IDEAS home Printed from https://ideas.repec.org/p/kue/epaper/e-23-007.html
   My bibliography  Save this paper

Sequential dictatorship rules in multi-unit objectassignment problems with money

Author

Listed:
  • Masahiro KAWASAKI
  • Ryosuke SAKAI
  • Tomoya KAZUMURA

Abstract

We study consistency in multi-unit object allocation problems with money. Objects are identical and each agent has a multi-demand and quasi-linear preferences. We consider the class of weak object monotonic preferences and that of single-peaked preferences. We first show that on those domains, if a rule satisfies consistency, strategyproofness, individual rationality, no subsidy, non-wasteful tie-breaking, and minimal tradability, then it is a sequential dictatorship rule. Since not all sequential dictatorship rule are strategy-proof and consistent, we then focus on a specific class of sequential dictatorship rules which we call sequential dictatorship rules with lowest tie-breaking. On the weakly object monotonic domain, when the reservation prices are increasing in the number of objects, sequential dictatorship rules with lowest tie-breaking satisfy consistency and independence of unallocated objects if and only if there is a common priority ordering for more than one object and this is an acyclic ordering of the priority ordering for one object. We also show that this condition is a necessary and sufficient condition for a sequential dictatorship rule with lowest tie-breaking to satisfy consistency and independence of unallocated objects on the single-peaked domain.

Suggested Citation

  • Masahiro KAWASAKI & Ryosuke SAKAI & Tomoya KAZUMURA, 2023. "Sequential dictatorship rules in multi-unit objectassignment problems with money," Discussion papers e-23-007, Graduate School of Economics , Kyoto University.
    • Handle: RePEc:kue:epaper:e-23-007
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Bettina Klaus & Alexandru Nichifor, 2020. "Serial dictatorship mechanisms with reservation prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 665-684, October.
    3. 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.
    4. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    5. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 505-515, September.
    6. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    7. Kumano, Taro, 2013. "Strategy-proofness and stability of the Boston mechanism: An almost impossibility result," Journal of Public Economics, Elsevier, vol. 105(C), pages 23-29.
    8. repec:bla:jpbect:v:3:y:2001:i:3:p:257-71 is not listed on IDEAS
    9. Hiroki Shinozaki, 2022. "Characterizing pairwise strategy-proof rules in object allocation problems with money," ISER Discussion Paper 1187, Institute of Social and Economic Research, Osaka University.
    10. Teytelboym, Alexander, 2014. "Gross substitutes and complements: A simple generalization," Economics Letters, Elsevier, vol. 123(2), pages 135-138.
    11. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, vol. 47(5), pages 1137-1144, September.
    12. 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.
    13. 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.
    14. Thomson, William, 2012. "On The Axiomatics Of Resource Allocation: Interpreting The Consistency Principle," Economics and Philosophy, Cambridge University Press, vol. 28(3), pages 385-421, November.
    15. Bettina Klaus & Eiichi Miyagawa, 2002. "Strategy-proofness, solidarity, and consistency for multiple assignment problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 421-435.
    16. Miyagawa, Eiichi, 2001. "House Allocation with Transfers," Journal of Economic Theory, Elsevier, vol. 100(2), pages 329-355, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Masahiro KAWASAKI & Ryosuke SAKAI & Tomoya KAZUMURA, 2024. "Sequential dictatorship rules in multi-unit object assignment problems with money," Discussion papers e-23-007-v2, Graduate School of Economics , Kyoto University.
    2. Yuji Fujinaka & Takuma Wakayama, 2011. "Secure implementation in Shapley–Scarf housing markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 147-169, September.
    3. Bettina Klaus & Alexandru Nichifor, 2020. "Serial dictatorship mechanisms with reservation prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 665-684, October.
    4. SHINOZAKI, Hiroki, 2024. "Shill-proof rules in object allocation problems with money," Discussion paper series HIAS-E-137, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    5. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    6. 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.
    7. Di Feng, 2023. "Endowments-swapping-proofness and Efficiency in Multiple-Type Housing Markets," Discussion Paper Series DP2023-14, Research Institute for Economics & Business Administration, Kobe University.
    8. 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.
    9. Hiroki Shinozaki, 2022. "Characterizing pairwise strategy-proof rules in object allocation problems with money," ISER Discussion Paper 1187, Institute of Social and Economic Research, Osaka University.
    10. SHINOZAKI, Hiroki, 2023. "Efficiency and strategy-proofness in object allocation problems with payments: Externalities with income effects," Discussion paper series HIAS-E-135, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    11. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.
    12. Gian Caspari, 2023. "A market design solution to a multi-category housing allocation problem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 75-96, December.
    13. Chen, Yajing & Jiao, Zhenhua & Zhang, Yang & Zhao, Fang, 2021. "Resource allocation on the basis of priorities under multi-unit demand," Economics Letters, Elsevier, vol. 202(C).
    14. Yuya Wakabayashi & Ryosuke Sakai & Hiroki Shinozaki, 2024. "Strategy-proof allocation problem with hard budget constraints and income effects: weak efficiency and fairness," OSIPP Discussion Paper 24E003, Osaka School of International Public Policy, Osaka University.
    15. Afacan, Mustafa Oğuz & Bó, Inácio, 2022. "Strategy-proof popular mechanisms," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    16. 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.
    17. Yu Zhou & Shigehiro Serizawa, 2019. "Minimum price equilibrium in the assignment market," ISER Discussion Paper 1047, Institute of Social and Economic Research, Osaka University.
    18. 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.
    19. 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.
    20. 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.

    More about this item

    Keywords

    Consistency; Strategy-proofness; sequential dictatorship rule; serial dictatorship rule; weakly object monotonic preferences; single-peaked preferences; acyclicity.;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kue:epaper:e-23-007. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Graduate School of Economics Project Center (email available below). General contact details of provider: https://edirc.repec.org/data/fekyojp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.