econs 425 - cartelss3.wp.wsu.edu/uploads/sites/1736/2017/10/23-cartels.pdfoct 23, 2017 ·...

EconS 425 - Cartels

Eric Dunaway

Washington State University

[email protected]

Industrial Organization

Eric Dunaway (WSU) EconS 425 Industrial Organization 1 / 32

Introduction

Today, we�re talking about the inner workings of cartels.

How and why do they work?How do governments discourage cartels from forming?


Cartels

Let�s start with a quick review of how cartels are sustained.

Two (or more) �rms agree on some collusive pro�t level πM whichrequires a price much higher than that seen in a competitiveenvironment (Cournot, perfect competition, etc.).Each �rm know that they can deviate from this price and receiveπD > πM for a single period, but after that, the cartel breaks downand they receive πN forever after.A �rm will cooperate in the cartel if the probability adjusted presentdiscounted value of lifetime pro�ts from cooperating is greater thantaking the one time payday and then reverting back to the competitivevalue, i.e.,

11� ρ

πM � πD +ρ

1� ρπN


Cartels

11� ρ

πM � πD +ρ

1� ρπN

We can solve this expression for ρ, the probability adjusted discountfactor to obtain

ρ � πD � πM

πD � πN

We can de�ne ρ� as the critical value of ρ where this holds withequality,

ρ� =πD � πM

πD � πN

as long as ρ > ρ�, it�s better for the �rms to cooperate with thecartel agreement than it is to deviate for the one-time "payday" andrevert back to the non-cooperative agreement forever after.


Cartels

The value of ρ� is vital in our study of cartels.

If outside factors increase ρ�, it becomes harder for a cartel to besustained.

We�ve already seen that the values of πM , πD , and πN all in�uencethe value of ρ� (obviously).

As the bene�t of deviating from the collusive agreement increasesrelative to the collusive agreement, the cartel is harder to sustain.As the di¤erence between payo¤s from the deviating payo¤ and thecompetitive payo¤ increases, the cartel becomes easier to sustain.

We can model several other real world factors into our discussion ofcartels, and they all in�uence the value of ρ�.


Cartels

In our �rst model, we used a grim trigger strategy.

When one �rm breaks the cartel agreement, the other �rms revert backto the non-cooperative agreement forever after.

What if we made the punishment stage temporary?

Suppose that if one �rm breaks the cartel agreement, now the other�rms produce the non-cooperative value for 3 periods, then revert backto the cartel agreement.How does this change our critical value, ρ�?


Cartels

When the �rms choose to cooperate, nothing changes in this model,and their payo¤ remains

πM + ρπM + ρ2πM + ... =1

1� ρπM

However, when they deviate now, the payo¤ now becomes

πD + ρπN + ρ2πN + ρ3πN + ρ4πM + ρ5πM + ...

It will be better for the �rm to cooperate with the cartel agreement iftheir payo¤ from cooperating is higher than their payo¤ fromdeviating, then accepting their punishment,

11� ρ

πM � πD + ρπN + ρ2πN + ρ3πN +ρ4

1� ρπM

πM + ρπM + ρ2πM + ρ3πM � πD + ρπN + ρ2πN + ρ3πN


Cartels

πM + ρπM + ρ2πM + ρ3πM � πD + ρπN + ρ2πN + ρ3πN

We can simplify this expression to obtain

ρ+ ρ2 + ρ3 � πD � πM

πM � πN

which is di¢ cult to solve for the critical value of ρ�.

However, we can use a bit of a trick to �gure out its relationship to ouroriginal model�s value.


Cartels

When we changed our model, the payo¤s from cooperating anddeviating did not change.

Only the payo¤ from the punishment changed.Since the punishment only lasts for 3 periods now, the lifetime payo¤from being punished actually increases. It goes from

ρπN + ρ2πN + ρ3πN + ρ4πN + ...

toρπN + ρ2πN + ρ3πN + ρ4πM + ...


Cartels

From our original de�nition of the critical value,

ρ� =πD � πM

πD � πN

this change makes the denominator smaller, which implies that thecritical value increases.

This should make sense. If the punishment isn�t as severe (since itonly lasts for a few periods), it�s now easier for �ms to cheat on thecollusive agreement, since they�ll get it back after a few periods.

For �rms that are very patient (high values of ρ), and agreement likethis is better than a grim trigger strategy since it allows room for bothcollusion and reconciliation when events break that initial collusion.

Let�s look at some other factors.


Cartels

What if we have N �rms?

Remember from Bertrand competition that the �rms share thecollusive pro�ts evenly. Thus, each �rm receives πM

N .

The pro�ts from deviating don�t change, as one �rm claims all of themarket pro�ts by undercutting the others.The pro�ts from being punished also don�t change, as they are zero. Ingeneral, it�s possible that these would also decrease, as well (As inCournot competition).


Cartels

ρ� =πD � πM

πD � πN

Thus, with N �rms, πM decreases and πN either decreases or staysthe same.

This implies that the numerator of our critical value expressionincreases, while the denominator increases (less than the numerator) orstays the same.

This causes the value of ρ� to increase, and makes it harder to sustaincollusion for the cartel.

Intuitively, since there is less to go around for each of the members ofthe cartel, it�s much more tempting to cheat on the cartelarrangement for each individual �rm.


Cartels

This closely relates to barriers to entry for the cartel.

If there are weak barriers to entry to a market, it�s easier for newcompetitors to enter the market.When competitors enter, they can either join the cartel or competeagainst them. Both of these options lower the collusive payo¤ for thecartel, which makes deviation more lucrative.

Thus, when barriers to entry are weak, it�s harder to sustain a cartel.


Cartels

Frequency of orders also plays a huge role in cartel sustainability.

Suppose that �rms have a probability adjusted critical discount factorof ρ� = 0.9 for each interraction.If �rms interract once per quarter, this is equivalent to a yearlyprobability adjusted discount factor of 0.94 = 0.66.If �rms interract twice per year, the equivalent yearly probabilityadjusted discount factor is 0.92 = 0.81.

With more frequent orders, it�s easier for the cartel to sustaincollusion since they are able to see what the other members are doingmore often.

On the other hand, with less frequent orders, it takes longer for acheating member to be punished by the others, so the incentive todeviate becomes stronger.


Cartels

What if the market were growing?

Suppose now that pro�ts increased by some growth rate g eachperiod. Our pro�ts from colluding become

πM + ρgπM + (ρg)2πM + ... =1

1� ρgπM

and our pro�ts from deviating become

πD + ρgπN + (ρg)2πN + ... = πD +ρg

1� ρgπN

and collusion can be sustained as long as

11� ρg

πM � πD +ρg

1� ρgπN


Cartels

11� ρg

πM � πD +ρg

1� ρgπN

Solving for our critical probability adjusted discount factor, we have

ρ� =1g

πD � πM

πD � πN

Thus, if g > 1 (a growing market), it actually becomes easier tosustain collusion. Firms are likely to work together to enjoy thatgrowing share of the collusive pro�ts.

On the other hand, if g < 1 (a shrinking market), collusion becomesharder to sustain, as cartel members might want to jump ship andtake the deviation pro�ts before they are all gone.


Cartels

What if the �rms weren�t symmetric?Suppose we had two �rms and something about them caused there tobe an uneven share of the monopoly pro�ts (di¤erent costs, etc.). Lets1 be �rm 1�s market share, s2 be �rm 2�s and s1 > s2, s1 + s2 = 1.If �rm i = 1, 2 cooperates, their probability adjusted presentdiscounted value of lifetime pro�ts are

11� ρ

siπM

whereas if they deviate, then revert back to the non-cooperative pro�tlevel,

πD +ρ

1� ρsiπN

and cooperation can be sustained if

11� ρ

siπM � πD +ρ

1� ρsiπN


Cartels

Solving this expression for the critical value of the probability adjusteddiscount value,

ρ� =πD � siπMπD � siπN

and di¤erentiating this expression with respect to market shares givesus

∂ρ�

∂si=

πD (πN � πM )

(πD � siπN )2< 0

This implies that as the market share for a �rm increases, it�s easierfor them to sustain collusion in the cartel. Obviously, since they aregetting the larger slice of the cartel pro�ts, they are happy to collude.

On the other hand, the �rm with the smaller share of the pro�t levelis less likely to collude, since the relative size of the deviation pro�tsare much higher for them.


Cartels

Interestingly, this problem can be mitigated if asymmetric �rmsinterracted in several markets.

If �rm 1 were the big �rm in market 1, but �rm 2 were the big �rm inmarket 2, it becomes easier for the �rms to collude in both markets.Deviating in one market could spell doom for the other market, so each�rm accepts their smaller market share in one market in exchange for alarger market share in the other.


Cartels

Lastly, what if the goods were di¤erentiated?

It�s easy when �rms all sell the same product in a cartel. When theproducts are di¤erent, however, there can be uncertainty about howthe price of one good a¤ects the price of the other similar goods soldby the cartel.In fact, it becomes easier to cheat on the Cartel agreement in this case,as detecting defection becomes harder.


Fighting Cartels

Now that our model for how cartels operate is fairly robust, let�s talkabout how regulators try to prevent cartels from forming.

Naturally, detecting cartels can be very di¢ cult. The members of thecartel have much more information than the regulators, and they areunlikely to share that information unless properly incentivized.

Thus, it is costly to investigate for the presence of a cartel.

Regulators can, however, investigate suspected cartels and impose�nes upon them should they be caught colluding.

Let�s look at that in our model.


Fighting Cartels

Suppose that two �rms operate as a cartel in a market and each earnpro�ts of πM . For every period they operate, there is a probability αthat their behavior will be detected by a regulatory agency.

If the agency detects the cartel, all members are �ned some level F andthen the �rm is forced into the non-cooperative equilibrium foreverafter.If the agency does not detect the cartel, business continues as normal.

Naturally, this adds another layer of complexity onto our model, butthe results illustrate a big picture on how the government �ghts cartelbehavior.


Fighting Cartels

Let V represent the total payo¤ to a �rm when they cooperate. Withprobability 1� α, the �rm isn�t caught and their payo¤ is

πM + ρV

With probability a, the �rm gets caught and their payo¤ becomes

πM � F + ρ

1� ρπN

and putting them together, we have the total payo¤ of

V = (1� α)hπM + ρV

i+ α

�πM � F + ρ

1� ρπN�

This is a reciprocal function (a function that is a function of itself),but we can treat V as just a variable and solve for it.


Fighting Cartels

V = (1� α)hπM + ρV

i+ α

�πM � F + ρ

1� ρπN�

After a lot of algebra, we can solve for V as

V =πM � αF + α

ρ1�ρ πN

1� (1� α)ρ

and note that if α = 0 (no chance of getting caught, V = 11�ρ πM ,

our standard value.

So what does the presence of an investigation and a �ne do here?

Naturally, as F increases, V decreases. A larger �ne decreases theexpected value of collusion, which makes it less likely for a cartel tocollude, as the potential punishment from the government is large.(Better to cheat and get out now before you get caught).


Fighting Cartels

We can di¤erentiate the previous expression with respect to α (I�llsave you from the math) to �nd out that

∂V∂α

< 0

which implies that as the probability of getting caught increases, theexpected value of collusion also decreases. This is similar to the �nein that it reduces the ability for �rms to collude; a �rm that knows itis likely to get caught would much rather cheat now and get outbefore they get caught.

Thus, if a regulator puts more e¤ort into investigating �rms, andlevies larger �nes on them, it becomes less likely that �rms will wantto collude in the �rst place.


Fighting Cartels

In the real world, the probability of catching a cartel, α, is quite low.

It�s very hard to distinguish between collusive and competitivebehaviors.

Most of the time, Regulators depend on steep �nes to prevent �rmsfrom wanting to collude.

These �nes can be in the order of hundreds of millions of dollarsdepending on the economic damages that the cartel has done to themarket.


Fighting Cartels

Since the advent of game theory, regulators have been using anothertechnique, as well, to �ght cartels: leniency programs.

They o¤er the �rst �rm to confess to cartel behavior a much morelenient �ne (or no �ne at all) in exchange for providing all of theinformation they need to prosecute the other cartel members.

This has been wildly successful. By forcing the �rms into a prisoner�sdilemma situation, they all have strong incentives to snitch on theother �rms to avoid a penalty.Applications for this program have increased cartel detection by 20-fold.


Fighting Cartels

There has been some discussion, however, that leniency programs canactually increase incentives to form a cartel.

Basically, we can form a cartel now when we normally wouldn�t sincewe know that if we snitch �rst, we can avoid the big �ne.This is an unintended consequence of those leniency programs, whichare still considered successful regardless.


Fighting Cartels

Interestingly, when cartel members apply for leniency is stronglycorrelated with unfavorable economic conditions.

When the economy enters a recession (negative growth), the incentiveto cheat on the cartel agreement increases. At this point, the cartel hasbecome volatile and is likely to self-implode soon.This is when we see a lot of �rms seek protection from their impendingcartel retribution.

Joseph Harrington presented this last year at the Leigh Lecture.

SHAMELESS PLUG: Edward Prescott, Nobel prize winningmacroeconomist, is speaking about the state of the US economy at theLeigh Lecture on Thursday night. You should be there.


Summary

At the end of the day, it�s di¢ cult for �rms to sustain collusion in acartel agreement.

Pressures from within the cartel and from outside regulators onlyinduce the members to defect in order to maximize their own gains.


Next Time

Horizontal Mergers

Under what conditions to two �rms want to combine into one larger�rm?


Homework 5-4

Consider a situation where two �rms who normally compete in pricesdecide to form a cartel. They implement a grim trigger pricingstrategy where they each receive half of the monopoly pro�ts whenthe collude, but if either defects (claiming all the monopoly pro�ts forthemselves), they revert back to the Bertrand equilibrium and earnzero pro�ts forever after. Suppose now that this market is growing bya constant rate g every period.

1. If ρ = 0.4 for each �rm, what is the minimum growth rate, g , requiredto sustain collusion?

2. If ρ = 0.8, for each �rm, what is the minimum growth rate, g , requiredto sustain collusion? Can collusion be sustained if the market isshrinking in this case?


econs 425 - cartelss3.wp.wsu.edu/uploads/sites/1736/2017/10/23-cartels.pdfoct 23, 2017 ·...

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