Unformatted text preview: that Z is a Fnite set. A lottery is a probability measure on Z , i.e., a lottery p is a function that assigns a nonnegative number p ( z ) to each prize z , where 6 z ∈ Z p ( z ) = 1. The number p ( z ) is taken to be the objective probability of obtaining the prize z given the lottery p . Denote by [ z ] the degenerate lottery for which [ z ] ( z ) = 1. We will use the notation α x ⊕ ( 1 − α) y to denote the lottery in which the prize x is realized with probability α and the prize y with probability 1 − α . Denote by L ( Z ) the (inFnite) space containing all lotteries with prizes in Z . Given the set of consequences Z , the space of lotteries L ( Z ) can be identiFed with a simplex in Euclidean space: { x ∈ < Z +  6 x z = 1 } . Recall that < Z + is the set of functions from Z into < + . The extreme points of the simplex correspond to the degenerate lotteries....
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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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