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ECON 100B (100)

CHAKRABORTY, D (10)

Lecture 8

Department

EconomicsCourse Code

ECON 100BProfessor

CHAKRABORTY, DLecture

8This

**preview**shows half of the first page. to view the full**2 pages of the document.**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

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