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Unformatted text preview: payo↵, so an
expected value must be used (remember Stat 200/Econ
106?) I The expected payo↵ if P1 uses the pure strategy s1 and P1
has beliefs ✓ 1 about the strategies of the other players is
given by
X
u 1 ( s1 , ✓ 1 ) =
✓ 1 ( s 1 ) ⇥ u 1 ( s1 , s 1 )
 {z }
 {z }
s I 1 2S 1 probability
that P1
thinks others
play s 1 payo↵ for
P1 if others
do play s 1 Please bear in mind that ‘payo↵ ’ need not mean ‘money.’ It
means ‘utility;’ one can e.g. be altruistic Expected payo↵ u 1 ( s1 , ✓ 1) =
s X 1 2S 1 ✓ 1 ( s 1 ) ⇥ u 1 ( s1 , s 1 )
 {z }
 {z }
probability
that P1
thinks others
play s 1 JW, Fig 4.1
M
R
12L
U 8,1 0,2 4,0
C 3,3 1,2 0,0
D 5,0 2,3 8,1 payo↵ for
P1 if others
do play s 1 Expected payo↵
u 1 ( s1 , ✓ 1) =
s X 1 2S 1 ✓ 1 ( s 1 ) ⇥ u 1 ( s1 , s 1 )
 {z }
 {z }
probability
that P1
thinks others
play s 1 payo↵ for
P1 if others
do p...
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This note was uploaded on 03/27/2014 for the course ECON 402 taught by Professor Krishna,vijayxu,haiqing during the Spring '09 term at Penn State.
 Spring '09
 KRISHNA,VIJAYXU,HAIQING

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