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Unformatted text preview: Problemset 1 Due Thursday September 15th before 5pm 1. A decision maker who obeys the vonNeumannMorgenstern axioms is choosing over 5 potential prizes X = { x 1 ,x 2 ,x 3 ,x 4 ,x 5 } . We know for sure that she ranks them according to x 1 ≻ x 2 ≻ x 3 ≻ x 4 ≻ x 5 . We normalize the best and worst prizes to have payoffs v ( x 1 ) = 100 and v ( x 5 ) = 0. Other than this all we know is the following: • The lottery A which gives her x 3 with certainty is ranked as in different to the lottery B which gives x 1 with 45 percent proba bility and x 5 with 55 percent probability. [We can write this as (0 , , 1 , , 0) = p A ∼ p B = (0 . 45 , , , , . 55).] • The lottery that gives x 2 with certainty is ranked as indifferent to the lottery which gives x 1 with 60 percent probability, x 2 with 20 per cent probability and x 5 with 20 percent probability. [(0 , 1 , , , 0) ∼ (0 . 6 , . 2 , , , . 2)] • The lottery that gives x 2 with probability onethird, and x 4 with probability twothird is strictly preferred to the lottery which gives...
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 Spring '08
 Staff
 Game Theory, 20 percent, 45 percent, percent probability

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