lecture 6 oligopoly

8/12/2019 Lecture 6 Oligopoly

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LECTURE

6 Oligopoly: Gamesand Strategies

This lecture discusses markets with a few firmscharactersied by strategic decision making

After studying this chapter, you will be able to

Define and identify oligopoly

Use game theory to explain how firms behave inoligopoly

Use game theory to explain other strategic decisions


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What Is Oligopoly?

Oligopoly is a market structure in which

there are a small number of firms

These firms can either compete or cooperate with eachother.

Decisions are interdependent .

Natural or legal barriers prevent the entry of new firms.

Small Number of Firms

Because an oligopoly market has only a few firms , theyare interdependent and face a temptation to cooperate .

Interdependence : With a small number of firms, eachfirms profit depends on other firms actions .

Temptation to Cooperate : Firms in oligopoly face thetemptation to form a cartel (a group of firms actingtogether to limit output , raise price , and increase profit ).

What Is Oligopoly?


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Oligopoly Games

Game theory is a tool for studying strategic decisionmaking ;

Each players decision takes into account the expectedbehaviour of others and the mutual recognition ofinterdependence .

The concepts that we are going to discuss today include:

Prisoners Dilemma

StrategiesPayoffsOutcome

The Prisoners Dilemma

In the prisoners dilemma game, two prisoners ( A and B)have been caught committing a petty crime .

Rules

Each prisoner is held in a separate cell and cannotcommunicate with the other.

Each is told that both are suspected of committing amore serious crime ; robbing a bank.

Oligopoly Games


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They are given the following options:

If one of them confesses , he will get a 1-year sentence forcooperating with the police while his accomplice will get a10-year sentence for both crimes.

If both confess to the more serious crime, each receives 3years in jail for both crimes.

If neither confesses , each receives a 2-year sentence forthe minor crime only.

Oligopoly Games

Strategies

A and B each have two possible actions:

1. Confess to the larger crime.2. Deny having committed the larger crime.With two players and two actions for each player (a 2X2 game), there are four possible outcomes:1. Both confess .2. Both deny .3. A confesses and B denies .4. B confesses and A denies .

Oligopoly Games


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Payoffs

We can tabulate the outcomes in the following payoffmatrix .

Oligopoly Games

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny

Outcome: Nash Equilibrium

If both players are rational and act in their self-interest , theoutcome is an equilibrium called Nash equilibrium firstproposed by John Nash.

Oligopoly Games


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Outcome

What should a self-interested A do if B confesses ?

Oligopoly Games

3 Years

10 Years

Bs Strategies

Confess

AsStrategies

Confess

Deny

Outcome

What should a self-interested A do if B confesses ?

Oligopoly Games

3 Years

10 Years

Bs Strategies

Confess

AsStrategies

Confess

Deny


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Outcome

What should a self-interested A do if B denies ?

Oligopoly Games

1 Year

2 Years

Bs Strategies

Deny

AsStrategies

Confess

Deny

Outcome

What should a self-interested A do if B denies ?

Oligopoly Games

1 Year

2 Years

Bs Strategies

Deny

AsStrategies

Confess

Deny


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Outcome

What should a self-interested B do if A confesses ?

Oligopoly Games

Bs Strategies

Confess Deny

AsStrategies

Confess

Outcome

What should a self-interested B do if A confesses ?

Oligopoly Games

Bs Strategies

Confess Deny

AsStrategies

Confess


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Outcome

What should a self-interested B do if A denies ?

Oligopoly Games

Bs Strategies

Confess Deny

AsStrategies

Deny

Outcome

What should a self-interested B do if A denies ?

Oligopoly Games

Bs Strategies

Confess Deny

AsStrategies

Deny


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This is when both A and B simultaneously play their beststrategies

Oligopoly Games

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny

Oligopoly Games

The Dilemma

The Nash equilibrium is not the best possible solution forthe two players.

In fact, both will be better off if they chose deny (thecooperative solution ) rather than confess.

So, it is possible for each player to adopt a strategy that isrational from his or her individual point of view eventhough a different choice would have yielded a betteroutcome .

Can the better outcome be achieved ? No .


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Oligopoly GamesIncentives to Cheat

Let us start from a situation where both players deny (thecooperative solution)

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny


A thinks that if he switches his strategy to Confess (with B still playing Deny ), he will be better off

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny


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Similarly B thinks that if she switches her strategy toConfess (with A still playing Deny ), she will be better off

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny

Incentives to Cheat

When both A and B simultaneously cheat (switch toConfess) they are back at the Nash equilibrium

Oligopoly Games

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny


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A Special Case: Dominant Strategy Solution

A strategy that always gives a player a better payoff irrespective of the strategy chosen by the rival player .

In the prisoners dilemma Confess is the dominant strategy for each player .

On the other hand, Deny is the dominated strategy that willnever be played by either players.

When both players play their dominant strategy we arrive atthe dominant strategy solution which, in this case, is thesame as the earlier Nash equilibrium .

Oligopoly Games

As Dominant Strategy

Since Confess always gives player A a better payoff (3 isbetter than 10 and 1 is better than 2) irrespective of Bsstrategy .

Oligopoly Games

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny


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As Dominant Strategy

. So Confess is the dominant strategy for player A

Oligopoly Games

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny

Bs Dominant Strategy

Since Confess always gives player B a better payoff ( 3 isbetter than 10 and 1 is better than 2) irrespective of Asstrategy .

Oligopoly Games

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny


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Bs Dominant Strategy

. So Confess is the dominant strategy for player B

Oligopoly Games

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny

Dominant Strategy Solution

Since both players only play their dominant strategy so thesolution is Confess-Confess same as the Nashequilibrium

Oligopoly Games

3 Years

10 Years

1 Year

2 Years

Bs Strategies

Confess Deny

AsStrategies

Confess

Deny


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An Oligopoly Price-Fixing Game A game similar to the prisoners dilemma is played induopoly ; A duopoly is a market in which there are onlytwo producers .

Firms A and B can form a cartel by entering into acollusive agreement ; an agreement between two (ormore) firms to restrict output , raise the price , andincrease profits (such agreements are illegal in many

countries) ... .. or the firms can compete with each other byproducing greater output and charging a lesser price .

Oligopoly Games

Strategies

A and B each have two possible actions:

1. High Production .2. Low Production (Restrict output) .With two players and two actions for each player (a 2X2 game), there are four possible outcomes:1. Both with high production .2. Both with low production .3. A with high and B with low production .4. B with high and A with low production .

Oligopoly Games


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The Payoff MatrixIf both have low production , each firm makes $2 million aweek in profits .

If both have high production , each firm makes zero economic profit .

If A has low production and B has high production , A incurs an economic loss of $1 million and B makes an

economic profit of $4.5 million .If B has low production and A has high production , B incurs an economic loss of $1 million and A makes aneconomic profit of $4.5 million .

Oligopoly Games

Payoffs


Oligopoly Games

0

-1

4.5

2

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction

LowProduction


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Outcome

What should a self-interested A do if B has high production ?

Oligopoly Games

0

-1

Bs Strategies

HighProduction

AsStrategies

HighProduction

LowProduction

Oligopoly Games

0

-1

Bs Strategies

HighProduction

AsStrategies

HighProduction

LowProduction

Outcome

What should a self-interested A do if B has high production ?


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Oligopoly Games

4.5

2

Outcome

What should a self-interested A do if B has low production ?

Bs Strategies

LowProduction

AsStrategies

HighProduction

LowProduction

Oligopoly Games

4.5

2

Outcome

What should a self-interested A do if B has low production ?

Bs Strategies

LowProduction

AsStrategies

HighProduction

LowProduction


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Oligopoly GamesOutcome

What should a self-interested B do if A has high production ?

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction


What should a self-interested B do if A has high production ?

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction


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What should a self-interested B do if A has low production ?

Bs Strategies

HighProduction

LowProduction

AsStrategies

LowProduction


What should a self-interested B do if A has low production ?

Bs Strategies

HighProduction

LowProduction

AsStrategies

LowProduction


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This is when both A and B simultaneously play their beststrategies

Oligopoly Games

0

-1

4.5

2

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction

LowProduction

Nash Equilibrium in the Duopolists Dilemma

The Nash equilibrium is that both firms choose highproduction .

The quantity and price are those of a competitivemarket , and firms make zero economic profit .

The dilemma is that both firms can do better if they decideto cooperate with each other and behave like amonopolist .

But individual self-interest prevents them from doing so.

Oligopoly Games


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Collusion and Incentives to Cheat

Suppose we start from a situation where the two firms enterinto a collusive agreement .

As mentioned earlier, such agreements are illegal.

Further, cartels are inherently unstable due to incentives tocheat for each firm involved.

Oligopoly Games

Oligopoly GamesCollusion and Incentives to Cheat

Let us start from a situation where both players choose lowproduction (the cooperative solution)

0

-1

4.5

2

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction

LowProduction


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A thinks that if it switches its strategy to high production (with B still choosing low production ), it will be better off

0

-1

4.5

2

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction

LowProduction


Similarly B thinks that if it switches its strategy to high production (with A still choosing low production ), it will bebetter off

0

-1

4.5

2

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction

LowProduction


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Collusion and Incentives to Cheat

When both A and B simultaneously cheat (switch toHigh Production) they are back at the Nash equilibrium

Oligopoly Games

0

-1

4.5

2

Bs Strategies

HighProduction

LowProduction

AsStrategies

HighProduction

LowProduction

The Advertising Game (prisoners dilemma again .)

Oligopoly Games

15

-10

35

30

Bs Strategies

Advertise Do Not Advertise

AsStrategies

Advertise

Do Not Advertise

Both firms end up advertising. Why?


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An R&D Game (the chicken game)

Two firms have to make a decision regarding whether ornot to spend on research and development .

In absence of patents , both firms have an opportunity tobenefit from the new technology developed by othersspending on R&D (free riding ).

The game has more than one Nash equilibrium .

Suppose that either Apple or Samsung can spend ondeveloping a new touch-screen technology that both would end up being able to use , regardless of which firmdevelops the new technology.

Oligopoly Games

Payoffs


Oligopoly Games

5

10

1

0

Apples Strategies

R&D No R&D

SamsungsStrategies

R&D

No R&D


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Outcome

What should a self-interested Samsung do if Apple spendson R&D ?

Oligopoly Games

5

10

Apples Strategies

R&D

SamsungsStrategies

R&D

No R&D

Outcome

What should a self-interested Samsung do if Apple spendson R&D ?

Oligopoly Games

5

10

Apples Strategies

R&D

SamsungsStrategies

R&D

No R&D


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Outcome

What should a self-interested Samsung do if Apple doesnot spend on R&D ?

Oligopoly Games

1

0

Apples Strategies

No R&D

SamsungsStrategies

R&D

No R&D

Outcome

What should a self-interested Samsung do if Apple doesnot spend on R&D ?

Oligopoly Games

1

0

Apples Strategies

No R&D

SamsungsStrategies

R&D

No R&D


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Outcome

What should a self-interested Apple do if Samsung spendson R&D ?

Oligopoly Games

Apples Strategies

R&D No R&D

SamsungsStrategies

R&D

Outcome

What should a self-interested Apple do if Samsung spendson R&D ?

Oligopoly Games

Apples Strategies

R&D No R&D

SamsungsStrategies

R&D


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Outcome

What should a self-interested Apple do if Samsung doesnot spend on R&D ?

Oligopoly Games

Apples Strategies

R&D No R&D

SamsungsStrategies

No R&D

Outcome

What should a self-interested Apple do if Samsung doesnot spend on R&D ?

Oligopoly Games

Apples Strategies

R&D No R&D

SamsungsStrategies

No R&D


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Outcome: Two Nash Equilibria

The equilibrium suggests that just one firm spends on R&D .But which firm? We do not know in the simultaneous movegame .

Oligopoly Games

5

10

1

0

Apples Strategies

R&D No R&D

SamsungsStrategies

R&D

No R&D

Oligopoly GamesAn R&D Game with sequential moves

Essentially the same game with one firm moving before the other.

Samsung moves before Apple in the following decisiontree , i.e.,

Samsung decides first whether to spend on R&D or not . Apple then makes its decision.

Notice: This game has a first movers advantage ; thefirm that moves first ends up with the higher payoff/profit


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Oligopoly GamesSamsung Moves First

Samsung

Apple

Apple

5

R&D

R&D

No R&D

No R&D

R&D

No R&D

1

10

0

Oligopoly GamesSamsung Moves First: Solving the decision treeWe start solving the tree from extreme right ( Apple s choicesgiven Samsung s strategies)

Samsung

Apple

Apple

5

R&D

R&D

No R&D

No R&D

R&D

No R&D

1

10

0


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Oligopoly GamesSamsung Moves First: Solving the decision treeWe start solving the tree from extreme right ( Apple s choicesgiven Samsung s strategies)

Samsung

Apple

Apple

5

R&D

R&D

No R&D

No R&D

R&D

No R&D

1

10

0

Oligopoly GamesSamsung Moves First: Solving the decision treeWe reduce the tree by eliminating the choices that give Apple a lesser payoff given Samsung s strategies.

Samsung

Apple

Apple

R&D

No R&D

No R&D

R&D

1

10


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Oligopoly GamesSamsung Moves First: Solving the decision treeAfter reducing the tree we solve for Samsung s choices

Samsung

R&D

No R&D

1

10

Oligopoly GamesSamsung Moves First: Solving the decision treeAfter reducing the tree we solve for Samsung s choices

Samsung

R&D

No R&D

1

10


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Oligopoly GamesSamsung Moves First: Solving the decision treeWe reduce the tree by eliminating the choices that giveSamsung a lesser payoff .

Samsung

No R&D 10

Oligopoly GamesSamsung Moves First: The OutcomeSamsung chooses No R&D and Apple responds bychoosing R&D

Samsung

Apple

Apple

5

R&D

R&D

No R&D

No R&D

R&D

No R&D

1

10

0


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Oligopoly GamesApple Moves First

Apple

Samsung

Samsung

5

R&D

R&D

No R&D

No R&D

R&D

No R&D

10

1

0

Oligopoly Games

Apple

Samsung

Samsung

5

R&D

R&D

No R&D

No R&D

R&D

No R&D

10

1

0

Apple Moves First: The Outcome Apple chooses No R&D and Samsung responds bychoosing R&D (Work it out yourself? )


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Repeated Games and Sequential GamesA Repeated Oligopoly Price-Fixing Game

If the game is played repeatedly , it is possible foroligopolists to successfully collude and make a monopolyprofit .

Repeated interaction enables firms to punish others whenthey cheat .

One possible punishment strategy is a tit-for-tat strategy ; afirm cooperates in the current period if the other firmcooperated in the previous period but cheats in the currentperiod if the other cheated in the previous period .

This enables the firms to comply and achieve a cooperativeequilibrium and share the monopoly profit .

lecture 6 oligopoly

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