game theory group4 final

8/3/2019 GAME THEORY Group4 Final

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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

game theory group4 final

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