Question
Prove Suppose that the VNM utility function u( )represents . Then the VNM utility function, v( ), represents those same preferences if and only if
Prove
Suppose that the VNM utility function u()represents. Then the VNM utility function, v(), represents those same preferences if and only if for some scalarand some scalar >0,
v(g)=+u(g),
for all gambles g.
this is the the Theorem 2.8, in the text book "Adcanced Microeconomic Theory" by Philip J. Reny, the 3rd edition.
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Economics of Strategy
Authors: David Besanko, David Dranove, Mark Shanley, Scott Schaefer
6th edition
978-1118273630, 111827363X, 978-1118319185
