oli go poly and game theory

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Game TheoryApplications in

Oligopoly



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Copyright c 2004 by The McGraw-HillCompanies, Inc. All rights reserved.

Chapter 10: Thinking Strategically Slide 2

Imperfect Competition - 2

Monopoly → Oligopoly → Monopolistic Comp.→ Perfect Com

Oligopoly (more efficient than a monopoly)A limited number of firms producing the same product.Duopoly: Two firms producing the same product.

Monopolistic Competition A large number of firms that produce slightlydifferentiated products that are imperfect substitutesfor one another



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Oligopoly and Game Theory

In oligopoly, unlike in monopoly and perfectcompetition, profit maximization decisions shouldtake into account the competitor’s action.

Similarly, competitor will take my action intoaccount in its decision. Hence, I will calculatecompetitor’s action which will be formed based onits calculation of my action.

Such situations are analyzed using Game Theory .



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Example: Should United Airlines spend moreon advertising?The Payoff Matrix for an Advertising Game

Raise adspending

Leave adspendingthe same

Raise adspending


Americangets $5,500

Americangets $2,000

Americangets $8,000 Americangets $6,000

United gets$5,500

United gets$8,000

United gets$6,000

United gets$2,000

American’s Choice

United’s Choice



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Simultaneous Game Model

Assumptions:

1) All information summarized in the

payoff matrix is commonly available toall players.

2) Players act simultaneously (without

knowing each other’s action).



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The Theory of Games

Dominant StrategyOne that yields a higher payoff in at least one case, andno lower payoff.

Dominated Strategy Any other strategy which yields a lower payoff in at leastone case, and no better payoff.

Dominant Strategy Equilibrium: When each playerhas a dominant strategy, equilibrium occurs wheneach player follows that strategy.

Iteratively Dominant Strategy Equilibrium: dominantstrategy equilibrium achieved in several iterations



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Equilibrium When OnePlayer Lacks a Dominant Strategy

Raise adspending


Raise adspending


Americangets $4,000

Americangets $3,000


United gets$3,000

United gets$8,000

United gets$5,000

United gets$4,000

American’s Choice

United’s Choice



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Another example

Raise adspending


Raise adspending


Americangets $2,000

Americangets $3,000


United gets$3,000

United gets$4,000

United gets$3,000

United gets$2,000

American’s Choice

United’s Choice



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The Theory of Games

Nash Equilibrium Any combination of strategies in whicheach player’s strategy is her or his bestchoice, given the other player’s strategies.

A Game may have one single Nashequilibrium, more than 1 Nash equilibria

(multiple equilibria), or no Nash equilibrium(no – solution games).



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Initiating Friendship

keen cold

keen 3, 3 -3, 1cold 1, -3 0, 0



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Another Nash Equilibrium Example

4, 1 0, 2 -1, 32,-2 1, 1 2, 21, 3 3, 0 0, -1



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The Prisoner’s Dilemma

Prisoners ’ Dilemma A game in which each player has adominant strategy, and when each plays it,the resulting payoffs are smaller than ifeach had played a dominated strategy



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Should the prisoners confess?

ConfessRemainsilent

Confess

Remainsilent

Jasper gets5 years

Jasper gets20 years

Jasper gets0 years Jasper gets1 years

Horace gets5 years

Horace gets0 years

Horace gets1 years

Horace gets20 years

Jasper’s Choice

Horace’s Choice



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Which of These GamesIs a Prisoner’s Dilemma?

Don’t Invest

Don’t Invest

Invest

10 forChrysler

12 forChrysler

4 forChrysler 5 forChrysler

10 forGM

4 forGM

5 forGM

12 forGM

Chrysler’s Choice

GM’s Choice

GAME 1

Invest



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Which of These GamesIs a Prisoner’s Dilemma

12 forChrysler

5 forChrysler

10 forChrysler 4 forChrysler

4 forGM

5 forGM

12forGM

10 forGM

Chrysler’s Choice

GM’s Choice

GAME 2

Don’t Invest

Don’t Invest

Invest

Invest



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The “Battle of Sexes”(Coordination Games)

Nancy and Tom try to decide whether they shouldgo to a football game or to the opera

Two Nash-equilibria

Tom

Nancy

Opera FootballOpera 2; 1 0; 0Football 0; 0 1; 2



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Prisoner’s Dilemmas Confronting ImperfectlyCompetitive Firms

Cartel :

A coalition of firms that agrees to restrict outputfor the purpose of earning an economic profit.

Economic NaturalistWhy are cartel agreements notoriously unstable?



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The Market Demandfor Mineral Water

P r i c e

$ / b o t

t l e )

Bottles/day

Assume• 2 firms (A vs. B)• MC = 0• Cartel is formed & agree

to equally split outputand profits

2,000

D

1.00

1,000

MR

2.00

Impact of Cartel• Q = 1,000 bottles/day• P = $1/bottle• Each firm makes $500/day



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The Temptation toViolate a Cartel Agreement

P r i c e

$ / b o t

t l e )

Bottles/day

D

1.00

1,000 2,000

MR

2.00

1,100

0.90

Aquapure lowers P• P = $.90/bottle• Q = 1,100 bottles/day

Mountains Spring retaliates

• P = $.90/bottle• Both firms split 1,100

bottles/day @ $.90• Profit = $495/day

h ff



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The Payoff Matrixfor a Cartel Agreement

Charge $1 Charge $0.90

Charge$1

Charge$0.90

Mountain Spring’s Choice

Aquapure’s Choice

$990/day for

Mountain Spring

$0/day forMountain Spring

$495/day forMountain Spring

$500/day forAquapure

$0/day forAquapure



$500/day for

Mountain Spring



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Cigarette Advertisingas a Prisoner’s Dilemma

Advertise on TV Don’t advertise on TV

Advertiseon TV

Don’t Advertiseon TV

$10 million/yearfor Philip Morris

$5 million/yearfor Philip Morris

$35 million/yearfor Philip Morris $20 million/yearfor Philip Morris

$10 million/year for RJR




Philip Morris’s Choice

RJR’s Choice

y o peop e s an a concer s even



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y o peop e s an a concer s, eventhough they can see just as wellwhen everyone sits?

Stand Sit

Stand

Sit

Other People’s Choice

Your Choice

-2 for others

-2 for you 1 for you

0 for you-3 for you

-3 for others

1 for others 0 for others



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Economic NaturalistWhy do people shout at parties?



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Tit-for- Tat and the Repeated Prisoner’sDilemma

Cooperation between players will increase thepayoff in a prisoner’s dilemma. There is a motive to enforce cooperation.

(Implicit Collusion)

Tit-for-tat strategy for repeated games Players cooperate on the first move, then mimictheir partner’s last move on each successive move

Th S i R l



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The Strategic Roleof Preferences

Game theory assumes that the goal ofthe players is to maximize theiroutcome.

In most games, players do not attain thebest outcomes.

Altering psychological incentives mayalso improve the outcome of a game.



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MONOPOLISTIC COMPETITION

Competitor’s products imperfect substitutes

Therefore, demand curve is downward-sloping

(unlike perfect competition)Free entry and exit (unlike monopoly)

An entry ( exit ) results in a leftward ( rightward )shift of the incumbent’s demand curve.

Long-term economic profits are zero.



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Copyright c 2004 by The McGraw-Hill

Characteristics of monopolistic competition:

Price mark-up

Excess capacity ATC not minimized

P > MC (therefore, Mon.Comp.Firm is keen on

advertising)

oli go poly and game theory

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