Lecture 17 - Game Theory ppt

8/13/2019 Lecture 17 - Game Theory ppt

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The bird flu epidemic is expected to hit yourtown and it is estimated that 600 people will die.Which of following two drugs, A or B will yourecommend to combat the epidemic given thefollowing information?

If Drug A is used: 200 will be savedIf Drug B is used: 1/3 chance that all 600 will besaved and 2/3 chance that nobody will be saved.


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The bird flu epidemic is expected to hit yourtown and it is estimated that 600 people will die.Which of following two drugs, C or D will yourecommend to combat the epidemic given thefollowing information?

If Drug C is used: 400 will dieIf Drug D is used: 1/3 chance that nobody willdie, and 2/3 chance that 600 will die.


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Three Elements of a Game

1)The players

how many players are there?does nature/chance play a role?

2) A complete description of the strategies of each player

3) A description of the consequences (payoffs) for eachplayer for every possible profile of strategy choices of allplayers.


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Why Game theory?

Managers make decisions on pricing & outputBased on their anticipation or reaction to the decisionsmade by their competitors.

The kinked demand model:Explains : Why prices in such markets tend to be verysimilarBut does not explain : how & why this price isestablished in the first place

Gam e theory he lps in und ers tand ing these dec is ions


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Game theory

How individuals make decisions - when they are aware thattheir actions effect each other & when each individual takesthis into account

The perquisites:Interdependence

Your decisions effect others & their decisions effect youUncertainty

You dont know what decisions will they take nor dothey know what decisions will you take


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In Oilgopolistic market situationThe problem is to choose a rational course of action Strategy.

A Strategy is a course of action or policy which player orparticipant in a game will adopt during the play of the game.

The various alternative strategies are:1) Changing the price2) Changing the level of output3) Increasing advertisement expenditure4) Varying the product

STRATEGY


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A firm behaves strategically, that is while taking its decision regardingprice, output, advertising it takes into account how its rivals firms willreact assuming them to be rational i.e they will do there best to promotetheir interest while making decisions.

Kinds of Games:

Cooperative Games: A binding contract that permits them to adopt a strategy tomaximise joint profits .

Non- Cooperative Games:Competing firm take each other actions into account but they takedecisions independently and adopt strategies.


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Dominant Strategy

A Strategy which will be successful or optimal for a firmregardless of what others do, i.e no matter what the strategy therival firm adopts.

For example:Two companies A & BFirms need to promote its sales and profitsStrategy for them is to Advertise or Not Advertise


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DOMINANT STRATEGYPay- Off Matrix for Advertising Games

Firm B

Advertise Not Advertise

FIr

mA

Advertise

Not Advertise

5

10

0

15

8

6

2

10

DominantStrategy

Dominant StrategyIn Rs Crores


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DOMINANT STRATEGYPay- Off Matrix for Advertising Games

Firm A: Choice of advertising is optimal for it irrespective whateverdecision firm B makes

Firm B: Choice of advertising is optimal for it irrespective whateverdecision firm A makes

Since it is assumed that both firms behave rationally each of them willchoose the strategy of Advertising and the outcome will be profits of Rs10 cr for firm A and Rs 5 cr for firm B


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Absence of Dominant Strategy

Pay- Off Matrix for Advertising Games

Firm B

Advertise Not Advertise

FIr

m A

Advertise

Not Advertise

5

10

0

15

8

6

2

20

In Rs Crores


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Absence of Dominant Strategy

Optimal strategy for Firm A depends on which strategy the firm Badopts.

Advertising strategy is optimal for firm A, given that firm B adopts the

same.Non- Advertising by firm A is better given that firm B adopts the same.

Thus there is no Dominant strategy existing

But how does firm make an optimal decision regarding choice ofstrategy if both the firm choose their strategies simultaneously.


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Nashs Equilibrium Nash equilibrium (named after John Forbes Nash) is asolution concept of a game involving two or more players.

Each player is assumed to know the equilibrium strategiesof the other players, and no player has anything to gain bychanging only his or her own strategy (i.e., by changingunilaterally).

If each player has chosen a strategy and no player canbenefit by changing the strategy while the other playerskeep theirs unchanged, then the current set of strategychoices and the corresponding payoffs constitute a Nashequilibrium.


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Nashs Equilibrium

In a Nash equilibrium, each player must respondnegatively to the question: "Knowing the strategies of theother players, and treating the strategies of the otherplayers as set in stone, can I benefit by changing mystrategy?

However, Nash equilibrium does not necessarily mean thebest cumulative payoff for all the players involved; in manycases all the players might improve their payoffs if theycould somehow agree on strategies different from theNash equilibrium (e.g. competing businessmen forming a

cartel in order to increase their profits).


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Prisoners Dilemma

SUSPECT 1

Confess Not ConfessSUS

PECT2

Confess

Notconfess

4

4

7

1

1

7

2

2

DominantStrategy

Dominant Strategy


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Prisoners Dilemma

In this model the decision of each prisoner in favour ofconfession is quite rational because each person worksin self- interest and tries to make the best of the worstoutcome in an uncertain situation.

Prisoners Dilemma can never be resolved if youapproach the problem from outside, that is from theothers viewpoint first .The problem offers a resolution only if you approach theproblem from inside, that is , from your own self .


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Prisoners Dilemma

The only way to resolve the dilemma is to ask,Whats the right course of action that could be

best for BOTH .

If you look inward, no matter how selfish you are,

you will find the correct resolution to the dilemma.


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Show Dilbert Video


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Game Theory Rules

Choose your strategy by asking whatmakes most sense for you


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In the context of companies

COMPANY 1Cheat Cooperate

COMPANY2

Cheat

Cooperate

5

5

2

25

25

2

15

15

Equilibrium State

In Rs Lakhs


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In the context of companies

If both the firm cooperate and abide by cartel they sharehuge amount of profits.

Each firm has strong incentive to cheat

Its the pursuit of self - interest rather than commoninterest that prompts the firms to cheat each other.

Thus if both the firm cheat they will break down thecartel.


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Steal v/s SplitPlayer 1

Split StealP

L AYER2

Split

Steal

5007550075

100150

0

In $

100150

0 0

0

If its a one time game then a the chances of steal are high but arepeated game would make the players split.


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Repeated Games & Tit- for Tat

StrategyThe Games so far are played just once, so they cancheat.

However in case of repeated games the oligopolist mayadopt a cooperative behaviour which enables them toearn large profits

In repeated game one firm has the the opportunity topenalise the other for his previous bad behaviour Titfor TAT Strategy


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Lecture 17 - Game Theory ppt

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