Description
Game Theory is the mathematical modeling of strategic interaction among rational and irrational agents.
The movies like "The Beautiful Mind" are an exemplary display of the concept.
GAME THEORY
AN 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 individual 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
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Conclusion: • Dominant Firm will always lead. • But what about the Subordinate firm?
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Conclusion: • No dominant strategy for the Subordinate firm. • Does this mean we cannot predict what they will do?
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Conclusion: • Subordinate firm will always follow, because dominant firm will always lead.
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
The numbers at the end of each branch, measured in thousand or millions of dollars, are the payoffs.
L A H B H 6,3 B H 5,4 L 7,5
L
6,4
The Advertising Game in Decision Tree Form
• 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 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 Mudra’s strategies
L H L 7, 5 6, 4 H 5, 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.
Dominant Strategies and Nash Equilibria
• 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.
Waltz’s Strategies
L 7, 5 6, 4 H 5, 4 6, 3
Mudra’s Strategy
L H
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.
Dominant Strategies and Nash Equilibria
• 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.
CASE II: APPLICATION OF GAME THEORY IN TWO TELEVISION CHANNELS
Business Example: Rating War
MTV
TV Drama Music Game Show Program Game Show 35, 65 TV Drama 10, 90 Music Program 60, 40
Channel V
45, 55
55, 45
65, 35
40, 60
10, 90
75, 25
Business Example: Rating War
MTV
TV Drama Music Game Show Program Game Show TV Drama Music Program
35, 65
10, 90
60, 40
Channel V
45, 55
55, 45
65, 35
40, 60
10, 90
75, 25
PRISONER ’S DILEMMA
Prisoner’s Dilemma
• The prisoner's dilemma is a fundamental problem in game theory that demonstrates why two people or groups might not
cooperate even 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.
Case : Terrorism
• 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
• 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.
Case : Terrorism
PROBLEM: Should we send our team to Chiang Mai or Phuket?
Case : Terrorism
The Rival Team
Our Team
Go Chiang Mai
Go Chiang Mai
Go Phuket
(250, 250)
(500, 300)
Go Phuket 500 guests in Chiang Mai hotel / 300 guests in Phuket hotel
(300, 500)
(150, 150)
Case : Terrorism
• 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
The answer is…
Case : Terrorism
• 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
• Knowing what they know, both teams must go to
Chiang Mai.
• To go to Chiang Mai is Dominant strategy, though
not the best strategy.
Case : Terrorism
QUES: What if there are only 200 people in Phuket hotel? ANS: We should always go to Chiang Mai since we will save more lives no matter where the other team is going.
Case : Terrorism
The Rival Team
Our Team
Go Chiang Mai
Go Chiang Mai
Go Phuket
(250, 250)
(500, 200)
Go Phuket 500 guests in Chiang Mai hotel / 200 guests in Phuket hotel
(200, 500)
(100, 100)
Case : Terrorism
• 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
• 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)
doc_507210792.ppt
Game Theory is the mathematical modeling of strategic interaction among rational and irrational agents.
The movies like "The Beautiful Mind" are an exemplary display of the concept.
GAME THEORY
AN 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 individual 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
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Conclusion: • Dominant Firm will always lead. • But what about the Subordinate firm?
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Conclusion: • No dominant strategy for the Subordinate firm. • Does this mean we cannot predict what they will do?
Dominant Firm Game
Dominant
Subordinate
Lead Lead Follow
(0.5, 4)
(3, 2)
Follow
(1, 8)
(0.5, 1)
Dominant Firm Game
Conclusion: • Subordinate firm will always follow, because dominant firm will always lead.
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
The numbers at the end of each branch, measured in thousand or millions of dollars, are the payoffs.
L A H B H 6,3 B H 5,4 L 7,5
L
6,4
The Advertising Game in Decision Tree Form
• 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 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 Mudra’s strategies
L H L 7, 5 6, 4 H 5, 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.
Dominant Strategies and Nash Equilibria
• 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.
Waltz’s Strategies
L 7, 5 6, 4 H 5, 4 6, 3
Mudra’s Strategy
L H
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.
Dominant Strategies and Nash Equilibria
• 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.
CASE II: APPLICATION OF GAME THEORY IN TWO TELEVISION CHANNELS
Business Example: Rating War
MTV
TV Drama Music Game Show Program Game Show 35, 65 TV Drama 10, 90 Music Program 60, 40
Channel V
45, 55
55, 45
65, 35
40, 60
10, 90
75, 25
Business Example: Rating War
MTV
TV Drama Music Game Show Program Game Show TV Drama Music Program
35, 65
10, 90
60, 40
Channel V
45, 55
55, 45
65, 35
40, 60
10, 90
75, 25
PRISONER ’S DILEMMA
Prisoner’s Dilemma
• The prisoner's dilemma is a fundamental problem in game theory that demonstrates why two people or groups might not
cooperate even 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.
Case : Terrorism
• 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
• 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.
Case : Terrorism
PROBLEM: Should we send our team to Chiang Mai or Phuket?
Case : Terrorism
The Rival Team
Our Team
Go Chiang Mai
Go Chiang Mai
Go Phuket
(250, 250)
(500, 300)
Go Phuket 500 guests in Chiang Mai hotel / 300 guests in Phuket hotel
(300, 500)
(150, 150)
Case : Terrorism
• 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
The answer is…
Case : Terrorism
• 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
• Knowing what they know, both teams must go to
Chiang Mai.
• To go to Chiang Mai is Dominant strategy, though
not the best strategy.
Case : Terrorism
QUES: What if there are only 200 people in Phuket hotel? ANS: We should always go to Chiang Mai since we will save more lives no matter where the other team is going.
Case : Terrorism
The Rival Team
Our Team
Go Chiang Mai
Go Chiang Mai
Go Phuket
(250, 250)
(500, 200)
Go Phuket 500 guests in Chiang Mai hotel / 200 guests in Phuket hotel
(200, 500)
(100, 100)
Case : Terrorism
• 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
• 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)
doc_507210792.ppt