Illegal and Legal Behaviour:
Evidence Proving Collusion
Dr. Kenneth Danger
OECD
Acknowledgements


Greg Werden
Andreas Reindl
2
Helpful Articles


Greg Werden “Economic Evidence on the
Existence of Collusion: Reconciling Antitrust Law
with Oligopoly Theory,” Antitrust Law Journal,
71, 719-800.
Blair D. Blair and Jill Boylston Herndon, Inferring
Collusion from Economic Evidence, Antitrust,
Summer, 2001.
3
Overview




Classic oligopoly games
Some history on economics of coordination
Definition and proof of an agreement
Plus factors and action contrary to self
interest
4
Classic Oligopoly Games



Cournot
Bertrand
Dominant firm price leadership
5
Simple Strategic Games

Optimization algorithm





Firms choose optimal level of output or price given rival(s)
decisions.
Non cooperative equilibrium is the key concept.
Best responses to best responses determine the
equilibrium. This is known as the Nash equilibrium
concept.
Game is played for one period only.
Simple strategic games we are not concerned with
for the moment with include predation, vertical
integration, etc.
6
Cournot-Nash (Output Choice)



Assume two firms only
Homogeneous good
Market demand curve is linear: P(Q) = a – bQ





P = market price
Q = total market output
q1 is firm 1’s output, q2 is firm 2’s output
Thus Q = q1 + q2
Average costs are constant and equal to c for
each firm.
7
Two Firm Optimization Problem
Firm 1’s problem
π1  TR - TC
 P(Q)q1 - cq1
 [a - b(q1  q 2 )]q1 - cq1
Firm 2’s problem
π 2  TR - TC
 PQ q 2 - cq 2
 [a - b(q1  q 2 )]q 2 - cq 2
8
Graphical Representation of Decision
Facing Cournot Rival
Market demand curve shifts in by the amount of total rival
production leaving a firm with the “residual” (left over) demand.
Q
Market demand curve
Residual demand curve
q rival
Marginal cost
q rival
q
P
9
First Order Optimality Conditions
Firm 1’s problem
Firm 2’s problem
π1  [a - b(q1  q2 )]q1 - cq1
π2  [a - b(q1  q2 )]q 2 - cq2
Taking the derivative we get
Taking the derivative we get
π
 a - 2bq1 - bq 2 - c  0
q1
Which implies that
q1 
a - c q2
2b 2
π
 a - 2bq 2 - bq1 - c  0
q 2
Which implies that
q2 
a - c q1
2b 2
10
Cournot Reaction Curves
Note: Another name for reaction
function is optimality function.
Firm 2
q2
This graph plots the first order optimality
conditions from the prior slide.
R1
a -c
2b
a -c
3b
R2
a -c
3b
a -c
2b
Firm 1
q1
11
Two Firm Cournot Solution

Solution concept:

Solve all competitors’ optimization problem simultaneously.
a – 2bq1 – bq2 – c = 0 and a – 2bq2 – bq1 – c = 0
Solving gives
a -c
q1  q 2 
3b
Inserting these output back into the demand function we get
P = a – b(q1 + q2) =
a  2c
3
12
Oligopolistic Interdependence

In general when there are few firms
producing a good or service their fortunes are
interdependent.

Firm 1’s fortune depends upon what firm 2
does. And, firm 2’s fortune depends upon
what firm 1 does.
13
N Firm Cournot Equilibrium
Number of Firms
Price P = a – b(q1 + q2 + … + qn)
1 = Monopolist
(a + c)/2
2
(a + 2c)/3
3
(a + 3c)/4
4
(a + 4c)/5
5
(a + 5c)/6
6
(a + 6c)/7
7
(a + 7c)/8
8
(a + 8c)/9
9
(a + 9c)/10
10
(a + 10c)/11
Infinite
P = (a + nc)/[(n+1)] = c
14
Herfindahl-Herschman Index (HHI)


Hirschman-Herfindahl index (HHI) is a measure of concentration
Definition: n firms, each with share si
n
HHI   si
2
i 1


Example: 5 firms with 15%, 15%, 20%, 20%, 30% market shares
HHI=225+225+400+400+900=2150

Merger of 30% with 15% would create a change of 900, to 3050
(Change in HHI = 2s1s2).

HHI is only one measure of concentration and can provide some initial guidance




low HHI and low HHI change in correctly defined market can suggest little competitive effect from
merger
high HHI and high HHI change does not establish competitive effect.
In general an investigation must develop much more evidence
15
Cournot Model (Identical Firms) and
Herfindahl – Hirshman Index (HHI)
Cournot Optimization problem is:
πi  P(Q)qi - cqi
Note η is the market elasticity of demand.
Differentiating we get
π i
P(Q)
 P(Q) 
qi - c  0
q i
q i
Rearranging gives
P-c s

P
η
Multiplying both sides by s gives
P - c s2
s

P
η
Summing up over n
firms gives
P - c HHI

P
η
E.g., Cournot prediction is that a 20% increase in the HHI leads to a 20% in the
margin. And if costs are constant (as they are here) then prices rise by 20%.
16
More General Link Between Cournot and HHI

When firms have different cost structures market shares will
differ under Cournot.

General relationship between HHI and margins is:
P - ci HHI
i si P  η
The Cournot prediction is that the weighted average
margin is proportional to the HHI.
17
Is This Type of Behaviour Illegal?
Imagine that you have 3 markets with the following fact patterns.
Firms compete in a Cournot fashion and marginal cost is identical and
constant across firms and markets and equal to 3.
What would you do?
Market 1
3 firms
P = 7.25
Si = 1/3
Market 2:
5 firms
6.4
Si = 1/5
Market 5
9 firms
4.7
Si = 1/9
18
Bertrand-Nash (Price Choice)

Essential Features of Bertrand Model





Two firms selling homogeneous products
Each sells from the same location
Each firm chooses price
Each firm’s demand is a function of its own price
and that of its rival
Average cost is constant and equal to c
19
The Bertrand Solution and “Paradox”
1.
Assume firm 2 sets the monopoly price. Then firm 1 should
set a price just below firm 2 and get the entire market.
2.
If firm 1 sets a price just below firm 2 then firm 2 sells
nothing. Firm 2 needs to lower its price to below firm 1 and
if it does it will get the entire market.
3.
This process continues until each firm sets its price at
marginal cost and earns zero profits.
Only two firms are required to achieve the competitive outcome.
This is known as the Bertrand paradox.
20
Bertrand Competition With 3 Or More Firms

Adding more firms to the forgoing analysis
does not make the market more competitive.

Shares decline, though they need not for
everyone.
21
Heterogeneous Goods and Bertrand Competition

The less differentiated the products are, the
lower the equilibrium price. When the goods
are perfect substitutes perfect competition is
obtained.

The more differentiated the products are the
higher the price. When the products cease to
be come substitutes at all the monopoly price
is obtained.
22
Is This Type of Behaviour Illegal?

Imagine you have 3 firms. Firms compete on
the basis of price. Two firms innovate and
lower their production costs. The third does
not.

Bertrand price competition implies that the
third firm will be driven out of business.

Is this illegal? What would you do?
23
Dominant Firm Price Leadership

First some basics.

If Firm A’s supply curve is P = a + bQA and Firm B’s supply curve is P = a + bQB
we can the combined supply curve.

First we solve for Q and get

Q = P/b – a/b for both firms. Adding up the supply at any given price means that
the total supply at a given price is

QA + QB = QS = P/b – a/b + P/b – a/b = 2P/b – 2a/b.

Rearranging gives P = a + bQS/2.

This means that the supply curve rotates around the intercept. But be careful
when you have different intercepts. The above cannot be done as the true
function is piecewise linear.
24
Graphic Representation of Adding Supply Curves
P
Supply curve for A and B lie on same line
QA, QB
QS
Sum of supply curves
Supply curve rotates out when underlying supply curves have
the same intercept.
Q
25
Dominant Firm Price Leadership Model

There are two types of industry participants:


A large firm with low costs and
A large number of smaller firms (the competitive
fringe) all with costs that are higher than the
“dominant firm.”
26
Graphical Analysis of Dominant Firm Model
Sf
P
If fringe supply all output, price is set
at Pf and output is Qf.
Pf
Market Demand
Qf
Q
27
Graphical Analysis of Dominant Firm Model
Sf
P
At prices below Pf the fringe do not supply
enough output to meet demand. The
residual demand is the demand that is left
over at prices below Pf.
Pf
Residual Demand
Market Demand
Q
28
Graphical Analysis of Dominant Firm Model
Sf
P
Associated with the residual demand
curve is a marginal revenue curve.
Pf
Marginal revenue curve
Residual Demand
Market Demand
Q
29
Graphical Analysis of Dominant Firm Model
Sf
P
Dominant firm output is associated
Found at nexus of MCD and MR
Pf
MCD
Marginal revenue curve
QD
Residual Demand
Market Demand
Q
30
Graphical Analysis of Dominant Firm Model
Sf
P
Notice price in market is lower with
a low cost, but large firm and total
output is higher.
Pf
PD
MCD
Marginal revenue curve
QD Qf
Residual Demand
Market Demand
Q
31
Some Implications of Dominant Firm Price Leadership


There is one price in market
Dominant firm’s low cost advantage enables
them to earn profits at the margin (P > MC)
while the competitive fringe sets price equal
to marginal cost (P = MC).
32
Is This Type of Behaviour Illegal?

If an industry is appropriately characterized
by this model and the dominant firm’s cost
decreases then




All firm’s follow the price leader (the dominant
firm) and simultaneously lower price
The dominant firm’s market share increases
Some fringe firms exit
Is it predation, collusion, both or something else?
What would you do?
33
Summary of Some Implications From
Classic Oligopoly Games


Dominant firm, Cournot and Bertrand Games
indicate a variety of outcomes are possible,
yet none of them indicate that firms are
colluding.
Alternatively, all three models do indicate that
mergers can be harmful. Essential
mechanism is that demand facing firms
becomes more inelastic and firm’s price
higher in response.
34
Some History On The Economics Of Coordination

Chamberlin’s impact





Coordinated effects
Merger law
Game theory
Stigler’s model
Repeated games
35
Chamberlin’s Impact On Understanding Coordination

Edward Chamberlin wrote that the usual assumption of profit
maximization implies “a monopoly price for any fairly small number of
sellers,” because no competitor has any incentive to cut price below the
monopoly level, realizing “his move has a considerable effect upon his
competitors, and that this makes it idle to suppose that they will accept
without retaliation the losses he forces upon them” by cutting price.

Chamberlin indicated that this form of interdependent pricing should not
be viewed as the product of an agreement: [W]hen there are only two or
a few sellers, their fortunes are not independent…. Each is forced by
the situation to take into account the policy of his rival in determining his
own, and this cannot be construed as a ‘tacit agreement’ between the
two.”

See Werden, Gregory J. “Economic Evidence on the Existence of
Collusion: Reconciling Antitrust Law with Oligopoly Theory,” Antitrust
Law Journal, 71, 719-800.
36
Note On Coordination And Merger Law

Chamberlin had a significant impact in
merger law.

In many jurisdictions, mergers can be
enjoined if the effect of the acquisition tends
to substantially lessen competition through an
increase in coordinated activity.
37
Chamberlin’s Impact on Defence Analyses

Chamberlin’s analysis naturally helped
defence teams in their analysis. They could
now argue that evidence on non-competitive
performance was simply an outcome of
interdependent decision making
38
Game Theory: Prisoners’ Dilemma
Prisoner 1 Denies
Prisoner 1
Confesses
Prisoner 2 Denies
Both Get Off
Without Charge
Prisoner 2 Serves
10 Years, Prisoner 1
Serves 0 Years
Prisoners 2
Confesses
Prisoner 2 Serves 0
Years, Prisoner 1
Serves 10 Years
Both Serve 2 Years
39
Lessons From The Prisoners’ Dilemma
(One Period Game)

Time served is lowest each suspect does not confess.

However, each suspect’s private interest conflicts with
their collective interest.

Dominant strategy for both players is to confess.

Assuming a similar setup, the key lesson for competition
policy is that the best response for each firm, regardless
of what the other is doing, is to compete.
40
Stigler’s Model
Basic idea:




Firms want to collude to raise profits.
However, “if any member of any agreement can violate it,
he will gain larger profits than by conforming to it.”
Thus, firms should focus on problem of policing of
agreement.
Implications

1.
2.
Note: how very different Stigler’s theory is from
Chamberlin’s.
Firms infer cheating if they lose unexpectedly many sales
or gain too few new sales.
41
Repeated Games – Folk Theorem

Basic idea is that firms can be induced to act in the collective interests,
rather than in their individual interest.






1.
2.
3.
Folk theorem does not state that the set of jointly profit maximizing prices is
the equilibrium but only one equilibrium of an infinite set. In other words,
anything can happen.
The folk theorem only goes through with infinite repetition (see next slide).
Folk theorem says nothing about how the rules of the game become known
to players and how the equilibrium is evolved toward.
Folk theorem has predicted monopoly outcomes even with a large number of
competitors (400!).1
Uncertainty creates price wars in repeated game models as competitors
cannot be certain if a player has defected or if demand has fallen.2
Other models predict that when demand is high defection occurs as that is
when it pays the most to defect.3
See Val Eugene Lambson, “Self Enforcing Collusion in Large Dynamic Markets,” 34, Journal of Economic
Theory, 282, (1984)
See Edward J. Green and Robert H. Porter, Noncooperative Collusion Under Imperfect Price Information,
52 Econometrica, 87 (1984).
Julio J. Rotermberg and Garth Saloner, “A supergame-theoretic Model of Price Wars During Booms, 76.
American Economic Review, 390, (1986).
42
Note On Repeated Games that End

In general optimal strategies are found by working
backwards. Such backward induction leads to games that
are said to be sub-game perfect. Consider the following two
period game. Period 2 is in red box and Period 1 is in blue.
Player 2
Player 2
Low
High
Low
20,20
5,30
21,21
6,31
30,5
1,1
31,6
2,2
Low
Player 1
High
High
Period 1 profits are higher by the Nash equilibrium amounts in period 2.
43
Summary on Some History on the Economics of
Coordination


Firms want to achieve higher (monopoly)
profits, but if an agreement is achieved they
are tempted to cheat
Firms can achieve higher (monopoly) profits
without an explicit agreement, yet here too
they are tempted to “cheat” in ways that
increase private profits at the expense of
other firms
44
Definition And Proof Of An Agreement


Types of agreements
Selected cases



Eastern States
Masonite
American Tobacco
45
Agreement Nomenclature

Spoken agreement results from anything akin to language and
the product of a spoken agreement is a traditional conspiracy.
Because winks, nods and the like communicate much as words
do, laws probably should not require the exchange of mutual
assurances.


Sometimes explicit or express agreement might be used or even
explicit or express collusion.
Unspoken agreement results from communications purely in the
form of marketplace actions. It does not stretch the meaning of
the terms to say that communication occurs when rivals observe
each others’ prices, outputs, and other marketplace actions.
Examples include Bertrand and Cournot communications as well
as communications in repeated play such as Tit-for-Tat.

Sometimes tacit agreement might be used or even tacit collusion but
you have to be careful with these terms because people get
confused.
46
Eastern States

Defendant lumber retailers in Eastern States circulated
“blacklists” containing the names of lumber wholesalers selling
directly to consumers. This had the effect of causing such
retailers to withhold their purchases from the list of concern.
Information supplied during the case indicated that when a dealer
was added to the list, retailers stopped purchasing from him and
his trade was directly and appreciably impaired.

Did lumber retailers come to an agreement to collectively boycott
offending lumber wholesalers?
1. Easters States Retail Lumber Dealers’ Association v. United States, 234 U.S.
600 (1914).
47
Eastern States


Is exchanging certain kinds of information the
same thing as agreeing to boycott.
Were their actions in their self interest or their
collective interest?

What evidence might you look for?

E.g., high costs of switching from one wholesaler to
another might imply action contrary to self interest
48
Masonite

Masonite held several patents on a hardboard product that
continues to bear its names, and it sued competing hardboard
producers for patent infringement. After one appeals court
sustained an infringement finding, Masonite began to enter into
agreements with the competitors under which they
acknowledged the validity of Masonite’s patents and became its
agents, selling Masonite board at prices set by Masonite.

Did Masonite practices facilitate an agreement among firms
selling Masonite products? Was Masonite the ringmaster of the
cartel?

United States v. Masonite Corp., 316 U.S. 265 (1942)
49
Masonite findings By Supreme Court

“In negotiating and entering into the first agreements, each
appellee other than Masonite, acted independently of the others,
negotiated only with Masonite, desired the agreement regardless
of the action that might be taken by any of the others, did not
require as a condition of its acceptance that Masonite make such
an agreement with any of the others, and had no discussions
with any of the others. It is not clear at what precise time each of
the appellee became aware of the fact that its contract was not
an isolated transaction but part of a larger arrangement. But it is
clear, that as the arrangement continued, each became familiar
with it purpose and scope. It is enough that, knowing that
concerted action was contemplated and invited, the distributors
gave their adherence to the scheme and participated in it.”

Does knowledge of other dealings create an unlawful concert of
action?
50
American Tobacco

American Tobacco involved three big tobacco
companies and their purchases of tobacco and in the
sale of cigarettes. The court record indicates that on
June 23, 1931, in the depth of the Depression, the big
three all increased prices of their leading brands to the
same level, and no economic justification for the raise
was demonstrated. Other parallel price changes
followed over the next few years.

Was there an agreement?

American Tobacco Company v. United States, 328 U.S. 781,
(1946).
51
Summary of Definition and Proof of an Agreement

There is a significant difference between



spoken agreements and
learning about competitor prices, outputs and
strategies through market place actions and
“understanding” what others are communicating.
Price increases that are not cost justified are
indicative of explicit collusion, however they
can also be indicative of non collusive
strategic behaviour.
52
Plus Factors and Action Contrary to Self Interest

Defining plus factors



Examples
Foley
Action contrary to self interest


Petroleum Products Antitrust Litigation
Reserve Supply
53
What Is A Plus Factor?

Plus factors is a term that is used to denote
practices other than mere parallel pricing or
other parallel practices that can be shown to
support the inference of an agreement.

Such factors when taken alone may not
support the inference of an illegal spoken
agreement, but when taken together and put
in the context of the case point toward that
conclusion.
54
Why Are Plus Factors Important

“Consciously parallel business behaviour is circumstantial
evidence from which an agreement …. can be inferred but …
such evidence, without more, is insufficient unless circumstances
under which it occurred make the inference of rational
independent choice less attractive than that of concerted action.”

This would be true even more so in criminal cases where the
standard is beyond a “reasonable doubt”.
See Bogosian v. Gulf Oil Corp., 561 F. 2d 434, 446 (3d Cir. 1977)
55
But What Are Plus Factors?

Publication of retail prices and price announcements?
Outside meetings and conversations between competitors?
Nearly simultaneous price increases?
Refusals to deals with suppliers that compete in downstream market?
Decisions by orthopaedists to oppose podiatrist privileges at hospital based
on quality concerns?
Meeting a competitors price?
Encouragement by marketing manager to gather information on competitor
prices (including price lists) and to improve margins?
Low prices in areas with a greater number of competitors?
Capacity announcements and decisions to put in place less capacity than
announced?
Past history of collusion?
Advance knowledge of price moves?

What do you think of these plus factors? Are any unambiguous?










56
Ambiguous Evidence

the ambiguity of economic evidence has led
to a greater emphasis on direct evidence in
public cartel enforcement.
57
Should All Ambiguous Evidence Be Excluded

Some have argued that ambiguous evidence does
not assist the decision maker reach the conclusion
that collusion is a more likely hypothesis than not
and should therefore be excluded.

Others argue that the story woven by the plaintiff is
important in understanding the ambiguous evidence
and that lots of ambiguous evidence counts
(potentially a lot).
58
Foley

At a dinner party attended by leading realtors, Mr.
Foley announced that his firm was raising its
commission rate from six to seven percent. After the
announcement there was discussion about the rate
increase. Following the dinner party there were
many subsequent discussions about whether
particular firms were complying with their
agreement. Over the course of the next months the
seven percent commission rate was substantially
adopted.
59
Defining Action Contrary to Self Interest

Actions that are taken, that but for the hypothesis of
joint action, would not be in its own interest.

It is behaviour that could better be explained on the
hypothesis of collusion than on the hypothesis that
each was embarked on an individual rather than
concerted course of action.


Evidence consistent with both independent and collection
action does not do much when examined alone
Criminal cases require significantly more evidence than
that suggested above.
60
Reserve Supply – Actions Contrary To Self Interest?

Reserve Supply involved insulation. Facts indicated a series of parallel
price increases during a period of weak demand.

Defendants claimed that “it would have been irrational to attempt to
increase sales by maintaining lower prices, because lower prices would
be met by their competitors, leaving no increase in market share and
reduced profit levels.”

Court concluded that failing to maintain lower prices “does not suggest
that [the defendants] acted in a way that, but for a hypothesis of joint
action, would not have been in [their] interest.’”

What do you think of the defence statements? What do you think of the
courts reasoning?

Reserve Supply Corp. v. Owens-Corning Fiberglas Corp., 971 F. 2d 37
(1992).
61
Reserve Supply Analysis

Court did not appreciate the fact that
competition among firms leads to lower
prices as firms pursue their unilateral self
interests.

US courts tend to appreciate evidence that
indicates that firms did something that is
inconsistent with their own unilateral self
interests as also seen in American Tobacco.
62
But Determining Self Interest Can Be Difficult

Economic models of price leadership imply
that the leader adjusts its price and the others
follow suit.


If the good is homogeneous then prices for the
leader and the rivals will be identical.
If the good is heterogeneous the equilibrium price
differentials will remain the same.
63
Events and Self Interest

Pricing behaviour that changes markedly at a
point in time and that does not correspond to
expected unilateral reactions based on prior
behaviour may aid the decision maker in
reaching a finding of agreement

Obviously changes in cost and demand need to
be accounted for in this kind of analysis
64
Summing Up
Something more than parallel behaviour must be
shown before an agreement can be inferred.
The existence of an agreement cannot be inferred
from actions that are consistent with Nash,
noncooperative equilibrium such as Cournot,
Bertrand, or price leader models.
Action contrary to self interest is a critical plus
factor.
The existence of an agreement should not be
inferred absent some evidence of communication
of some kind among defendants through which an
agreement could have been negotiated.
1.
2.
3.
4.
1.
If this is not a requirement what would be the remedy?
65