game theory: an intoduction
TRANSCRIPT
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GAME THEORYAN INTRODUCTION
Njdeh Tahmasian Savarani
Winter 2014
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History
Interdisciplinary (Economic and Mathematic)
approach to the study of human behavior
Founded in the 1920s by John von Neumann
1994 Nobel prize in Economics awarded to
three researchers
“Games” are a metaphor for wide range of
human interactions
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Applications
Market:
pricing of a new product when other firms have similar new
products
deciding how to bid in an auction
Networking:
choosing a route on the Internet or through a transportation
networks
Politic:
Deciding whether to adopt an aggressive or a passive stance in
international relations
Sport:
choosing how to target a soccer penalty kick and choosing how
to defend against
Choosing whether to use performance-enhancing drugs in a
professional sport
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What is a (Mathematical) Game?
Rules
Outcomes and payoffs
Uncertainty of the Outcome
Decision making
No cheating
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Classification of Games
Number of players
Simultaneous or sequential game
Random moves
Perfect information
Complete information
Zero-sum games
Communication
Cooperative or non-cooperative game
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Two Players Games
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Two Players, Zero-sum
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Three or More Players
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The Prisoner’s Dilemma
Two burglars, Jack and Tom, are captured
and separated by the police
Each has to choose whether or not to confess
and implicate the other
If neither confesses, they both serve one
year for carrying a concealed weapon
If each confesses and implicates the other,
they both get 4 years
If one confesses and the other does not, the
confessor goes free, and the other gets 8
years
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Prisoners dilemma
Introduction
Tom
Not
Confess
Confess
Jack
Not
Confess-1, -1 -8, 0
Confess 0, -8 -4, -4
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Jack’s Decision Tree
If Tom Does Not ConfessIf Tom Confesses
Jack
4 Years in Prison
8 Years in Prison
Free1 Years in
Prison
Jack
Not ConfessConfess Confess Not Confess
Best
StrategyBest
Strategy
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Dominant strategy
A players has a dominant strategy if that
player's best strategy does not depend on
what other players do.
P1(S,T) >= P1 (S’, T)
Strict Dominant strategy
P1(S,T) > P1 (S’, T)
Games with dominant strategies are easy to
play
No need for “what if …” thinking
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Prisoner's Dilemma
Strategies must be undertaken without the
full knowledge of what other players will do.
Players adopt dominant strategies
BUT they don't necessarily lead to the best
outcome.
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Nash Equilibrium
A Nash equilibrium is a situation in which
none of them have dominant Strategy and
each player makes his or her best response
(S, T) is Nash equilibrium if S is the best strategy to
T and T is the best strategy to S
John Nash shared the 1994 Nobel prize in
Economic for developing this idea!
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Coordination Game
Your Partner
Power
Point
Keynote
You
Power
Point1, 1 0, 0
Keynot
e0, 0 1, 1
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Other samples of Coordination Game
Using Metric units of measurement of English
Units
Two people trying to find each other in a
crowded mall with two entrance
…
These games has more than one Nash
Equilibrium
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Unbalanced Coordination Game
Your Partner
Power
Point
Keynote
You
Power
Point1, 1 0, 0
Keynot
e0, 0 2, 2
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Battle of the Sexes
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Mixed Strategies- Matching Pennies
Zero-sum GamePlayer 2
Head Tail
Player 1
Head -1, +1 +1, -1
Tail +1, -1 -1, +1
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Three or More Players
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References