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

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Econ 100B Lecture 8 - May 8, 2018
MIxed Strategy
ā—Games
ā—‹One period / simultaneous game
ā– 2 players have a dominated strategy
ā—Dominant strategy equilibrium
ā– One player has a dominated strategy while the other one does not
ā—Unique equilibrium
ā– None of the player has a dominated strategy
ā—Multiple nash equilibrium ā†’ mixed strategy nash equilibrium
ā—‹Pure strategy
ā—‹Dynamic games / multiple period games
ā– Sequential games
ā– Repeated games
Mixed strategy
ā—Example; penalty kick in a soccer game that will lead to a win or loss in the game
ā—‹Actions: kick left or kick right and dive left or dive right
ā—‹Players: kicker and goalie
ā—‹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
ā—No nash equilibrium
ā—All the simultaneous move games, players chose a specific strategy that
maximizes his or her payoffs
ā—The strategy are called pure strategy and the equilibrium pure strategy nash
equilibrium
ā—Pure strategy nash equilibrium may not always exist
ā—Each play will randomize across different strategies
ā—‹Sometimes to kick right and sometimes to kick left
ā—The randomization is based on pre decided probability of taking an action
ā—‹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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