Unformatted text preview: inFnite space Z requires strengthening of the continuity assumption so that if p Â 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
 aswa
 Utility, St. Petersburg paradox, VNM utility function

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