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Characterizing the Vickrey combinatorial auction by induction

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  • Soo Chew
  • Shigehiro Serizawa

Abstract

This note studies the allocation of heterogeneous commodities to agents whose private values for combinations of these commodities are monotonic by inclusion. This setting can accommodate the presence of complementarity and substitutability among the heterogeneous commodities. By using induction logic, we provide an elementary proof of Holmstrom's (1919) characterization of the Vickrey combinatorial auction as the unique efficient, strategy-proof, and individually rational allocation rule. Our proof method can also be applied to domains to which his proof cannot be.
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  • Soo Chew & Shigehiro Serizawa, 2007. "Characterizing the Vickrey combinatorial auction by induction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 393-406, November.
    • Handle: RePEc:spr:joecth:v:33:y:2007:i:2:p:393-406
    DOI: 10.1007/s00199-006-0130-6
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    Cited by:

    1. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
    2. SHINOZAKI, Hiroki, 2024. "Shutting-out-proofness in object allocation problems with money," Discussion paper series HIAS-E-138, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    3. Hultkrantz, Lars & Lunander, Anders, 2013. "Design of a Combinatorial Bidding Market for Green Corridor Freight," Working Papers 2013:6, Örebro University, School of Business.
    4. Itai Sher, 2012. "Optimal shill bidding in the VCG mechanism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 341-387, June.
    5. Francisco Robles, 2016. "An implementation of the Vickrey outcome with gross-substitutes," UB School of Economics Working Papers 2016/353, University of Barcelona School of Economics.
    6. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    7. Tsuyoshi Adachi & Takumi Kongo, 2013. "First-price auctions on general preference domains: axiomatic characterizations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 93-103, May.
    8. Christopher P. Chambers & Michael Richter, 2023. "Ordinal allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 5-14, January.
    9. SHINOZAKI, Hiroki, 2023. "Non-obvious manipulability and efficiency in package assignment problems with money for agents with income effects and hard budget constraints," Discussion paper series HIAS-E-136, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    10. Soo Chew & Shigehiro Serizawa, 2007. "Characterizing the Vickrey combinatorial auction by induction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 393-406, November.
    11. Tomoya KAZUMURA, 2020. "When can we design efficient and strategy-proof rules in package assignment problems?," Discussion papers e-21-008, Graduate School of Economics , Kyoto University.
    12. Alva, Samson & Manjunath, Vikram, 2019. "Strategy-proof Pareto-improvement," Journal of Economic Theory, Elsevier, vol. 181(C), pages 121-142.
    13. Kerber, Manfred & Lange, Christoph & Rowat, Colin, 2016. "An introduction to mechanized reasoning," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 26-39.
    14. Toyotaka Sakai, 2013. "Axiomatizations of second price auctions with a reserve price," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 255-265, September.
    15. Shigehiro Serizawa, 2006. "Strategy-Proof and Anonymous Allocation Rules of Indivisible Goods: A New Characterization of Vickrey Allocation Rule," ISER Discussion Paper 0648, Institute of Social and Economic Research, Osaka University.
    16. Itai Ashlagi & Shigehiro Serizawa, 2012. "Characterizing Vickrey allocation rule by anonymity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 531-542, March.
    17. Yu Zhou & Youngsub Chun & Shigehiro Serizawa, 2022. "A characterization of the Vickrey rule in slot allocation problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 38-49, March.
    18. Sano, Ryuji, 2013. "Vickrey-reserve auctions and an equilibrium equivalence," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 112-117.
    19. Takumi Kongo, 2020. "Similarities in axiomatizations: equal surplus division value and first-price auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 199-213, December.
    20. Nanyang Bu, 2016. "Joint misrepresentation with bribes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 115-125, January.
    21. Shinji Ohseto, 2021. "Strategy-proof and Pareto efficient allocation of indivisible goods: general impossibility domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 419-432, June.
    22. Miki Kato & Shinji Ohseto & Shohei Tamura, 2015. "Strategy-proofness versus symmetry in economies with an indivisible good and money," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 195-207, February.
    23. Tomoya Tajika & Tomoya Kazumura, 2019. "Non-manipulability of uniform price auctions with a large number of objects," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 543-569, June.
    24. Marina Núñez & Francisco Robles, 2023. "Overbidding and underbidding in package allocation problems," UB School of Economics Working Papers 2023/440, University of Barcelona School of Economics.

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    More about this item

    Keywords

    Vickrey auction; Strategy-proofness; Induction; Heterogenous commodities; D44; C78; D71; D61; D82;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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