By Dewatripont M., Hansen L.P., Turnovsky S.J. (eds.)
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7. Suppose that there are two buyers and one good. Assume that buyer 2’s signal s2 is, as usual, one-dimensional but that buyer 1’s signal s1 has two components: s1 =(s11 , s12 ). Let v 1 (s11 , s12 , s2 ) = s11 + s12 + αs2 Auctions and Efﬁciency 19 and v 2 (s11 , s12 , s2 ) = s2 + βs11 + γ s12 . Because of independence, buyer 1’s objective function is the same for any pairs (s11 , s12 ) that add up to the same constant, and thus, he will behave the same way for any such pairs. In particular, if (s11 , s12 ) and (s11 , s12 ) are pairs such that s11 + s12 = s11 + s12 , then, in any auction, the equilibrium outcome must be identical for the two pairs.
Speciﬁcally, suppose that in our two-good model, each buyer wants at most one good (this is not essential). Assume that the true value of good A to buyer i, yi A , is the sum of a component z A common to all buyers and a component of z i A that is idiosyncratic to him. That is, yi A = z A + z i A . Similarly, assume that buyer i’s true valuation of good B, yi B , satisﬁes yi B = z B + z i B . Suppose, however, that buyer i does not directly observe his true valuations, but only noisy signals of them.
Auction Theory 31 easier. Furthermore, the RET was also useful in the actual analysis of the more complex games that Bulow and Klemperer (1999) used to approximate this game. In addition, anyone armed with a knowledge of the RET can simplify the analysis of the basic two-player war of attrition. 3. Queueing and Other “All-Pay” Applications The preceding applications have both been variants of “all-pay” auctions. , for tickets to a sporting event). ) will make no difference to the social cost of the queueing mechanism.