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OLIGOPOLY IIOLIGOPOLY II
By: GROUP 4By: GROUP 4
Ekta SuriEkta SuriAnirban ChakrabortyAnirban ChakrabortyVishal MohlaVishal Mohla
SumitSumitSwati KarkiSwati Karki
When I am getting ready to reason with a man I spend oneWhen I am getting ready to reason with a man I spend one--third of my timethird of my time
thinking about myself and what I am going to say, and twothinking about myself and what I am going to say, and two--thirds thinkingthirds thinking
about him and what he is going to say.about him and what he is going to say.--Abraham LincolnAbraham Lincoln
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FLOW OF PRESENTATIONFLOW OF PRESENTATION
Oligopoly and Game TheoryOligopoly and Game Theory
What is Game Theory?What is Game Theory?
Payoff MatrixPayoff MatrixNash EquilibriumNash Equilibrium
Strategies employed in Game TheoryStrategies employed in Game Theory
Types Of GamesTypes Of GamesPrisoners DilemmaPrisoners Dilemma
Cournot ModelCournot Model
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Oligopoly and Game TheoryOligopoly and Game Theory
y Oligopoly is a market structure in which the
number of sellers is small.
y Oligopoly requires strategic thinking, unlike
perfect competition, monopoly, and
monopolistic competition.
y The techniques ofgame theory are used to
solve for the equilibrium of an oligopoly
market.
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y Developed in 1950s by mathematicians
John von Neumann and economist Oskar
Morgenstern
y Designed to evaluate situations where
individuals and organizations can have
conflicting objectives
Game TheoryGame Theory
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GAME: Any situation with two or more people requiring
decision making
STRATEGY: A course of action taken by one of the
participants in a game
PAYOFF: Result or outcome of the strategy
A game is a description of strategic interaction that includes the constraints
on the actions that the players can take and the players interests, but does
not specify the actions that players do take
Game theory is about finite choices
Game theory cannot often determine the best possible strategy, but it can
determine whether there exists one
Game theorists may assume players always act in a way to directly
maximize their wins
What is Game Theory?What is Game Theory?
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Objective Increase profits by price change Strategies:1. Maintain prices at the present level2. Increase prices
Above matrix shows the outcomes or payoffs thatresult from each combination of strategies adoptedby the two participants in the game
10,10 100, -30
-20, 30 140, 35
No Price
Change
Price Increase
No Price Change
Price Increase
Firm 2
Firm 1
Payoff MatrixPayoff Matrix
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Defined as a set of strategies such that noneof the participants in the game can improvetheir payoff, given the strategies of the otherparticipants.
Identify equilibrium conditions where therates of output allowed the firms tomaximize profits and hence no need tochange.
No price change is an equilibrium becauseneither firm can benefit by increasing itsprices if the other firm does not
NASH EQUILIBRIUMNASH EQUILIBRIUM
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Limitations of Nash EquilibriumLimitations of Nash Equilibrium
y For some games, there may be no Nash
equilibrium; continuously switch from one
strategy to another
y There can be more than one equilibrium
10,10 100, -30
-20, 30 140, 25
Firm 2
Firm1
No Price
ChangeNo Price
Change
Price
Increase
Price
Increase
Both firms increasing their price is also a Nash
equilibrium
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STRATEGIES EMPLOYED IN GAMESTRATEGIES EMPLOYED IN GAME
THEORYTHEORY
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y One firms best strategy may not dependon the choice made by the otherparticipants in the game
y Leads to Nash equilibrium because theplayer will use the dominant strategy andthe other will respond with its best
alternative
y Firm 2s dominant strategy is not to change
price regardless of whatFirm 1 does
Dominant StrategiesDominant Strategies
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Dominated StrategiesDominated Strategies
y An alternative that yields a lower payoff thansome other strategies
y
a strategy is dominated if it is always better toplay some other strategy, regardless of whatopponents may do
y
It simplifies the game because they are optionsavailable to players which may be safelydiscarded as a result of being strictly inferior toother options.
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Continued.Continued.
y A strategy s in set S is strictly dominatedfor
player i if there exists another strategy, s
in S such that,i(s) > i(s)
y In this case, we say that s strictly dominatess
y In the previous example for Firm 2 no pricechange is a dominant strategy and pricechange is a dominated strategy
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MaximinMaximin StrategiesStrategies
y Highly competitive situations (oligopoly)
y Risk-averse strategy worst possible
outcome is as beneficial as possible,
regardless of other players
y Select option that maximizes the
minimum possible profit
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Each firm first determines the minimum profitthat could result from each strategy
Second, selects the maximum of the minimums Hence, neither firm should introduce a new
product because guaranteed a profit of at least$3 million
Maximin outcome not Nash equilibrium- lossavoidance rather than profit maximization
4, 4 3, 6
6, 3 2, 2Firm 1
Firm 2
Firm 2 Minimum
Firm 1 MinimumNew
Product
No New
Product
No New Product
New Product
3
2
23
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Mixed StrategiesMixed Strategies
y Pure strategy Each participant selects
one course of action
y Mixed strategy requires randomly mixing
different alternatives
y Every finite game will have at least one
equilibrium
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Types of GamesTypes of Games
y Non cooperative games
y Cooperative games
y Repeated games
y Sequential games
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Not possible to negotiate with other participants
Because the two participants are interrogated separately,
they have no idea whether the other person will confess
or not
Non CoNon Co--operative Gamesoperative Games(Prisoners Dilemma)(Prisoners Dilemma)
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The Prisoners DilemmaThe Prisoners Dilemma
The prisoner's dilemma is a fundamental
problem in game theory
A simple game that has become the dominant
paradigm for social scientists since it was invented
about 1960
How the game works -- a simple narrative.
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Modeling PD gamesModeling PD games
PD addresses the decision making of two
prisoners
Prisoners aim is to minimize the years of
imprisonment
Decide individually to confess or deny the
crime but depend upon the possible
decisions of the other prisonerEach one chooses his dominant strategy
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Which are the dominant strategies in this game?Which are the dominant strategies in this game?
From the point of view ofprisoner A
y If B confesses, I should also
confess (5 years are less than
20 years)
y If B denies, I should again
confess (0 year is less than 1
years)
Strategy of A:
y I confess irrespective of thedecision of B
y "Confess" is the dominant
strategy of A (5 years
imprisonment).
From the point of view ofprisoner B
If A confesses, I should also
confess (5 years are less than
20 years)
If B denies, I should again
confess (0 year is less than 1
years)
Strategy of B:
"Confess" is his dominantstrategy, too (5 years
imprisonment).
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y Possibility of negotiations between
participants for a particular strategy
y If prisoners jointly decide on not
confessing, they would avoid spending any
time in jail
y Such games are a way to avoid prisoners
dilemma
CoCo--Operative GamesOperative Games
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DILEMMA MODELDILEMMA MODEL APPLIEDAPPLIED
TO OLIGOPOLYTO OLIGOPOLY
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Contd..Contd..
y FIRM A's PAYOFF IS HIGHER IF IT ADVERTISESREGARDLESS OFTHE STRATEGY USED BY FIRM B
y IFFIRM B CHOOSES TO ADVERTISE, FIRM A WOULD BE
BETTER OFF, BY 70 TO 40, IFFIRM A ADVERTISES
y FIRM B CHOOSES NOT TOADVERTISE, FIRM A WOULD BE BETTER OFF, BY 100 TO80, IFFIRM A ADVERTISES
y EITHER WAY, FIRM A WOULD BE BETTER OFF IF ITCHOOSES TO ADVERTISE
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Contd..Contd..
y IF EACH FIRM IN THIS EXAMPLE CHOOSES ITS DOMINANTSTRATEGY, EACH WILL CHOOSE TO ADVERTISE. FIRM A WILLEARN A PAYOFF OF 70, ANDFIRM B WILL EARN A PAYOFF OF80
y
IF
C
OOPERATION WERE POSSIBLE: EAC
H WOULD
BE BETTEROFF BY CHOOSING THE OPPOSITE STRATEGY, WHICH IS NOTTO ADVERTISE
y FIRM A WOULD EARN A PAYOFF OF 80, ANDFIRM B WOULDEARN A PAYOFF OF 90.
ONE STRATEGY BASED ON COMPETITION. THE OPPOSITESTRATEGY BASED ON COOPERATION.
y THAT IS THE PRISONER'S DILEMMA.
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Repeated GamesRepeated Games Yet another way to escape prisoners dilemma
If exercise is repeated multiple times,reactions become predictable
According to eg in PD, both firms select highadvertising & capture max. profit
But, if this exercise is repeated, outcomes maychange
Advantage becomes temporary
Winning strategy- tit for tat
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Sequential GamesSequential Games
y One player acts first & then the other
responds
y 2 firms contemplating the introduction of anidentical product in the market
y 1st firm- develop brand loyalties, associateproduct with the firm in minds of consumers
y
Thus, first mover advantage
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An example for sequential gamesAn example for sequential games
Firm 2
No new product
Introduce new
product
Firm 1
No new product $2, $2 $-5, $10
Introduce new
product$10, $-5 $-7, $-7
Assume firms use maximum criterion, so neithershould introduce a new product and earn $2 mn each
Firm 1 introduces a new product, firm 2 will still decideto stay out because right now it is losing $5 mn,opposed to $7 mn otherwise.
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Cournot Model of OligopolyCournot Model of Oligopoly
Assumptions:
y Only two firms
y They compete on basis of price.
y Market demand curve is linear.
y Marginal costs are constant.
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y
We determine how eachfirm reacts to a change inthe output of the otherfirm.
y A point is reached where
neither firm desires tochange what it is doing.
y The equilibrium is theintersection of the twofirms reaction functions.
y The reaction functionshows how one firmreacts to the quantitychoice of the other firm.
As
Output
Bs
Output
As
Reaction
Function
Bs
Reaction
Function
45
45
90
90
Cournot Model of OligopolyCournot Model of Oligopoly
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y The firm 1s demand function is
P = (M - Q2) - Q1Assume M=60 is the market
marginal cost is CM=12
y By following the profit maximization rule ofequating marginal revenue to marginal costs
y Firm 1s total revenue function is
RT = Q1 P = Q1(M - Q2 - Q1)= M Q1- Q1 Q2 - Q1
2
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RM= M-Q2-2Q1
RM =C
MM - Q2 - 2Q1= CM
2Q1 = (M-CM) - Q2Q
1
= (M-CM
)/2 - Q2
/2
= 24 - Q2/2(1)
Similarly,
Q2 = 2(M-CM) - 2Q2 = 96 - 2
Q1..(2)To determine the equilibrium you can solve
the equations simultaneously