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Serial Vickrey Mechanism. (2020). Serizawa, Shigehiro ; Zhou, YU.
In: ISER Discussion Paper.
RePEc:dpr:wpaper:1095.

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  1. A characterization of the Vickrey rule in slot allocation problems. (2022). Serizawa, Shigehiro ; Chun, Youngsub ; Zhou, YU.
    In: International Journal of Economic Theory.
    RePEc:bla:ijethy:v:18:y:2022:i:1:p:38-49.

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  2. A characterization of the Vickery rule in slot allocation problems. (2021). Serizawa, Shigehiro ; Chun, Youngsub ; Zhou, YU.
    In: ISER Discussion Paper.
    RePEc:dpr:wpaper:1120.

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  33. [40] Zhou, Y, Serizawa, S., 2018. Strategy-proofness and e ciency for non-quasilinear common-tiered-object preferences: Characterization of minimum price rule. Games and Economic Behavior 109, 327-363. Appendix Part A gives the proofs of results in Section 5. Part B gives the proofs of results in Section 6. Part C gives the proofs of results in Section 7. Appendix A: Proofs of Proposition 1, Lemma 1, Theorems 1 and 2 De…nition A.1: (i) A non-empty set M0 M of objects is overdemanded at p if jfi 2 N : Di(p) M0 gj > jM0 j. (ii) A non-empty set M0 M of objects is (weakly) underdemanded at p if [8x 2 M0 , px > 0] ) jfi 2 N : Di(p) \ M0 6= ;gj ( ) < jM0 j .

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  38. > 0. Thus, by (9), (10) and Fact C.6, NU nfi g N0 U . Thus by (8), NU = N0 U [ fi g, and so by (9), MU = M0 U [ fk + 1g. Q.E.D. Appendix D: Di culties with DGS auctions under general preferences We construct two examples below to show that the “exact DGS auction”and “approximate DGS auction”substantially overshoot the MPE prices when general preferences are considered. Examples can be similarly constructed to show that when the price increment is larger than the measurement of agents’valuation, the auction in Mishra and Parkes (2009) substantially undershoots the MPE price, and the auctions in Andersson and Erlanson (2013) and Liu and Bagh (2019) either substantially overshoots or undershoots the MPE price.
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  39. By Demange and Gale (1985), there is an equilibrium with reserve price r and the set of equilibrium prices with reserve price r is a complete lattice. Thus, there is an MPE with reserve price r. Let the MPE rule with reserve price r be a mapping from each preference pro…le to an MPE with reserve price r.
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  40. Fact A.1 (Mishra and Talman, 2010; Morimoto and Serizawa, 2015). p is an equilibrium price vector () no set is overdemanded and no set is underdemanded at p.
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