Game theory and some examples like Prisoner's Dilemma, Matching Pennies, Battle of Sexes, High Definition Standards War, and Laboratory Experiments.

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
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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
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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
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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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16. ANY QUESTION..?
THANK YOU
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