By Dewatripont M., Hansen L.P., Turnovsky S.J. (eds.)

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4), that v 3B (s1B , s2B , s3B ) − v 2B (s1B , s2B , s3B ) must be independent of s1B . Expressed differently, we have ∂ ∂ v 3B (s1B , s2B , s3B ) = v 2B (s1B , s2B , s3B ). ∂s1B ∂s1B Repeating the argument for all other pairs of buyers and for good B, we have ∂v j H ∂v k H = , ∂si H ∂si H for all j =i =k and H = A, B. 5) Next, let us fix the signal values of buyers 2 and 3 at levels such that, as we vary s1A and s1B , either (iii) it is efficient to allocate A to buyer 1 and B to 2 or (iv) it is efficient to allocate B to buyer 1 and A to 2.

From the buyer’s perspective, it is as if sellers were independently making sealed-bid offers in ignorance of the competition. Of course, the analogies are imperfect,31 but they serve as a starting point for analysis. What, therefore, does auction theory suggest? Because, under the conditions of the revenue equivalence theorem, there is no difference between the auction forms for either consumer or producer welfare, we consider the implications of the most important violations of the conditions.

Hence, in any auction, the equilibrium outcome must be the same for any value of . 11) applies cannot depend on ’s value. , only if ∂v 2A ∂v 2B = . ∂s1A ∂s1B Repeating the argument for the other buyers, we have ∂v j B ∂v j A = ∂si A ∂si B for all i and j = i. 12), due to Jehiel and Moldovanu (2001), are certainly restrictive. Nevertheless, as shown in Eso and Maskin (2000a), there is a natural class of cases in which they are automatically satisfied. Specifically, suppose that in our two-good model, each buyer wants at most one good (this is not essential).

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Advances in economics and econometrics, vol. 1 by Dewatripont M., Hansen L.P., Turnovsky S.J. (eds.)
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