Simultaneous games. Oligopoly. (Lecture 2)

Сентябрь 14, 2022

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Simultaneous games. Oligopoly. (Lecture 2)

Содержание

2. Oligopoly Extreme forms of market structure are uncomplicated: Monopoly: one producer, no strategic interaction Perfect competition:
3. Strategic interactions and oligopoly When making strategic decisions (on prices, quantity, advertising, innovation etc.) the oligopolist
4. Demand and costs Demand: The market price is a function of the total quantity produced in
5. Monopoly The monopolist chooses Q to maximize profit: Outcome: Low output to keep prices high and
6. Perfect competition Many producers, the price is given. In equilibrium, Q is such that P=MC, i.e.
7. The Cournot model What is the Cournot model? Model of industry structure where producers’ strategic decision
8. Demand The more producers jointly produce, the lower the market price Example:
9. Costs and profit Suppose that the marginal cost is 0.28: Profit of Firms 1 and 2:
10. Discrete choices Suppose there are just three possible quantities that each firm i=1,2 can choose qi
11. Discrete choices Nash Equilibrium
12. Continuous choices Discrete games are not suitable to analyze the decision of how much to produce
13. Continuous choices Simplifying the profit function:
14. Best responses We find the Nash equilibrium by deriving the best response functions. To maximize profit,
15. Best responses
16. Best responses 360 720 q1 q2 0 The more Firm 2 produces, the lower the market
17. 360 720 q1 q2 Best responses Firm 2’s best response The more Firm 1 produces, the
18. Nash equilibrium Nash Equilibrium is where best responses meet. Firm 1’s equilibrium strategy is his best
19. 360 720 q1 q2 NE=(240,240) Nash equilibrium EQUILIBRIUM BR1 BR2 240 240
20. Nash equilibrium 360 720 q1 q2 Convergence towards Nash equilibrium: Why are other production levels not
21. Effect of market structure Oligopoly delivers an intermediary outcome between two extreme forms of market structure.
22. Effect of market structure Cournot with more than 2 producers:
23. Effect of market structure Having fewer producers is associated with: Lower total output Higher prices Higher
24. Wouldn’t the two producers be better off cooperating rather than competing? YES Both producers could maximize
25. Cartel “The OPEC cartel agreed on Wednesday to reduce production by 2.2 million barrels a day,
26. 360 720 q1 q2 NE=(240,240) Cartel stability BR1 BR2 (180,180) Problem with the cartel solution: Cooperation
27. Cartel stability Each producer makes more profit by deviating from the cartel quantity. For instance, if
28. Cartel stability “The coffee bean cartel, the Association of Coffee Producing Countries, whose members produce 70%
29. Cartel stability To summarize… Producers have incentive to form cartels, but cartels are unstable. Q: How
30. Comparative statics If Firm 1’s marginal cost is 0.25 rather than 0.28, how does it affect
32. Скачать презентацию

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Oligopoly
Extreme 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

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Strategic 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).

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Demand and costs
Demand: The market price is a function of the

total quantity produced in the industry, e.g:
e.g:
Costs: Suppose that the marginal cost is 0.28

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Monopoly
The monopolist chooses Q to maximize profit:
Outcome:
Low output to keep prices

high and maximize profit.

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Perfect competition
Many 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.

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The Cournot model
What is the Cournot model?
Model of industry structure where

producers’ strategic decision is about how much to produce.
Two producers, Firm 1 and Firm 2 (oligopoly).
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

Слайд 8

Demand
The more producers jointly produce, the lower the market price
Example:

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Costs and profit
Suppose that the marginal cost is 0.28:
Profit of Firms

1 and 2:

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Discrete choices
Suppose there are just three possible quantities that each firm

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:

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Discrete choices
Nash Equilibrium

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Continuous choices
Discrete 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.

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Continuous choices
Simplifying the profit function:

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Best responses
We find the Nash equilibrium by deriving the best response

functions.
To maximize profit, differentiate and set equal to zero:
Do the same for Firm 2:

Firm 1’s best response

Firm 2’s best response

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Best responses

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Best responses
360
720
q1
q2
0
The more Firm 2 produces, the lower the market
price, and

the less Firm 1 chooses to produce.

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360
720
q1
q2
Best responses
Firm 2’s best response
The more Firm 1 produces, the lower

the market
price, and the less Firm 2 chooses to produce.

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Nash equilibrium
Nash 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.

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360
720
q1
q2
NE=(240,240)
Nash equilibrium
EQUILIBRIUM
BR1
BR2
240
240

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Nash equilibrium
360
720
q1
q2
Convergence towards Nash equilibrium:
Why are other production levels

not equilibrium?
Start from (0,360)

BR1

BR2

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Effect of market structure
Oligopoly delivers an intermediary outcome between two
extreme forms

of market structure.

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Effect of market structure
Cournot with more than 2 producers:

Слайд 23

Effect of market structure
Having 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.

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Wouldn’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).

Cartel

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Cartel
“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)

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360
720
q1
q2
NE=(240,240)
Cartel stability
BR1
BR2
(180,180)
Problem with the cartel solution:
Cooperation is not stable

Слайд 27

Cartel stability
Each 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:
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).

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Cartel stability
“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)

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Cartel stability
To 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

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Comparative statics
If Firm 1’s marginal cost is 0.25 rather than 0.28,

how does it affect the outcome?
Equilibrium:

Increase of 17%

Simultaneous games. Oligopoly. (Lecture 2)

Содержание

OligopolyExtreme forms of market structure are uncomplicated:Monopoly: one producer, no strategic

Strategic interactions and oligopolyWhen making strategic decisions (on prices, quantity, advertising,

Demand and costsDemand: The market price is a function of the

MonopolyThe monopolist chooses Q to maximize profit:Outcome:Low output to keep prices

Perfect competitionMany producers, the price is given.In equilibrium, Q is such

The Cournot modelWhat is the Cournot model?Model of industry structure where

DemandThe more producers jointly produce, the lower the market priceExample:

Costs and profitSuppose that the marginal cost is 0.28:Profit of Firms

Discrete choicesSuppose there are just three possible quantities that each firm

Discrete choicesNash Equilibrium

Continuous choicesDiscrete games are not suitable to analyze the decision of

Continuous choicesSimplifying the profit function:

Best responsesWe find the Nash equilibrium by deriving the best response

Best responses

Best responses360720q1q20The more Firm 2 produces, the lower the marketprice, and

360720q1q2Best responsesFirm 2’s best responseThe more Firm 1 produces, the lower

Nash equilibriumNash Equilibrium is where best responses meet.Firm 1’s equilibrium strategy

360720q1q2NE=(240,240)Nash equilibriumEQUILIBRIUMBR1BR2240240

Nash equilibrium360720q1q2 Convergence towards Nash equilibrium: Why are other production levels

Effect of market structureOligopoly delivers an intermediary outcome between twoextreme forms

Effect of market structureCournot with more than 2 producers:

Effect of market structureHaving fewer producers is associated with:Lower total outputHigher