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Collusion and Cartels

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**1. ** Collusion and Cartels

**2. **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

**3. **Collusion and Cartels Cartels have always been with us
electrical conspiracy of the 1950s
Alitalia
Some are explicit and difficult to prevent
OPEC
De Beers

**4. **Collusion and Cartels Other less explicit attempts to control competition
formation of producer associations
publication of price sheets
peer pressure
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 (USA)

**5. **Recent cartel violations

**6. **Recent cartel violations 2 Fines steadily grew during the 1990s

**7. **Collusion and Cartels What constrains cartel formation?
they are generally illegal
per se violation of anti-trust law in US and EU
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

**8. **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

**9. **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

**10. **The Incentive to Cheat

**11. **The Incentive to Cheat

**12. **The Incentive to Cheat (cont.)

**13. **The Incentive to Cheat (cont.)

**14. **The Incentive to Cheat (cont.)

**15. **The incentive to cheat (cont.) This is a prisoners’ dilemma game
mutual interest in cooperating
but cooperation is unsustainable
However, cartels do form
So there must be more to the story

**16. **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

**17. **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

**18. **Example 1: Cournot duopoly

**19. **Example 2: A Bertrand Game

**20. **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

**21. **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

**22. **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

**23. **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

**24. **Industrial Organization: Chapter 7 24 Example 2 / 1 Consider the following pricing game

**25. **Industrial Organization: Chapter 7 25 Example 2 /2 There are two Nash equilibria

**26. **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(p1) = $9.1 + $8.5 = $17.6 million
PV2(p2) = $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.

**27. **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

**28. **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?

**29. **Industrial Organization: Chapter 7 29 Example 2/3

**30. **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

**31. **A finitely repeated game Suppose that the discount factor R < 1
Reward to “good” behavior is reduced
PVc(p1) = $9.1 + $8.5R
Profit from undercutting in period 1 is
PVd(p1) = $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

**32. **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?

**33. **A finitely repeated game Profit from the agreement
PVc(p1) = $9.1 + $8.5R + $8.5R2
Profit from cheating in period 1
PVd(p1) = $10 + $7.3125R + $7.3125R2
The cartel is stable in period 1 if R > 0.504 (discount rate of less than 98.5 percent)

**34. **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.

**35. **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

**36. **A Digression: The Discount Factor How do we evaluate a profit stream over an indefinite time?
Suppose that profits are expected to be p0 today, p1 in period 1, p2 in period 2 … pt in period t
Suppose that in each period there is a probability r that the market will last into the next period
probability of reaching period 1 is r, period 2 is r2, period 3 is r3, …, period t is rt
Then expected profit from period t is rtpt
Assume that the discount factor is R. Then expected profit is
PV(pt) = p0 + Rrp1 + R2r2p2 + R3r3p3 + … + Rtrtpt + …
The effective discount factor is the “probability-adjusted” discount factor G = rR.

**37. **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”

**38. **Cartel Stability (cont.) Take example 1 but suppose that there is a probability r 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?

**39. **Example 1: Cournot duopoly

**40. **Cartel Stability (cont.) Profit from sticking to the agreement is:
PVC = 1.8 + 1.8R + 1.8R2 + …

**41. **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 pM
profits from deviating from the agreement are pD
profits in the Nash equilibrium are pN
we expect that pD > pM > pN
Cheating on the cartel does not pay so long as:

**42. **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

**43. **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 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

**44. **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

**45. **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

**46. **The Folk Theorem Take example 1. The feasible pay-offs describe the following possibilities

**47. **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

**48. **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

**49. **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

**50. **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
Similarity in costs

**51. **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

**52. **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

**53. **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

**54. **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

**55. **Meet-the-competition clause

**56. **Example 2: A Bertrand Game