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ECON 100B (100)
Lecture 8

ECON 100B Lecture Notes - Lecture 8: Repeated Game, Simultaneous Game, Nash Equilibrium


Department
Economics
Course Code
ECON 100B
Professor
CHAKRABORTY, D
Lecture
8

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Econ 100B Lecture 8 - May 8, 2018
MIxed Strategy
Games
One period / simultaneous game
2 players have a dominated strategy
Dominant strategy equilibrium
One player has a dominated strategy while the other one does not
Unique equilibrium
None of the player has a dominated strategy
Multiple nash equilibrium → mixed strategy nash equilibrium
Pure strategy
Dynamic games / multiple period games
Sequential games
Repeated games
Mixed strategy
Example; penalty kick in a soccer game that will lead to a win or loss in the game
Actions: kick left or kick right and dive left or dive right
Players: kicker and goalie
Payoffs: 0 if loss and 1 if win
Goalie
Kicker
Dive Left
Dive Right
Kick Left
0,1
1,0
Kick Right
1,0
0,1
No nash equilibrium
All the simultaneous move games, players chose a specific strategy that
maximizes his or her payoffs
The strategy are called pure strategy and the equilibrium pure strategy nash
equilibrium
Pure strategy nash equilibrium may not always exist
Each play will randomize across different strategies
Sometimes to kick right and sometimes to kick left
The randomization is based on pre decided probability of taking an action
For example: the kicker formed a strategy that he will kick right 60% of
the time and left remaining 40% of the time
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