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9/18/2008
1
MAXIMIN
≤
MINIMAX
±
9 soldiers, three are 5 feet tall, three are 6
feet tall, three are 7 feet tall
567
Min = 5
±
MAXIMIN = 5 < 7 = MINIMAX
7
5
6
675
Min = 5
Min = 5
Max = 7 Max = 7 Max = 7
A Note About Equilibria
±
Some games –
±
Get feel for what an equilibrium might be
±
Show that if everyone does it, nobody has an
incentive to change
±
Show everything else isn’t equilibrium: for
each other possible strategy profile, somebody
has an incentive to change
±
Others games – when you’re clueless
±
Calculate best responses
±
Equilibria occur where best responses cross
Continuous Strategy Sets
±
Our examples have involved discrete action
sets with a small number of possible actions
±
Even chess and go are discrete
±
We now consider strategy sets that are
We now consider strategy sets that are
continuous:
±
Why?
±
So we can use CALCULUS
±
Players 1 & 2 take actions
0
3
e
π
Finding Nash Equilibria
±
In general, NE occur where “best
response curves” cross
Finding Nash Equilibria
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 Spring '07
 Emre

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