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On the impossibility of core-selecting auctions

Author

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  • , K.

    (Economics Discipline Group, University of Technology Sydney)

  • ,

    (Department of Economics, Hong Kong University of Science and Technology)

Abstract
When goods are substitutes, the Vickrey outcome is in the core and yields competitive seller revenue. In contrast, with complements, the Vickrey outcome is efficient but not necessarily in the core and revenue can be low. Non-core outcomes may be perceived as unfair since there are bidders willing to pay more than the winners' payments. Moreover, non-core outcomes render the auction vulnerable to defections as the seller can attract better offers afterwards. To avoid instabilities of this type, Day and Raghavan (2007), Day and Milgrom (2008), and Day and Cramton (2012) have suggested adapting the Vickrey pricing rule so that outcomes are in the core with respect to bidders' {\em reported} values. If truthful bidding were an equilibrium of the resulting auction then the outcome would also be in the core with respect to bidders' {\em true} values. We show, however, that when the equilibrium outcome of any auction is in the core, it is equivalent to the Vickrey outcome. In other words, if the Vickrey outcome is not in the core, no core-selecting auction exists. Our results further imply that the competitive equilibrium outcome, which always exists when goods are substitutes, can only be implemented when it coincides with the Vickrey outcome. Finally, for a simple environment we show that compared to Vickrey prices the adapted pricing rule yields lower expected efficiency and revenue as well as outcomes that are on average further from the core.

Suggested Citation

  • , K. & ,, 2016. "On the impossibility of core-selecting auctions," Theoretical Economics, Econometric Society, vol. 11(1), January.
    • Handle: RePEc:the:publsh:1198
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    References listed on IDEAS

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    Cited by:

    1. Isa Hafalir & Hadi Yektaş, 2015. "Core deviation minimizing auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 367-376, May.
    2. Lamprirni Zarpala & Dimitris Voliotis, 2022. "A core-selecting auction for portfolio's packages," Papers 2206.11516, arXiv.org, revised Feb 2024.
    3. Sano, Ryuji, 2012. "Non-bidding equilibrium in an ascending core-selecting auction," Games and Economic Behavior, Elsevier, vol. 74(2), pages 637-650.
    4. Ignacio Palacios-Huerta & David C. Parkes & Richard Steinberg, 2024. "Combinatorial Auctions in Practice," Journal of Economic Literature, American Economic Association, vol. 62(2), pages 517-553, June.
    5. Heczko, Alexander & Kittsteiner, Thomas & Ott, Marion, 2018. "The Performance of Core-Selecting Auctions: An Experiment," EconStor Preprints 176842, ZBW - Leibniz Information Centre for Economics.
    6. 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.
    7. Janssen, Maarten & Karamychev, Vladimir, 2016. "Spiteful bidding and gaming in combinatorial clock auctions," Games and Economic Behavior, Elsevier, vol. 100(C), pages 186-207.
    8. Nicolas C. Bedard & Jacob K. Goeree & Philippos Louis & Jingjing Zhang, 2020. "The Favored but Flawed Simultaneous Multiple-Round Auction," Working Paper Series 2020/03, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    9. Nicholas C. Bedard & Jacob K. Goeree & Philippos Louis & Jingjing Zhang, 2024. "Sealed-bid versus ascending spectrum auctions," Experimental Economics, Springer;Economic Science Association, vol. 27(2), pages 299-324, April.
    10. Bichler, Martin & Paulsen, Per, 2018. "A principal-agent model of bidding firms in multi-unit auctions," Games and Economic Behavior, Elsevier, vol. 111(C), pages 20-40.
    11. Ryuji Sano, 2018. "An equilibrium analysis of a core-selecting package auction with reserve prices," Review of Economic Design, Springer;Society for Economic Design, vol. 22(3), pages 101-122, December.
    12. Thomas Kittsteiner & Marion Ott & Richard Steinberg, 2022. "Competing Combinatorial Auctions," Information Systems Research, INFORMS, vol. 33(4), pages 1130-1137, December.
    13. Benedikt Bünz & Benjamin Lubin & Sven Seuken, 2022. "Designing Core-Selecting Payment Rules: A Computational Search Approach," Information Systems Research, INFORMS, vol. 33(4), pages 1157-1173, December.
    14. Martin Bichler & Zhen Hao & Gediminas Adomavicius, 2017. "Coalition-Based Pricing in Ascending Combinatorial Auctions," Information Systems Research, INFORMS, vol. 28(1), pages 159-179, March.
    15. Paul Karaenke & Martin Bichler & Stefan Minner, 2019. "Coordination Is Hard: Electronic Auction Mechanisms for Increased Efficiency in Transportation Logistics," Management Science, INFORMS, vol. 65(12), pages 5884-5900, December.
    16. Ott, Marion & Beck, Marissa, 2013. "Incentives for Overbidding in Minimum-Revenue Core-Selecting Auctions," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79946, Verein für Socialpolitik / German Economic Association.
    17. Daniel Marszalec, 2016. "Auctions For Complements –An Experimental Analysis," CIRJE F-Series CIRJE-F-1018, CIRJE, Faculty of Economics, University of Tokyo.
    18. Bichler, Martin & Goeree, Jacob K., 2017. "Frontiers in spectrum auction design," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 372-391.
    19. Jeong, Seungwon (Eugene) & Lee, Joosung, 2024. "The groupwise-pivotal referral auction: Core-selecting referral strategy-proof mechanism," Games and Economic Behavior, Elsevier, vol. 143(C), pages 191-203.
    20. Lawrence M. Ausubel & Oleg Baranov, 2020. "Core-selecting auctions with incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 251-273, March.
    21. Ott, Marion, 2019. "Simple Bayesian and Ex-Post Equilibria in Combinatorial Auctions," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203616, Verein für Socialpolitik / German Economic Association.
    22. Mochon, A. & Saez, Y. & Gomez-Barroso, J.L. & Isasi, P., 2012. "Exploring pricing rules in combinatorial sealed-bid auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 462-478.
    23. Martin Bichler & Nils Kohring & Stefan Heidekrüger, 2023. "Learning Equilibria in Asymmetric Auction Games," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 523-542, May.
    24. Marszalec, Daniel, 2018. "Fear not the simplicity - An experimental analysis of auctions for complements," Journal of Economic Behavior & Organization, Elsevier, vol. 152(C), pages 81-97.
    25. Maarten Janssen & Vladimir Karamychev, 2013. "Gaming in Combinatorial Clock Auctions," Tinbergen Institute Discussion Papers 13-027/VII, Tinbergen Institute, revised 16 Dec 2013.

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    More about this item

    Keywords

    Core outcomes; Vickrey auction; substitutes; complements; competitive equilibrium; Bayesian implementability;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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