i the expected payo if p1 uses the pure strategy s1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online