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Chapter 4

# i the expected payo if p1 uses the pure strategy s1

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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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