Rubinstein2005-page108

Rubinstein2005-page108 - Independence (I): or any p , q , r...

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

View Full Document Right Arrow Icon
October 21, 2005 12:18 master Sheet number 106 Page number 90 90 Lecture Eight Figure 8.1 The compound lottery K k = 1 α k p k . We think of K k = 1 α k p k as a compound lottery with the following two stages: Stage 1 : It is randomly determined which of the lotteries p 1 , ... , p K is realized; α k is the probability that p k is realized. Stage 2 : The prize Fnally received is randomly drawn from the lottery determined in stage 1. When we compare two compound lotteries, α p ( 1 α) r and α q ( 1 α) r , we tend to simplify the comparison and form our pref- erence on the basis of the comparison between p and q . This intu- ition is translated into the following axiom:
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Independence (I): or any p , q , r L ( Z ) and any ( 0, 1 ) , p % q iff p ( 1 ) r % q ( 1 ) r . The following property follows from I : I : K k = 1 k p k % K k = 1 k q k when p k = q k for all k but k iff p k % q k . To see it, k = 1, ... , K k p k = k p k ( 1 k )( k 6= k [ k /( 1 k ) ] p k ) % k q k ( 1 k )( k 6= k [ k /( 1 k ) ] q k ) = K k = 1 k q k iff p k % q k ....
View Full Document

Ask a homework question - tutors are online