Problem_Set_4

# Problem_Set_4 - /OR4350 Introduction to Game Theory Spring...

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/OR4350 Introduction to Game Theory Spring 2010 Problem Set #3 Due : Wednesday, March 10, 2010 at noon in the dropbox (on 2 nd floor of Rhodes Hall) Reminder : Write your Section and NetID on the first page of your homework!!! Answers must always include complete explanations/justifications. 1. Binmore, Section 4.11, Number 6. Suppose a b and b c. By definition a b implies that a b, and by transitivity a b, b c a c. Assume (by contradiction) a c. By the definition of a c, c a holds. Together with b c it implies that b a. However this is impossible, since a b means that a b and not a b, whereas a b and b a implies that a b. This is a contradiction. Thus a c and not(a c) a c. a b and b c a c 2. Binmore, Section 4.11, Number 11. Define the Von Neumann and Morgenstern utility function u: →ℝ Ω as a=u( )<u( )=b. Then ? (u( 1 )) = 0.6 u( )+0.4u( ) = 0.6a+0.4b ? (u( 2 )) = 0.2 u( )+0.8u( ) = 0.2a+0.8b a<b a < ? (u( 1 )) < ? (u( 2 )) < b, i.e. u( ) < ? (u( 1 )) < ? (u( 2 )) < u( ) u represents the preferences ℒ ℒ 1 2 To determine Pandora s preference in

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## This note was uploaded on 02/06/2011 for the course ORIE 4350 at Cornell.

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Problem_Set_4 - /OR4350 Introduction to Game Theory Spring...

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