Rubinstein2005-page112

Rubinstein2005-page112 - October 21, 2005 12:18 94 master...

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October 21, 2005 12:18 master Sheet number 110 Page number 94 94 Lecture Eight Furthermore, assume that W ( p ) = 6 z p ( z ) w ( z ) represents the pref- erences % as well. We will show that w must be a positive af±ne transformation of v . To see this, let α> 0 and β satisfy w ( M ) = α v ( M ) + β and w ( m ) = α v ( m ) + β (the existence of 0 and β is guaranteed by v ( M )> v ( m ) and w ( M w ( m ) ). For any z Z we have [ z ]∼ v ( z ) M ( 1 v ( z )) m ,so it must be that w ( z ) = v ( z ) w ( M ) + ( 1 v ( z )) w ( m ) = v ( z ) [ α v ( M ) + β ]+ ( 1 v ( z )) [ α v ( m ) + β ]= α v ( z ) + β. The Dutch Book Argument There are those who consider expected utility maximization to be a normative principle. One of the arguments made to support this view is the following Dutch book argument. Assume that L 1 Â L 2 but that α L ( 1 α) L 2 Â α L ( 1 L 1 . We can perform the fol- lowing trick on the decision maker: 1. Take α L ( 1 L 1 (we can describe this as a contingency with random event E , which we both agree has probability 1 α ). 2. Take instead α L ( 1
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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