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Unformatted text preview: Model I The true value of the item being auctioned is v , but v is unknown to all bidders. Each bidder i receives a signal, s i , about the true value, which is given by the sum of the true value v and a random variable ˜ e i , which you should think of as a private noise term: s i = v + ˜ e i , We assume that ˜ e i satisfies E [˜ e i ] = 0 and hence each bidders signal has the property that E [ s i ] = v . That is, the expected value of each bidder’s signal is equal to the true value. Rod Garratt ECON 177: Auction Theory With Experiments We will use this model to illustrate the winner’s curse. In particular, we will look at what happens to the winning bidder (in terms of her payoff) if she bids too large a fraction of her signal. We will discuss how this depends on the number of bidders and on how big the noise parameter can be relative to the true value. For concreteness, we will consider a specific random variable ˜ e i , that meets our requirement that E [˜ e i ] = 0 . Rod Garratt ECON 177: Auction Theory With Experiments Assume that the each bidders realized signal e i is determined by a draw from the uniform distribution on [ 1000 , 1000] . Hence, the probability that bidder i ’s signal is less than or equal to some value e ∈ [ 1000 , 1000] , is H ( e ) = 1000 + e 2000...
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 Fall '09
 GARRATT
 Variance, Probability theory, probability density function, Rod Garratt

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