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Unformatted text preview: inFnite space Z requires strengthening of the continuity assumption so that if p q , then small changes in the prizes, and not just in probabilities, leave the preferences unchanged. rom here on we focus the discussion on preference relations over the space of lotteries for which there is a continuous function u (referred to as a vNM utility function), such that the preference relation is represented by the function Eu ( p ) = z Z p ( z ) u ( z ) . This function assigns to the lottery p the expectation of the random variable that receives the value u ( x ) with a probability p ( x ) . The following argument, called the St. Petersburg Paradox , is sometimes presented as a justiFcation for assuming that vNM utility functions are bounded. Assume that a decision maker has an unbounded vNM utility function u . Consider playing the following trick on him:...
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 Fall '10
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