Industrial Organization: Chapter 71 Chapter 7 Collusion and Cartels

Industrial Organization: Chapter 7 1

Chapter 7

Collusion and Cartels


Collusion and Cartels• What is a cartel?

– attempt to enforce market discipline and reduce competition between a group of suppliers

– cartel members agree to coordinate their actions• prices

• market shares

• exclusive territories

– prevent excessive competition between the cartel members


Collusion and Cartels• Cartels have always been with us

– electrical conspiracy of the 1950s

– garbage disposal in New York

– Archer, Daniels, Midland

– the vitamin conspiracy

• Some are explicit and difficult to prevent– OPEC

– De Beers

– shipping conferences


Collusion and Cartels• Other less explicit attempts to control competition

– formation of producer associations

– publication of price sheets

– peer pressure (NASDAQ?)

– violence

• Cartel laws make cartels illegal in the US and Europe

• Authorities continually search for cartels

• Have been successful in recent years– Nearly $1 billion in fines in 1999


Collusion and Cartels• What constrains cartel formation?

– they are generally illegal• per se violation of anti-trust law in US

• substantial penalties if prosecuted

– cannot be enforced by legally binding contracts

– the cartel has to be covert• enforced by non-legally binding threats or self-interest

– cartels tend to be unstable• there is an incentive to cheat on the cartel agreement

– MC > MR for each member

– cartel members have the incentive to increase output

– OPEC until very recently


The Incentive to Collude• Is there a real incentive to belong to a cartel?

• Is cheating so endemic that cartels fail?

• If so, why worry about cartels?

• Simple reason– without cartel laws legally enforceable contracts could be written

by cartel members• De Beers is tacitly supported by the South African government

• gives force to the threats that support this cartel

– not to supply any company that deviates from the cartel

• Without contracts the temptation to cheat can be strong


The Incentive to Cheat• Take a simple example

– two identical Cournot firms making identical products– for each firm MC = $30– market demand is P = 150 – Q where Q is in thousands– Q = q1 + q2

Price

Quantity

150

150

Demand

30 MC


The Incentive to CheatProfit for firm 1 is: 1 = q1(P - c)

= q1(150 - q1 - q2 - 30)

= q1(120 - q1 - q2)

To maximize, differentiate with respect to q1:

1/q1 = 120 - 2q1 - q2 = 0

Solve this for q1Solve this for q1

q*1 = 60 - q2/2This is the best response

function for firm 1

This is the best responsefunction for firm 1The best response function for firm 2 is then:

q*2 = 60 - q1/2


The Incentive to CheatThese best response functions are easily illustrated

q2

q1

q*1 = 60 - q2/2

60

120

q*2 = 60 - q1/2

R2

120

60

Solving these gives the Cournot-Nash outputs:

qC1 = qC

2 = 40 (thousand)

40

40C

R1

The market price is:PC = 150 - 80 = $70

Profit to each firm is:==(70 - 30)x40 = $1.6 million


The Incentive to Cheat (cont.)What if the two firms agree to collude?

q2

q1

60

120

R2

120

6040

40C

R1

==(90 - 30)x30 = $1.8 million

They will agree on the monopoly outputThis gives a total output of 60 thousand

Price is PM = (150 - 60) = $90Profit for each firm is:

Each firm produces 30 thousand

30

30


The Incentive to Cheat (cont.)Both firms have an incentive to cheat on their agreement

q2

q1

60

120

R2

120

6040

40 C

R1

If firm 1 believes that firm 2 will produce 30 units then firm 1 should produce more than 30 units

30

30

Firm 1’s best response is:qD

1 = 60 - qM2/2 = 45 thousand

45

Total output is 45 + 25 = 70 thousandPrice is PD = 150 - 75 = $75

Profit of firm 1 is (75 - 30)x45 = $2.025 million

Profit for firm 2 is (75 - 30)x25 = $1.35

million

Cheatingpays!!


The Incentive to Cheat (cont.)Firm 2 can make the same calculations!This gives the following pay-off matrix:

Firm 1

Fir

m 2

Cooperate (M)

Cooperate (M)

Deviate (D)

Deviate (D)

(1.8, 1.8) (1.35, 2.025)

(2.035, 1.35) (1.6, 1.6)

This is the Nashequilibrium

This is the Nashequilibrium

(1.6, 1.6)

Both firms have theincentive to cheat on

their agreement


Cartel Stability• The cartel in our example is unstable

• This instability is quite general

• Can we find mechanisms that give stable cartels?– violence in one possibility!

– are there others?• must take away the temptation to cheat

• staying in the cartel must be in a firm’s self-interest

• Suppose that the firms interact over time– Then it might be possible to sustain the cartel

• Make cheating unprofitable

– Reward “good” behavior

– Punish “bad” behavior


Repeated Games• Formalizing these ideas leads to repeated games

– a firm’s strategy is conditional on previous strategies played by the firm and its rivals

• In the example: cheating gives $2.025 million once

• But then the cartel fails, giving profits of $1.6 million per period

• Without cheating profits would have been $1.8 million per period

• So cheating might not actually pay

• Repeated games can become very complex– strategies are needed for every possible history

• But some “rules of the game” reduce this complexity– Nash equilibrium reduces the strategy space considerably

• Consider two examples


Example 1: Cournot duopolyThe pay-off matrix from the simple Cournot game

Firm 1

Fir

m 2

Cooperate (M)

Cooperate (M)

Deviate (D)

Deviate (D)

(1.8, 1.8) (1.35, 2.025)

(2.025, 1.35) (1.6, 1.6)(1.6, 1.6)


Example 2: A Bertrand Game

Firm 1

Fir

m 2

$105

$105 (8.25, 7.25)

$130

(7.3125, 7.3125)

(8.5, 8.5)(7.25, 8.25)

(5.525, 9.375)

(7.3125, 7.3125)

$130 $160

$160 (7.15, 10)

(9.375, 5.525)

(10, 7.15)

(9.1, 9.1)

(8.5, 8.5)


Repeated Games (cont.)• Time “matters” in a repeated game

– is the game finite? T is known in advance• Exhaustible resource

• Patent

• Managerial context

– or infinite? • this is an analog for T not being known: each time the game is played

there is a chance that it will be played again


Repeated Games (cont.)• Take a finite game: Example 1 played twice

• A potential strategy is:– I will cooperate in period 1

– In period 2 I will cooperate so long as you cooperated in period 1

– Otherwise I will defect from our agreement

• This strategy lacks credibility– neither firm can credibly commit to cooperation in period 2

– so the promise is worthless

– The only equilibrium is to deviate in both periods


Repeated Games (cont.)• What if T is “large” but finite and known?

– suppose that the game has a unique Nash equilibrium

– the only credible outcome in the final period is this equilibrium

– but then the second last period is effectively the last period• the Nash equilibrium will be played then

– but then the third last period is effectively the last period• the Nash equilibrium will be played then

– and so on

• The possibility of cooperation disappears– The Selten Theorem: If a game with a unique Nash equilibrium is

played finitely many times, its solution is that Nash equilibrium played every time.

– Example 1 is such a case


Repeated Games (cont.)• How to resolve this? Two restrictions

– Uniqueness of the Nash equilibrium

– Finite play

• What if the equilibrium is not unique?– Example 2

– A “good” Nash equilibrium ($130, $130)

– A “bad” Nash equilibrium ($105, $105)

– Both firms would like ($160, $160)

• Now there is a possibility of rewarding “good” behavior– If you cooperate in the early periods then I shall ensure that we

break to the Nash equilibrium that you like

– If you break our agreement then I shall ensure that we break to the Nash equilibrium that you do not like


A finitely repeated game• Assume that the discount rate is zero (for simplicity)• Assume also that the firms interact twice• Suggest a cartel in the first period and “good” Nash in the

second– Set price of $160 in period 1 and $130 in period 2

• Present value of profit from this behavior is:– PV2(1) = $9.1 + $8.5 = $17.6 million

– PV2(2) = $9.1 + $8.5 = $17.6 million

• What credible strategy supports this equilibrium?– First period: set a price of $160

– Second period: If history from period 1 is ($160, $160) set price of $130, otherwise set price of

$105.


A finitely repeated game• These strategies reflect historical dependence

– each firm’s second period action depends on the history of play

• Is this really a Nash subgame perfect equilibrium?– show that the strategy is a best response for each player


A finitely repeated game• This is obvious in the final period

– the strategy combination is a Nash equilibrium

– neither firm can improve on this

• What about the first period?– why doesn’t one firm, say firm 2, try to improve its profits by

setting a price of $130 in the first period?

• Consider the impact– History into period 2 is ($160, $130)

– Firm 1 then sets price $105

– Firm 2’s best response is also $105: Nash equilibrium

– Profit therefore is PV2(1) = $10 + $7.3125 = $17.3125 million

– This is less than profit from cooperating in period 1

Defection does notpay in this case!


A finitely repeated game• Defection does not pay!• The same applies to firm 1• So we have credible strategies that partially support the

cartel• Extensions

– More than two periods• Same argument shows that the cartel can be sustained for all but the

final period: strategy– In period t < T set price of $160 if history through t – 1 has been

($160, $160) otherwise set price $105 in this and all subsequent periods

– In period T set price of $130 if the history through T – 1 has been ($160, $160) otherwise set price $105

– Discounting


A finitely repeated game• Suppose that the discount factor R < 1

– Reward to “good” behavior is reduced

– PVc(1) = $9.1 + $8.5R

– Profit from undercutting in period 1 is

– PVd(1) = $10 + $7.3125R

• For the cartel to hold in period 1 we require R > 0.756 (discount rate of less than 32 percent)

• Discount factors less than 1 impose constraints on cartel stability

• But these constraints are weaker if there are more periods in which the firms interact


A finitely repeated game• Suppose that R < 0.756 but that the firms interact over

three periods.

• Consider the strategy– First period: set price $160

– Second and third periods: set price of $130 if the history from the first period is ($160, $160), otherwise set price of $105

• Cartel lasts only one period but this is better than nothing if sustainable

• Is the cartel sustainable?


A finitely repeated game• Profit from the agreement

– PVc(1) = $9.1 + $8.5R + $8.5R2

• Profit from cheating in period 1– PVd(1) = $10 + $7.3125R + $7.3125R2

• The cartel is stable in period 1 if R > 0.504 (discount rate of less than 98.5 percent)


Cartel Stability (cont.)• The intuition is simple enough

– suppose the Nash equilibrium is not unique

– some equilibria will be “good” and some “bad” for the firms

– with a finite future the cartel will inevitably break down

– but there is the possibility of credibly rewarding good behavior and credibly punishing bad behavior

• make a credible commitment to the good equilibrium if rivals have cooperated

• to the bad equilibrium if they have not.


Cartel Stability (cont.)• Cartel stability is possible even if cooperation is over a

finite period of time– if there is a credible reward system

– which requires that the Nash equilibrium is not unique

• This is a limited scenario

• What happens if we remove the “finiteness” property?

• Suppose the cartel expects to last indefinitely– equivalent to assuming that the last period is unknown

– in every period there is a finite probability that competition will continue

– now there is no definite end period

– so it is possible that the cartel can be sustained indefinitely


A Digression: The Discount Factor• How do we evaluate a profit stream over an indefinite

time?– Suppose that profits are expected to be 0 today, 1 in period 1, 2

in period 2 … t in period t

– Suppose that in each period there is a probability that the market will last into the next period

• probability of reaching period 1 is , period 2 is 2, period 3 is 3, …, period t is t

– Then expected profit from period t is tt

– Assume that the discount factor is R. Then expected profit is

– PV(t) = 0 + R1 + R222 + R333 + … + Rttt + …

– The effective discount factor is the “probability-adjusted” discount factor = R.


Cartel Stability (cont.)• Analysis of infinitely or indefinitely repeated games is less

complex than it seems

• Cartel can be sustained by a trigger strategy– “I will stick by our agreement in the current period so long as you

have always stuck by our agreement”

– “If you have ever deviated from our agreement I will play a Nash equilibrium strategy forever”


Cartel Stability (cont.)• Take example 1 but suppose that there is a probability in

each period that the market will continue:– Cooperation has each firm producing 30 thousand

– Nash equilibrium has each firm producing 40 thousand

• So the trigger strategy is:– I will produce 30 thousand in the current period if you have

produced 30 thousand in every previous period

– if you have ever produced more than 30 thousand then I will produce 40 thousand in every period after your deviation

• This is a “trigger” strategy because punishment is triggered by deviation of the partner

• Does it work?


Cartel Stability (cont.)• Profit from sticking to the agreement is:

– PVC = 1.8 + 1.8R + 1.8R2 + …

= 1.8/(1 - )• Profit from deviating from the agreement is:

– PVD = 2.025 + 1.6 + 1.6 2 + …

= 2.025 + 1.6 /(1 - )

• Sticking to the agreement is better if:– PVC > PVD

1.8

1 - > 2.025 +

1.6 1 -

this requires: which requires = R> 0.592

if = 1 we need r < 86%; if = 0.6 we need r < 13.4%

A cartel is more likelyto be stable the greater theprobability that the market

will continue and thelower is the interest rate


Cartel Stability (cont.)• This is an example of a more general result• Suppose that in each period

– profits to a firm from a collusive agreement are

– profits from deviating from the agreement are D

– profits in the Nash equilibrium are N

– we expect that D > >N

• Cheating on the cartel does not pay so long as:

> D - M

D - N

• The cartel is stable– if short-term gains from cheating are low relative to long-run losses

– if cartel members value future profits (high probability-adjusted discount factor)

This is the short-run gainfrom cheating on the cartel

This is the short-run gainfrom cheating on the cartel

This is the long-run lossfrom cheating on the cartel

This is the long-run lossfrom cheating on the cartel

There is always a value of < 1 for which

this equation issatisfied


Cartel Stability (cont.)• What about Example 2?

– two possible trigger strategies• price forever at $130 in the event of a deviation from $160

• price forever at $105 in the event of a deviation from $160

– Which?• there are probability-adjusted discount factors for which the first

strategy fails but the second works

– Simply put, the more severe the punishment the easier it is to sustain a cartel


Trigger strategies• Any cartel can be sustained by means of a trigger strategy

– prevents destructive competition

• But there are some limitations– assumes that punishment can be implemented quickly

• deviation noticed quickly

• non-deviators agree on punishment

– sometimes deviation is is difficult to detect

– punishment may take time

– but then rewards to deviation are increased

• The main principle remains– if the discount rate is low enough then a cartel will be stable

provided that punishment occurs within some “reasonable” time


Trigger strategies (cont.)• Another objection: a trigger strategy is

– harsh

– unforgiving

• Important if there is any uncertainty in the market– suppose that demand is uncertain

Price

Quantity

DEDL

DH

QEQL QH

PC

There is a possibilitythat demand may be

low

There is a possibilitythat demand may be

lowAnd a possibility

that demand may behigh

And a possibilitythat demand may be

highThis is the

expected marketdemand

This is theexpected market

demand

Suppose that theagreed price is PC

Suppose that theagreed price is PC

Expected sales areQE

Expected sales areQE

Actual sales varybetween QL and QH

Actual sales varybetween QL and QH

A firm in this cartel does not know if a decline

in sales is “natural”

or caused by cheating


Trigger strategies (cont.)• These objections can be overcome

– limit punishment phase to a finite period

– take action only if sales fall outside an agreed range

• Makes agreement more complex but still feasible

• Further limitation– approach is too effective

– result of the Folk Theorem

Suppose that an infinitely repeated game has a set of pay-offs that exceed the one-shot Nash equilibrium pay-offs for each

and every firm. Then any set of feasible pay-offs that are preferred by all firms to the Nash equilibrium pay-offs can be

supported as subgame perfect equilibria for the repeated game for some discount factor sufficiently close to unity.


The Folk Theorem• Take example 1. The feasible pay-offs describe the

following possibilities

$2.1

$2.1$1.5 $1.6

$2.0

$2.0

If the firms colludeperfectly they share

$3.6 million

If the firms colludeperfectly they share

$3.6 million

$1.6

If the firms competethey each earn$1.6 million

If the firms competethey each earn$1.6 million

The Folk Theorem statesthat any point in thistriangle is a potentialequilibrium for the

repeated game

The Folk Theorem statesthat any point in thistriangle is a potentialequilibrium for the

repeated game

Collusion onmonopoly giveseach firm $1.8

million

Collusion onmonopoly giveseach firm $1.8

million

$1.8

$1.8

$1.8 million to

each firm may not be sustainable but

something less will be


Stable cartels (cont.)• A collusive agreement must balance the temptation to cheat

• In some cases the monopoly outcome may not be sustainable– too strong a temptation to cheat

• But the folk theorem indicates that collusion is still feasible– there will be a collusive agreement:

• that is better than competition

• that is not subject to the temptation to cheat


Cartel Formation• What factors are most conducive to cartel formation?

– sufficient profit motive

– means by which agreement can be reached and enforced

• The potential for monopoly profit– collusion must deliver an increase in profits: this implies

• demand is relatively inelastic

– restricting output increases prices and profits

• entry is restricted

– high profits encourage new entry

– but new entry dissipates profits (OPEC)

– new entry undermines the collusive agreement


Cartel formation (cont.)• So there must be means to deter entry

– common marketing agency to channel output

– consumers must be persuaded of the advantages of the agency• lower search costs

• greater security of supply

• wider access to sellers

• denied access if buy outside the agency (De Beers)

– trade association• persuade consumers that the association is in their best interests


Cartel formation (cont.)• Costs of reaching a cooperative agreement

– even if the potential for additional profits exists, forming a cartel is time-consuming and costly

• has to be negotiated

• has to be hidden

• has to be monitored

• There are factors that reduce the costs of cartel formation– small number of firms (recall Selten)

– high industry concentration• makes negotiation, monitoring and punishment (if necessary) easier

– similarity in production costs

– lack of significant product differentiation


Cartel formation (cont.)• Similarity in costs

– suppose two firms with different costs

– if they collude they can attain some point on 12

12 is curved because the firms have different costs

If all output is madeby firm 2 this is

total profit


total profit


total profit


total profit

mm has a 450 slope and is tangent to 12 at M

m

m

Mm

m

at M firm 1 has profit 1m and firm 2 2m

assume Cournot equilibrium is at C

C

firm 2 will not agree to collude on M without a side payment from firm 1

C

C


Cartel formation (cont.)

m

m

Mm

m

C

C

C

with side payments it is possible to collude to somewhere on DE

without side payments it is only possible to collude to somewhere on AB

this type of collusion is difficult and expensive to negotiate: e.g. possibility of misrepresentation of costs

D

E

A

B

but side payments increase the risk of detection


Cartel formation (cont.)• Lack of product differentiation

– if products are very different then negotiations are complex

– need agreed price/output/market share for each product

– monitoring is more complex

• Most cartels are found in relatively homogeneous product markets

• Or firms have to adopt mechanisms that ease monitoring– basing point pricing


Cartel formation (cont.)• Low costs of maintaining a cartel agreement

– it is easier to maintain a cartel agreement when there is frequent market interaction between the firms

• over time

• over spatially separated markets

– relates to the discussion of repeated games• less frequent interaction leads to an extended time between cheating,

detection and punishment

• makes the cartel harder to sustain


Cartel formation (cont.)• Stable market conditions

– accurate information is essential to maintaining a cartel• makes monitoring easier

– unstable markets lead to confused signals• makes collusion “near” to monopoly difficult

– uncertainty can be mitigated• trade association

• common marketing agency

– controls distribution and improves market information

• Other conditions make cartel formation easier– detection and punishment should be simple and timely

– geographic separation through market sharing is one popular mechanism


Cartel formation (cont.)• Other tactics encourage firms to stick by price-fixing

agreements– most-favored customer clauses

• reduces the temptation to offer lower prices to new customers

– meet-the competition clauses• makes detection of cheating very effective


Meet-the-competition clause

Firm 2

Fir

m 1

High Price Low Price

High Price

Low Price

12, 12 5, 14

14, 5 6, 6

the one-shot Nash equilibrium is (Low, Low)

meet-the-competition clause removes the off-diagonal entries

now (High, High) is easier to sustain

5, 14

14, 5


Cartel Detection• Cartel detection is far from simple

– most have been discovered by “finking”

– even with NASDAQ telephone tapping was necessary

• If members of a cartel are sophisticated they can hide the cartel: make it appear competitive– “the indistinguishability theorem”

– ICI/Solvay soda ash case• accused of market sharing in Europe

• no market interpenetration despite price differentials

• defense: price differentials survive because of high transport costs

• soda ash has rarely been transported so no data on transport costs are available

• The Cournot model illustrates this “theorem”


The Indistinguishability Theorem

start with a standard Cournot model: C is the non-cooperative equilibrium

q2

q1

R1

R2

assume that the firms are colluding at M: restricting output

C

M can be presented as non-collusive if the firms exaggerate their costs or underestimate demand

this gives the apparent best response functions R’1 and R’2

R’1

R’2

M now “looks like” the non-cooperative equilibrium

M


An Example Suppose market demand is P = 100 - Q, that there are 3 firms and that each firm has true marginal costs of $20

The Cournot equilibrium market price and the outputs for each firm are given by the equations:

qi = (A - c)/(N + 1); PC = (A + cN)/(N + 1) where we have that A = 100, c = 20, N = 3

So we have: qi = 20 and PC = $40

Suppose the firms are colluding on the monopoly price, which is (A + c)/2 = $60

What production cost 20 + f would make this look like a Cournot price?We need (100 + 3(20 + f))/4 = 60;so 160 + 3f = 240

which gives f = $80/3 = $26.67

The same result can be obtained by overestimating the reservation price


Cartel detection (cont.)• Cartels have been detected in procurement auctions

– bidding on public projects; exploration

– the electrical conspiracy using “phases of the moon” • those scheduled to lose tended to submit identical bids

• but they could randomize on losing bids!

• Suggested that losing bids tend not to reflect costs– correlate losing bids with costs!

• Is there a way to beat the indistinguishability theorem?– Osborne and Pitchik suggest one test


Testing for collusion• Suppose that two firms

– compete on price but have capacity constraints

– choose capacities before they form a cartel

• Then they anticipate competition after capacity choice– a collusive agreement will leave the firms with excess capacity

– uncoordinated capacity choices are unlikely to be equal• one firms or the other will overestimate demand

– so both firms have excess capacity but one has more excess

• Collusion between the firms then leads to:– firm with the smaller capacity making higher profit per unit of

capacity

– this unit profit difference increases when joint capacity increases relative to market demand


An example: the salt duopolyBritish Salt and ICI Weston Point were suspected of operating a cartel

BS Profit

WP Profit

BS profit per unit of capacity

1980 1981 1982 1983 1984

WP profit per unit of capacity

Total Capacity/Total Sales

7065 7622 10489 10150 10882

7273 7527 6841 6297 6204

BS capacity: 824 kilotons; WP capacity: 1095 kilotons

8.6 9.3 12.7 12.3 13.2

6.6 6.9 6.3 5.8 5.7

1.5 1.7 1.7 1.9 1.9

But will this test be successful once it is widely known and applied?But will this test be successful once it is widely known and applied?

BS is the smallerfirm and makesmore profit perunit of capacity

BS is the smallerfirm and makesmore profit perunit of capacity

The profitdifference grows

with capacity

The profitdifference grows

with capacity



Example 2: A Bertrand Game

Firm 1

Fir

m 2

$105

$105 (8.25, 7.25)

$130

(7.3125, 7.3125)

(8.5, 8.5)(7.25, 8.25)

(5.525, 9.375)

$130 $160

$160 (7.15, 10)

(9.375, 5.525)

(10, 7.15)

(9.1, 9.1)


Basing Point Pricing

Birmingham Steel Company

PittsburghPittsburghSuppose that

the steel ismade here

Suppose thatthe steel ismade here

And that itis soldhere

And that itis soldhere

Then it was priced atthe mill price plus

transport costsfrom Pittsburgh

Documents

Industrial Organization: Chapter 71 Chapter 7 Collusion and Cartels