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A Characterization of the Minimum Price Walrasian Rule with Reserve Prices for an Arbitrary Number of Agents and Objects

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  • Yuya Wakabayashi
  • Ryosuke Sakai
  • Shigehiro Serizawa

Abstract

We consider the economy consisting of n agents and m heterogenous objects where the seller benefits v from objects. Our study focuses on the multi-object allocation problem with monetary transfers where each agent obtains at most one object (unit-demand). In the situation with arbitrary n, m and v, we show that the minimum price Walrasian rule with reserve prices adjusted to v on the classical domain is the only rule satisfying four desirable properties; efficiency, strategy-proofness, individual rationality and no-subsidy. Our result is an extension of that of Morimoto and Serizawa (2015), and so we can consider more general situation than them. Moreover, we characterize the minimum price Walrasian rules by efficiency, strategy-proofness and two-sided individual rationality.

Suggested Citation

  • Yuya Wakabayashi & Ryosuke Sakai & Shigehiro Serizawa, 2022. "A Characterization of the Minimum Price Walrasian Rule with Reserve Prices for an Arbitrary Number of Agents and Objects," ISER Discussion Paper 1161, Institute of Social and Economic Research, The University of Osaka.
    • Handle: RePEc:dpr:wpaper:1161
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    References listed on IDEAS

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    1. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Strategy-proof multi-object mechanism design: Ex-post revenue maximization with non-quasilinear preferences," Journal of Economic Theory, Elsevier, vol. 188(C).
    2. 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.
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    5. 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.
    6. Ryosuke Sakai & Shigehiro Serizawa, 2020. "Strategy-proof mechanism design with non-quasilinear preferences:," ISER Discussion Paper 1107, Institute of Social and Economic Research, The University of Osaka.
    7. 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.
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    10. 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.
    11. , & ,, 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.
    12. Tommy Andersson & Lars‐Gunnar Svensson, 2014. "Non‐Manipulable House Allocation With Rent Control," Econometrica, Econometric Society, vol. 82(2), pages 507-539, March.
    13. 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.
    14. Ryosuke Sakai & Shigehiro Serizawa, 2021. "A Characterization of Minimum Price Walrasian Rule in Object Allocation Problem for an Arbitrary Number of Objects," ISER Discussion Paper 1134, Institute of Social and Economic Research, The University of Osaka.
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