Ride the Storm: Navigating Through Unstable Periods / Katerina Rudko (Belka G...
Game theory and its applications
1. M O H A M M A D S A E E D S A F F A R I
A L L A M E H T A B A T A B A E I U N I V E R S I T Y
2 4 D E C , 2 0 1 9
Game Theory and its
Applications
2. Content
Definitions
Prisoner’s Dilemma
Matching Pennies
Battle of Sexes
High-Definition Standards War
Laboratory Experiments
Terrorism
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3. Definitions
Game Theory
Game
Strategy
Pay Off
Rationality
Common knowledge
Equilibrium
Game Theory - Saeed Saffari
Back
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4. Prisoner’s
Dilemma
Two suspects arrested for a crime
Prisoners decide whether to confess or not to
confess
If both confess, both sentenced to 3 years of
jail
If both do not confess, then both will be
sentenced to 2 years of jail
If one confesses and the other does not, then
the confessor sentenced to 1 year of jail and
the non-confessor sentenced to 10 years of jail
What should each prisoner do?
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5. Games
Game Theory - Saeed Saffari
Normal Form representation – Payoff Matrix
Confess Not Confess
Confess -3 , -3 -1 , -10
Not Confess -10 , -1 -2 , -2
Prisoner 1
Prisoner 2
Extensive Form
Dominant Strategy
Back
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6. Matching
Pennies
Game Theory - Saeed Saffari
Normal Form representation – Payoff Matrix
Heads Tails
Heads 1 , -1 -1 , 1
Tails -1 , 1 1 , -1
A
B
Extensive Form
Back
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7. Battle of
Sexes
A couple deciding how to spend the evening
Wife would like to go for a Ballet performance
Husband would like to go for a Boxing match
Both however want to spend the time together
Scope for strategic interaction
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8. Games
Game Theory - Saeed Saffari
Normal Form representation – Payoff Matrix
Ballet Boxing
Ballet 2 , 1 0 , 0
Boxing 0 , 0 1 , 2
Wife
Husband
Extensive Form
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9. Mixed-Strategy
Game Theory - Saeed Saffari
Wife’s best response to Husband’s Mixed strategy:
Ballet Boxing
Ballet 2 , 1 0 , 0
Boxing 0 , 0 1 , 2
Wife
Husband
h 1 - h
w
1 - w
(h)(2) + (1-h)(0)
= 2h
(h)(0) + (1-h)(1)
= 1-h
Best-response function
allowing for mixed
strategies
Python code
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10. The Sequential Battle of Sexes
Game Theory - Saeed Saffari
Always
go to
Ballet
Follow
his wife
Do the
opposite
Always
go to
Boxing
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11. High-Definition
Standards War Toshiba launched its HD-DVD player.
Sony launched its Blu-Ray player.
After that, Sony contracted with Disney and
Toshiba contracted with Paramount.
The outcome of the standards war hinged more on
the strategic behavior of consumers than the firms
involved. (Table)
In 2008, Sony win the War. Why?
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12. Games
Game Theory - Saeed Saffari
Standard Game:
After Bundling Blu-Ray:
Blue-Ray HD-DVD
Blue-Ray 1 , 1 0 , 0
HD-DVD 0 , 0 1 , 1
Consumer A
Consumer B
Back
Blue-Ray HD-DVD
Blue-Ray 2 , 1 1 , 0
HD-DVD 1 , 1 1 , 1
Consumer A
(have a PlayStation 3)
Consumer B
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13. Laboratory
Experiments Prisoner’s Dilemma
Repeat the game
Ultimatum Game
Splitting money with some conditional rules
Dictator Game
Splitting money with no conditional rules
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14. Terrorism
Defending Targets against Terrorism
The Government wants to minimize the expected damage
Terrorism wants to maximize expected damage.
We have two target.(Target 1 has more damage)
Assume terrorist can attack one of two targets.
The Government is protecting Target 1 with (𝑆1) probability.
Terrorism is successful in attack with (1 − 𝑆1) probability.
Bargaining with Terrorists
Game Theory - Saeed Saffari
Target 1 Target 2
Target 1 0 , -10 -5 , 5
Target 2 -10 , 10 0 , -5
Government
Terrorism
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15. Sources
Walter Nicholson, Christopher Snyder. (2014). Intermediate
microeconomics and its application (12th ed.).Chapter 5, Game Theory.
Ghahreman Abdoli. (1395). Game Theory and It’s Application.
H. E. Lapan and T. Sandler, ‘‘To Bargain or not to Bargain: That is the
Question,’’ American Economic Review (May 1988): 16–20.
https://en.wikipedia.org/wiki/Prisoner%27s_dilemma
http://www.econport.org/econport/request?page=man_gametheory_e
xp_prisondil
https://en.wikipedia.org/wiki/Dictator_game
https://en.wikipedia.org/wiki/Ultimatum_game
https://towardsdatascience.com/algorithmic-game-theory-with-
nashpy-a73caf14296b
youtube.com
Farshad Fatemi Online courses.
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