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Game TheoryApplications in
Oligopoly
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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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Chapter 10: Thinking Strategically Slide 3
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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Chapter 10: Thinking Strategically Slide 5
Example: Should United Airlines spend moreon advertising?The Payoff Matrix for an Advertising Game
Raise adspending
Leave adspendingthe same
Raise adspending
Leave adspendingthe same
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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Chapter 10: Thinking Strategically Slide 6
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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Chapter 10: Thinking Strategically Slide 7
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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Chapter 10: Thinking Strategically Slide 8
Equilibrium When OnePlayer Lacks a Dominant Strategy
Raise adspending
Leave adspendingthe same
Raise adspending
Leave adspendingthe same
Americangets $4,000
Americangets $3,000
Americangets $5,000 Americangets $2,000
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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Chapter 10: Thinking Strategically Slide 9
Another example
Raise adspending
Leave adspendingthe same
Raise adspending
Leave adspendingthe same
Americangets $2,000
Americangets $3,000
Americangets $3,000 Americangets $4,000
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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Chapter 10: Thinking Strategically Slide 10
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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Chapter 10: Thinking Strategically Slide 13
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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Chapter 10: Thinking Strategically Slide 14
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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Chapter 10: Thinking Strategically Slide 15
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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Chapter 10: Thinking Strategically Slide 16
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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Chapter 10: Thinking Strategically Slide 17
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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Chapter 10: Thinking Strategically Slide 18
The Prisoner’s Dilemma
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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Chapter 10: Thinking Strategically Slide 19
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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Chapter 10: Thinking Strategically Slide 20
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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Chapter 10: Thinking Strategically Slide 21
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
$495/day forAquapure
$990/day forAquapure
$500/day for
Mountain Spring
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Chapter 10: Thinking Strategically Slide 22
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
$35 million/year for RJR
$20 million/year for RJR
$5 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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Chapter 10: Thinking Strategically Slide 23
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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Chapter 10: Thinking Strategically Slide 24
The Prisoner’s Dilemma
Economic NaturalistWhy do people shout at parties?
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Chapter 10: Thinking Strategically Slide 25
The Prisoner’s Dilemma
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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Chapter 10: Thinking Strategically Slide 26
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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Characteristics of monopolistic competition:
Price mark-up
Excess capacity ATC not minimized
P > MC (therefore, Mon.Comp.Firm is keen on
advertising)
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