game theory
DESCRIPTION
Explained with 3 cases.TRANSCRIPT
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)