lecture 17 game theory

Game Theory

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

If Drug A is used: 200 will be saved If Drug B is used: 1/3 chance that all 600 will be

saved and 2/3 chance that nobody will be saved.

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

If Drug C is used: 400 will die If Drug D is used: 1/3 chance that nobody will

die, and 2/3 chance that 600 will die.

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 each player for every possible profile of strategy choices of all players.

Why Game theory?

Managers make decisions on pricing & output Based on their anticipation or reaction to the decisions

made by their competitors.

The kinked demand model: Explains : Why prices in such markets tend to be very

similar But does not explain : how & why this price is

established in the first place

Game theory – helps in understanding these decisions

Game theory

“How individuals make decisions - when they are aware that their actions effect each other & when each individual takes this into account”

The perquisites: Interdependence

Your decisions effect others & their decisions effect you Uncertainty

You don’t know what decisions will they take nor do they know what decisions will you take

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 or participant 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

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

Kinds of Games:

Cooperative Games: A binding contract that permits them to adopt a strategy to

maximise joint profits.

Non- Cooperative Games:Competing firm take each other actions into account but they

takedecisions independently and adopt strategies.

Dominant Strategy

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

For example:

Two companies A & B

Firms need to promote its sales and profits

Strategy for them is to Advertise or Not Advertise

DOMINANT STRATEGYPay- Off Matrix for Advertising Games

Firm B

Advertise Not Advertise

F

I

r

m A

Advertise

Not Advertise

5

10

0

15

8

6

2

10

Dominant Strategy

Dominant StrategyIn Rs Crores

DOMINANT STRATEGYPay- Off Matrix for Advertising Games

Firm A: Choice of advertising is optimal for it irrespective whatever

decision firm B makes

Firm B: Choice of advertising is optimal for it irrespective whatever

decision firm A makes

Since it is assumed that both firms behave rationally each of them will

choose the strategy of Advertising and the outcome will be profits of Rs

10 cr for firm A and Rs 5 cr for firm B

Absence of Dominant Strategy Pay- Off Matrix for Advertising Games

Firm B

Advertise Not Advertise

F

I

r

m A

Advertise

Not Advertise

5

10

0

15

8

6

2

20

In Rs Crores

Absence of Dominant Strategy

Optimal strategy for Firm A depends on which strategy the firm B adopts.

“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 of strategy if both the firm choose their strategies simultaneously.

Choice of an Optimal strategy in the absence of a Dominant Strategy.

Both the firm must put itself in other firms place and then decide.

If firm A choosers strategy of Advertising the firm B will make profit of 5 cr

Nash’s Equilibrium Nash equilibrium (named after John Forbes Nash) is a

solution concept of a game involving two or more players. Each player is assumed to know the equilibrium strategies

of the other players, and no player has anything to gain by changing only his or her own strategy (i.e., by changing unilaterally).

If each player has chosen a strategy and no player can benefit by changing the strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.

Nash’s Equilibrium

In a Nash equilibrium, each player must respond negatively to the question: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?“

However, Nash equilibrium does not necessarily mean the best cumulative payoff for all the players involved; in many cases all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium (e.g. competing businessmen forming a cartel in order to increase their profits).

In Dominant strategy equilibrium describes an optimal or best choice regardless of what strategy the other player adopts

Whereas

In Nash each player adopts a strategy that is best or optimal for him given the strategy of the other player

Prisoner’s Dilemma

SUSPECT 1

Confess Not Confess

SUSPECT 2

Confess

Not confess

4

4

7

1

1

7

2

2

Dominant Strategy

Dominant Strategy

Prisoner’s Dilemma

In this model the decision of each prisoner in favour of confession is quite rational because each person works in self- interest and tries to make the best of the worst outcome in an uncertain situation.

Prisoners Dilemma can never be resolved if you approach the problem from outside, that is from the other’s viewpoint first.

The problem offers a resolution only if you approach the problem from inside, that is , from your own self.

Prisoner’s 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.

Show Dilbert Video

Game Theory Rules

Choose your strategy by asking what makes most sense for you

In the context of companies

COMPANY 1

Cheat Cooperate

COMPANY 2

Cheat

Cooperate

5

5

2

25

25

2

15

15

Equilibrium State

In Rs Lakhs

In the context of companies

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

Each firm has strong incentive to cheat

It’s the pursuit of self- interest rather than common interest that prompts the firms to cheat each other.

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

Steal v/s Split

Player 1

Split Steal

P

L

A

Y

E

R 2

Split

Steal

50075

50075

100150

0

In $

100150

0 0

0

If it’s a one time game then a the chances of steal are high but a repeated game would make the players split.

Game Theory Rules

You should choose your strategy on the assumption that your opponent will act in his best interest

Repeated Games & Tit- for Tat Strategy

The Games so far are played just once, so they can cheat.

However in case of repeated games the oligopolist may adopt a cooperative behaviour which enables them to earn large profits

In repeated game one firm has the the opportunity to penalise the other for his previous bad behaviour – Tit for TAT Strategy

Nash’s Equilibrium

PEPSI

High Price Low Price

COKE

High Price

Low Price

200

200

150

20

20

150

50

50

Firms will form a cartel and go for high price than cheating on one another