By Dewatripont M., Hansen L.P., Turnovsky S.J. (eds.)
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Additional resources for Advances in economics and econometrics, vol. 1
S. system, and there is no offsetting effect. , Hughes and Snyder, 1995) that the American system leads to more trials than, for example, the British system. This last extension demonstrates that even where the RET in its simplest form fails, it is often possible to see how the result is modiﬁed; Appendix 1 shows how to use the RET to solve for the relative merits of a much broader class of systems in which those we have discussed are special cases. We also show there that a system that might be thought of as the exact opposite of Quayle’s system is optimal in this model.
4) Notice that buyer 1’s objective function does not depend on s1B [s1B affects only buyer 1’s valuation for good B, but buyer 1 is not allocated B in either case (i) or (ii)]. Hence, the equilibrium outcome of any auction cannot turn on the value of this parameter. 4)] holds cannot depend on s1B . 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.
6) < 0 v 1A ) and v 1∗∗ such that and ∗∗ v 1B + bˆ 2A (v 1∗∗ ) = bˆ 2AB (v 1∗∗ ), then buyer 1 pays (bˆ 2A (ˆv 1∗ ) − bˆ 2B (ˆv 1∗ )) + (bˆ 2AB (v 1∗∗ ) − bˆ 2A (v 1∗∗ )). 7) 5. If buyer 1 is allocated good B, then his payment is completely analogous to that of 4. 6. If buyer 1 is allocated goods A and B, then see the Appendix for his payment. 7. Buyer 2’s payments are completely analogous to those of buyer 1. Rules 1–3 so closely mirror rules 1–3 of the modiﬁed Vickrey auction in Section 4 that they do not require further comment.