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Equity in auction design with unit-demand agents and non-quasilinear preferences

Author

Listed:
  • Tomoya Kazumura
  • Debasis Mishra
  • Shigehiro Serizawa

Abstract

We study a model of auction design where a seller is selling a set of objects to a set of agents who can be assigned no more than one object. Each agent’s preference over (object, payment) pair need not be quasilinear. If the domain contains all classical preferences, we show that there is a unique mechanism, the minimum Walrasian equilibrium price (MWEP) mechanism, which is strategy-proof, individually rational, and satisfies equal treatment of equals, no-wastage (every object is allocated to some agent), and no-subsidy (no agent is subsidized). This provides an equity-based characterization of the MEWP mechanism, and complements the efficiency-based characterization of the MWEP mechanism known in the literature.

Suggested Citation

  • Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2026. "Equity in auction design with unit-demand agents and non-quasilinear preferences," ISER Discussion Paper 1304, Institute of Social and Economic Research, The University of Osaka.
    • Handle: RePEc:dpr:wpaper:1304
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    References listed on IDEAS

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    1. 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.
    2. Tsuyoshi Adachi, 2014. "Equity and the Vickrey allocation rule on general preference domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 813-830, April.
    3. Ken Binmore & Paul Klemperer, 2002. "The Biggest Auction Ever: the Sale of the British 3G Telecom Licences," Economic Journal, Royal Economic Society, vol. 112(478), pages 74-96, March.
    4. Elizabeth Baldwin & Ravi Jagadeesan & Paul Klemperer & Alexander Teytelboym, 2023. "The Equilibrium Existence Duality," Journal of Political Economy, University of Chicago Press, vol. 131(6), pages 1440-1476.
    5. , & ,, 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.
    6. Zhou, Yu & Serizawa, Shigehiro, 2018. "Strategy-proofness and efficiency for non-quasi-linear and common-tiered-object preferences: Characterization of minimum price rule," Games and Economic Behavior, Elsevier, vol. 109(C), pages 327-363.
    7. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    8. Malik, Komal & Mishra, Debasis, 2021. "Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity," Journal of Economic Theory, Elsevier, vol. 191(C).
    9. Svensson, Lars-Gunnar, 1987. "Erratum [Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness]," Econometrica, Econometric Society, vol. 55(2), pages 489-489, March.
    10. Tomoya Kazumura & Shigehiro Serizawa, 2016. "Efficiency and strategy-proofness in object assignment problems with multi-demand preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 633-663, October.
    11. 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.
    12. Teytelboym, Alexander, 2014. "Gross substitutes and complements: A simple generalization," Economics Letters, Elsevier, vol. 123(2), pages 135-138.
    13. Mishra, Debasis & Talman, Dolf, 2010. "Characterization of the Walrasian equilibria of the assignment model," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 6-20, January.
    14. Thành Nguyen & Rakesh Vohra, 2024. "(Near-)Substitute Preferences and Equilibria with Indivisibilities," Journal of Political Economy, University of Chicago Press, vol. 132(12), pages 4122-4154.
    15. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    16. Baisa, Brian, 2020. "Efficient multi-unit auctions for normal goods," Theoretical Economics, Econometric Society, vol. 15(1), January.
    17. Toyotaka Sakai, 2008. "Second price auctions on general preference domains: two characterizations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 347-356, November.
    18. Hiroki Saitoh & Shigehiro Serizawa, 2008. "Vickrey allocation rule with income effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 391-401, May.
    19. Wakabayashi, Yuya & Sakai, Ryosuke & Serizawa, Shigehiro, 2025. "A general characterization of the minimum price Walrasian rule with reserve prices," Games and Economic Behavior, Elsevier, vol. 150(C), pages 1-26.
    20. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2016. "Transferring ownership of public housing to existing tenants: A market design approach," Journal of Economic Theory, Elsevier, vol. 165(C), pages 643-671.
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