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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
â—ŹGames
â—‹One period / simultaneous game
â– 2 players have a dominated strategy
â—ŹDominant strategy equilibrium
â– One player has a dominated strategy while the other one does not
â—ŹUnique equilibrium
â– None of the player has a dominated strategy
â—ŹMultiple nash equilibrium â†’ mixed strategy nash equilibrium
â—‹Pure strategy
â—‹Dynamic games / multiple period games
â– Sequential games
â– Repeated games
Mixed strategy
â—ŹExample; penalty kick in a soccer game that will lead to a win or loss in the game
â—‹Actions: kick left or kick right and dive left or dive right
â—‹Players: kicker and goalie
â—‹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
â—ŹNo nash equilibrium
â—ŹAll the simultaneous move games, players chose a specific strategy that
maximizes his or her payoffs
â—ŹThe strategy are called pure strategy and the equilibrium pure strategy nash
equilibrium
â—ŹPure strategy nash equilibrium may not always exist
â—ŹEach play will randomize across different strategies
â—‹Sometimes to kick right and sometimes to kick left
â—ŹThe randomization is based on pre decided probability of taking an action
â—‹For example: the kicker formed a strategy that he will kick right 60% of
the time and left remaining 40% of the time