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# Simultaneous games. Oligopoly. (Lecture 2)

## 1. Lecture 2 Simultaneous games: Oligopoly

## 2. Oligopoly

2Extreme forms of market structure are uncomplicated:

Monopoly: one producer, no strategic interaction

Perfect competition: many producers, price is given, no

strategic interaction

Oligopoly: the industry is dominated by a small number of

large firms. Intermediate case, between perfect competition

and monopoly.

Smartphones industry

Oil producers

Accounting Big 4

Boeing and Airbus

## 3. Strategic interactions and oligopoly

3Strategic interactions and

oligopoly

When making strategic decisions (on prices, quantity,

advertising, innovation etc.) the oligopolist must consider

the actions/reactions of its competitors.

Payoff interdependency: A producer’s payoff depends

on what the other producers do.

Use of game theory.

Application of NE to oligopoly theory. Analysis of the

decision of how much to produce (quantity).

## 4. Demand and costs

4Demand: The market price is a function of the total

quantity produced in the industry, e.g:

P (Q) 1 0.001Q

Q 400 P 0.6

e.g:

Costs: Suppose that the marginal cost is 0.28

## 5. Monopoly

5The monopolist chooses Q to maximize profit:

M Q(1 0.001Q) 0.28Q 0.72Q 0.001Q 2

M

0 0.72 0.002Q 0 Q 360

Q

Outcome: Q 360

P 0.64

M 129.6

Low output to keep prices high and maximize profit.

## 6. Perfect competition

6Many producers, the price is given.

In equilibrium, Q is such that P=MC, i.e. P=0.28.

Producers make zero profit.

P = 1 − 0.001Q = 0.28, hence Q = 720,

Quantity is higher under perfect competition than

under monopoly.

## 7. The Cournot model

7What is the Cournot model?

Two producers, Firm 1 and Firm 2 (oligopoly).

Model of industry structure where producers’ strategic

decision is about how much to produce.

Produce the same good

Sell on the same market

One market price, which depends on the total output

No entry

Simultaneous game

Example: oil producing countries

## 8. Demand

The more producers jointly produce, the lower the marketprice

Q q1 q2

P (q1 q2 ) 1 0.001(q1 q2 )

Example: q1 q2 200 Q 400 P 0.6

## 9. Costs and profit

9Suppose that the marginal cost is 0.28:

C1 (q1 ) 0.28 q1

C (q ) 0.28 q2

Profit of Firms 1 and 2:

2

2

1 q1 P(q1 q2 ) C1 (q1 )

2 q2 P(q1 q2 ) C2 (q2 )

## 10. Discrete choices

Suppose there are just three possible quantities that eachfirm i=1,2 can choose qi = 180, 240 or 360.

There are 3x3=9 possible outcomes. For example, if firm 1

chooses q1=180, and firm 2 chooses q2=240, then:

P(180 240) 1 0.001 420 0.58

1 180 0.58 0.28 180 54

2 240 0.58 0.28 240 72

## 11. Discrete choices

Nash Equilibriumq1=18

0

Firm 1 q1=24

0

q1=36

0

Firm 2

q2=18 q2=24 q2=36

0

0

0

64.8 , 64.8

54, 72

32.4, 64.8

72, 54

57.6, 57.6

28.8, 43.2

64.8, 32.4

43.2, 28.8

0, 0

## 12. Continuous choices

12Discrete games are not suitable to analyze the

decision of how much to produce

Producers are not limited to just 3 levels of production.

Quantity is a continuous variable, not a discrete one.

We now assume that producers can produce any

quantity.

How much to produce?

More units sold means more volume, but lower price.

Essential to take into account the other producer’s behavior.

## 13. Continuous choices

13Simplifying the profit function:

1 q1 P(q1 q2 ) C1 (q1 )

1 q1 (1 0.001 (q1 q2 )) 0.28q1

2

1 0.72q1 0.001q1 0.001q1q2

2

2 0.72q2 0.001q2 0.001q1q2

## 14. Best responses

14We find the Nash equilibrium by deriving the best

response functions.

To maximize profit, differentiate and set equal to

zero:

1

0.72 0.002q1 0.001q2 0

q1

q1 360 0.5q2

Firm 1’s best response

Do the same for Firm 2:

q2 360 0.5q1

Firm 2’s best response

## 15. Best responses

15Firm 1 believes Firm 2

will sell q2:

Firm 1’s profitmaximizing q1 is:

0

360

100

310

200

260

240

240

300

210

360

180

400

160

720

0

## 16. Best responses

16q2

720

q1 360 0.5q2

The more Firm 2 produces, the lower the market

price, and the less Firm 1 chooses to produce.

0

q1

360

## 17. Best responses

17q2

The more Firm 1 produces, the lower the market

price, and the less Firm 2 chooses to produce.

360

q2 360 0.5q1

Firm 2’s best response

720

q1

## 18. Nash equilibrium

18Nash Equilibrium is where best responses meet.

Firm 1’s equilibrium strategy is his best response to

Firm 2’s equilibrium strategy which is also his best

response to Firm 1’s equilibrium strategy.

Joint best response, and no incentive for producers to

choose a different action.

q1 360 0.5q2 360 0.5(360 0.5q1 ) 180 0.25q1

q1 240

## 19.

Nash equilibrium19

q2

EQUILIBRIUM

q1 q2 240

P 1 0.001 480 0.52

1 2 240(0.52 0.28) 57.6

BR1

360

NE=(240,240

)

240

BR2

240

720

q1

## 20. Nash equilibrium

20q2

• Convergence towards Nash equilibrium:

• Why are other production levels not equilibrium?

• Start from (0,360)

BR1

360

BR2

0

720

q1

## 21. Effect of market structure

21Monopoly

Cournot

Perfect

competiti

on

Industry

Output

360

480

720

Price

Industry

Profit

0.64

129.6

0.52

115.2

0.28

0

Oligopoly delivers an intermediary outcome between two

extreme forms of market structure.

## 22. Effect of market structure

22Cournot with more than 2 producers:

Produce

rs

Price

q per

firm

Profit

per

firm

Industr Industr

yQ

y profit

2

0.52

240

57.6

480

115.2

3

0.46

180

32.4

540

97.2

10

0.34

65.5

4.3

654

42.8

100

0.28

7.1

0.05

712

5.1

## 23. Effect of market structure

23Having fewer producers is associated with:

Lower total output

Higher prices

Higher profitability

Empirical evidence shows that profitability is on

average higher in highly concentrated industries.

## 24. Cartel

24Wouldn’t the two producers be better off cooperating rather

than competing? YES

Both producers could maximize joint profit by jointly

producing the monopolist output level: Q=360, i.e. 180 for

each producer.

The monopolist profit (129.6) is then shared between the two

producers (i.e. 64.8 for each, instead of 57.6 if they play the

NE).

## 25. Cartel

25“The OPEC cartel agreed on Wednesday to reduce production by

2.2 million barrels a day, the group’s largest cut ever, in an effort

to put a floor on falling oil prices.

…Mr. Khelil (OPEC’s president) said the group wanted to

“eliminate” an overhang of oil inventories …and aimed to push

prices up to $70 to $80 a barrel.

“We have…excessive stocks that could really lead to a collapse

in prices,” Mr. Khelil said during a chaotic and confused news

conference after the meeting.

(NY Times, December 17, 2008)

## 26.

Cartel stability26

q2

Problem with the cartel solution:

Cooperation is not stable

BR1

360

NE=(240,240

)

BR2

(180,180)

720

q1

## 27. Cartel stability

27Each producer makes more profit by deviating from the

cartel quantity. For instance, if Firm 1 sticks to the cartel

quantity of 180, Firm 2’s best response is:

q2 360 0.5 x180 270

2 72.9

The cartel problem is a Prisoner’s dilemma situation: it is

collectively rational to cooperate (“optimal” outcome), but

it is individually rational to defect (NE).

## 28. Cartel stability

28“The coffee bean cartel, the Association of Coffee

Producing Countries, whose members produce 70% of

the global supply, will shut down in January after

failing to control international prices. [...] Mr Silva also

said the failure of member countries to comply with the

cartel’s production levels was a reason for the closure.”

(BBC News, October 19, 2001)

## 29. Cartel stability

29To summarize…

Producers have incentive to form cartels, but cartels are

unstable.

Q: How to explain the fact that some cartels are quite

stable, unlike what is predicted in the Cournot model?

List of cartel violations in the European Union

http://ec.europa.eu/competition/cartels/cases/cases.html

## 30. Comparative statics

30If Firm 1’s marginal cost is 0.25 rather than 0.28, how does

it affect the outcome?

C1 (q1 ) 0.25 q1

Equilibrium:

q1 260

q2 230

P 0.51

1 67.6

2 52.9

Increase of 17%

## 31. Summary

31Nash equilibrium and continuous choices.

Oligopoly and quantity competition: Cournot model.

Trade-off between high output and low price, or low

output and high price.

Strategic interactions yield a unique NE, with

intermediate output level.

The cartel solution is more profitable but not stable.