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1
Mixed Strategies
UGBA 143:
Game Theory and Business Decisions
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Overview
So far:
±
Used Nash equilibrium to solve games
±
Strategic outcome in which no player would
unilaterally deviate to choose another strategy
Next:
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What happens when we cannot find a Nash
equilibrium using earlier methods?
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Randomized strategies
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A Simple Game
Alice and Bob
simultaneously show
palmsup or palmsdown
Alice wins if they match
and Bob wins otherwise
(stake is $10)
Each should randomize
5050 between the two
choices
Up
Down
Down
Up
10
10
10
10
10
10
10
10
Alice
Bob
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Pure versus mixed strategies
Pure strategy: choose one strategy for sure
Mixed strategy: randomize among several options
There is no
purestrategy
Nash equilibrium
±
None of the four
purestrategy
action profiles
(U,U), (U,D), (D,U), (D,D) is a NE
Randomizing 5050 by both players is called a
mixedstrategy
Nash equilibrium
±
When both randomize 5050, neither can do
any better by switching his/her own
randomization probabilities
5
Mixed strategies
What if the stakes change?
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 Spring '08
 XuanmingSu
 Game Theory, Alice

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