and Jason Douglas, “The Geography of Trade on eBay
and Mercado Libre,”Working Paper, University of Chicago.
Jones, Franklin D. (1922), Trade Association Activities and The Law: A Discussion of theLegal and Economic Aspects of Collective Action through Trade Organizations, New
York: McGraw-Hill Book Company, Inc.

32

Kaysen, Carl (1951), “Collusion Under the Sherman Act 1,” Quarterly Journal of Economics 65(2), 263-270.
Kihlstrom, Richard E. and Xavier Vives (1992), “Collusion by Asymmetrically Informed
Firms,”Journal of Economics & Management Strategy 1(2), 371–396.
Marshall, Robert C. and Leslie M. Marx (2007), “Bidder Collusion,”Journal of Economic
Theory 133, 374–402.
McAfee, R. Preston and John McMillan (1992), “Bidding Rings,” American Economic
Review 82, 579–599.
Porter, Robert H. (1983), “Optimal Cartel Trigger Price Strategies,”Journal of Economic
Theory 29, 313–338.
Posner, Richard A. (1976), Antitrust Law: An Economic Perspective, Chicago: Universityof Chicago Press.
Posner, Richard A. and Frank H. Easterbrook (1981), Antitrust: Cases, Economic Notes,
and Other Materials, Second Edition, St. Paul, MN: West Publishing Co.
Skrzypacz, Andrzej and Hugo Hopenhayn (2004), “Tacit Collusion in Repeated Auctions,”
Journal of Economic Theory 114, 153–169.
Stigler, George J. (1964), “A Theory of Oligopoly,”Journal of Political Economy 72, 44–61.
Stocking, George W. and Myron W. Watkins (1991), Cartels in Action: Case Studies inInternational Business Diplomacy, Bu¤alo, NY: William S. Hein & Co., Inc.
Sullivan, E. Thomas and Je¤rey L. Harrison (1988), Understanding Antitrust and Its Economic Implications, New York: Matthew Bender & Company, Inc.
Tirole, Jean (1988), The Theory of Industrial Organization, Cambridge, MA: MIT Press.
Turner, Donald F. (1962), “The De…nition of Agreement Under the Sherman Act: Conscious
Parallelism and Refusals to Deal,”Harvard Law Review 75(4), 655-706.

33