GAME THEORYAN APPLICATION

Game Theory

A theory that attempts to mathematically

capture behavior in strategic situations or

games, in which an individual's success in

making choices depends on the choices of

others.

Game Theory – An Introduction

• Firstly presented by the legendary mathematician

“John Von Neumann”.

• Attempt to analyze competitions in which one indiv

idual does better at another’s expense (zero sum

games).

• Later developed by “John Nash”, the Nobel Prize

winner and a professor at Princeton University.

DOMINANT FIRM GAME

Dominant Firm Game

• Two firms, one large and one small.

• Either firm can announce an output level

(lead) or else wait to see what the rival does

and then produce an amount that does not

saturate the market.

Dominant Firm Game

Lead Follow

Dominant

Subordinate

Lead

Follow

(0.5, 4)

(1, 8)

(3, 2)

(0.5, 1)

Dominant Firm Game

Lead Follow

Dominant

Subordinate

Lead

Follow

(0.5, 4)

(1, 8)

(3, 2)

(0.5, 1)

Dominant Firm Game

Lead Follow

Dominant

Subordinate

Lead

Follow

(0.5, 4)

(1, 8)

(3, 2)

(0.5, 1)

Conclusion:

• Dominant Firm will always lead.

• But what about the Subordinate firm?

Dominant Firm Game

Dominant Firm Game

Lead Follow

Dominant

Subordinate

Lead

Follow

(0.5, 4)

(1, 8)

(3, 2)

(0.5, 1)

Dominant Firm Game

Lead Follow

Dominant

Subordinate

Lead

Follow

(0.5, 4)

(1, 8)

(3, 2)

(0.5, 1)

Conclusion:

• No dominant strategy for the Subordinate

firm.

• Does this mean we cannot predict what

they will do?

Dominant Firm Game

Dominant Firm Game

Lead Follow

Dominant

Subordinate

Lead

Follow

(0.5, 4)

(1, 8)

(3, 2)

(0.5, 1)

Conclusion:

• Subordinate firm will always follow,

because dominant firm will always lead.

Dominant Firm Game

NASH EQUILIBRIUM

Nash Equilibrium

• A solution concept of a game involving two

or more players .

• If each player has chosen a strategy and no

player can benefit by changing his or her

strategy while the other players keep theirs

unchanged, then the current set of strategy

choices constitute a Nash equilibrium.

CASE I: APPLICATION OF GAME THEORY IN TWO ADVERTISING AGENCIES

Advertising Agencies

• Two firms, Mudra Communication Pvt. Ltd and

Waltz Entertainment Pvt. Ltd must decide how

much to spend on advertising.

• Each firm may adopt either a high (H) budget or

a low (L) budget.

An Advertising Game

• Mudra makes the first move by choosing

either H or L at the first decision “node.”

• Next, Waltz chooses either H or L, but the

large oval surrounding Waltz’s two decision

nodes indicates that Waltz does not know

what choice Mudra made.

The Advertising Game in Decision Tree Form

7,5

L

LH

L

H

HB

B

A

5,4

6,4

6,3

The numbers at the end of each branch,

measured in thousand or millions of

dollars, are the payoffs.

• The numbers at the end of each branch,

measured in thousand or millions of

dollars, are the payoffs.

– For example, if Mudra chooses H and

Waltz chooses L, profits will be 6 for

firm Mudra and 4 for firm Waltz.

The Advertising Game in Decision Tree Form

The Advertising Game in Decision Tree Form

• The game in normal (tabular) form is where Mudra’s

strategies are the rows and Waltz’s strategies

are the columns.

• For example, if Mudra chooses H and Waltz chooses

L, profits will be 6 for firm Mudra and 4 for firm Waltz.

Waltz’s Strategies L H

Mudra’s strategies

L 7, 5 5, 4 H 6, 4 6, 3

Dominant Strategies and Nash Equilibria

• A dominant strategy is optimal regardless

of the strategy adopted by an opponent.

• The dominant strategy for Waltz is L since

this yields a larger payoff regardless of

Mudra’s Choice.

• If Mudra chooses H, Waltz’s choice of L yields

5, one better than if the choice of H was made.

• If Mudra chooses L, Waltz’s choice of L yields 4

which is also one better than the choice of H.

Dominant Strategies and Nash Equilibria

Waltz’s Strategies

L H

Mudra’s Strategy

L 7, 5 5, 4 H 6, 4 6, 3

Dominant Strategies and Nash Equilibria

• Mudra will recognize that Waltz has a dominant

strategy and choose the strategy which will

yield the highest payoff, given Waltz’s choice of L.

- Mudra will also choose L since the payoff of

7 is one better than the payoff from

choosing H.

• The strategy choice will be (Mudra: L, Waltz: L) with

payoffs of 7 to A and 5 to B.

• Since Mudra knows Waltz will play L,

Mudra’s best play is also L.

• If Waltz knows Mudra will play L, Waltz’s

best play is also L.

• Thus, the (Mudra: L, Waltz: L) strategy is a

Nash equilibrium: it meets the symmetry

required of the Nash criterion.

• No other strategy is a Nash equilibrium.

Dominant Strategies and Nash Equilibria

CASE II: APPLICATION OF GAME THEORY IN TWO TELEVISION CHANNELS

Business Example: Rating War

35, 65 10, 90 60, 40

45, 55 55, 45 65, 35

75, 2510, 9040, 60

MTV

Ch

ann

el V

Game Show TV Drama Music Program

Ga

me

Sh

ow

TV

Dra

ma

Mu

sic

Pro

gra

m

Business Example: Rating War

35, 65 10, 90 60, 40

45, 55 55, 45 65, 35

75, 2510, 9040, 60

MTV

Ch

ann

el V

Game Show TV Drama Music Program

Ga

me

Sh

ow

TV

Dra

ma

Mu

sic

Pro

gra

m

PRISONER ’S DILEMMA

Prisoner’s Dilemma

• The prisoner's dilemma is a fundamental pro

blem in game theory that demonstrates why

two people or groups might not cooperate e

ven if it is in both their best interests to do so

.

CASE III: TERRORISM

Case : Terrorism

• There is terrorism in Thailand. Two hotel buildings

were set on fire. One in Chiang Mai and the other one

in Phuket.

• There are 500 guests stuck in Chiang Mai hotel and

300 guests in Phuket hotel.

• It is the responsibility of the chief of the Rescue Team

stationed in Bangkok to send staff on the site(s) to

save lives.

• Unfortunately, the team has only one

helicopter.

• Since the 2 hotels are too far apart, we have

to select only one mission: to rescue people

in Chiang Mai OR in Phuket.

• However, there is the other Rescue Team

who is our arch rival. It also owns only one

helicopter as well.

Case : Terrorism

Case : Terrorism

• Now the leader of the other team has to make the

same decision as we do.

• We want to save as many lives as possible and they

want to do the same.

• Since both the parties hate each other so they two

cannot communicate.

PROBLEM:

Should we send our team to Chiang Mai

or Phuket?

Case : Terrorism

Case : Terrorism

Go Chiang Mai Go Phuket

The Rival Team

Our Team

Go Chiang Mai

Go Phuket

(250, 250)

(300, 500)

(500, 300)

(150, 150)

500 guests in Chiang Mai

hotel / 300 guests in

Phuket hotel

• Scenario I: Both teams go to Chiang Mai.

Each team rescues 250 people.

• Scenario II: Our team goes to Chiang Mai,

our rival goes to Phuket. We rescue 500,

they rescue 300.

Case : Terrorism

• Scenario III: Our team goes to Phuket, our

rival goes to Chiang Mai. We rescue 300,

they rescue 500.

• Scenario IV: Both the teams go to Phuket

and rescue 150 per team.

Case : Terrorism

Case : Terrorism

The answer is…

• Wherever our rival goes, we should go to

the other place to save most lives possible.

• However, we cannot know their decision

and they cannot know ours either.

• There is NO best strategy for both sides

because each team can never know where

the other team is going.

Case : Terrorism

Case : Terrorism

• Knowing what they know, both teams must go to

Chiang Mai.

• To go to Chiang Mai is Dominant strategy, though

not the best strategy.

QUES: What if there are only 200 people in

Phuket hotel?

Case : Terrorism

ANS: We should always go to Chiang Mai since

we will save more lives no matter

where the other team is going.

Case : Terrorism

Go Chiang Mai Go Phuket

The Rival Team

Our Team

Go Chiang Mai

Go Phuket

(250, 250)

(200, 500)

(500, 200)

(100, 100)

500 guests in Chiang

Mai hotel / 200 guests

in Phuket hotel

• If there are only 200 people in Phuket Hotel.

Then, to go to Chiang Mai is our “Dominant

Strategy”. It is also the best strategy

possible.

• “Dominant Strategy” only exists in some

situations.

Case : Terrorism

Case : Terrorism

• Dominant Strategy is the rational move that a

player will make no matter what the other

side’s decision is.

• Sometimes Dominant Strategy is the best strategy

in a situation, sometimes it is not.

• Anyway, a player will always use Dominant

Strategy as his choice.

CONCLUSION

• Mimics most real-life situations well.

• Solving may not be efficient.

• Applications are in almost all fields.

• Big assumption: players being rational.

– Can you think of “irrational” game theory?

A PRESENTATION BY:Amritanshu Mehra (11DCP008)

Kush Aggarwal (11DCP024)Ravi Gupta (11DCP038)