IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v82y2013icp369-387.html

Some searches may not work properly. We apologize for the inconvenience.

   My bibliography  Save this article

A Solomonic solution to the problem of assigning a private indivisible good

Author

Listed:
  • Athanasiou, Efthymios

Abstract

A benevolent Planner wishes to assign an indivisible private good to n claimants, each valuing the object differently. Individuals have quasi-linear preferences. Therefore, the possibility of transfers is allowed. A second-best efficient mechanism is a strategy-proof and anonymous mechanism that is not Pareto dominated by another strategy-proof and anonymous mechanism. In this context, we identify three conditions that are necessary and, together with Voluntary Participation, sufficient for a mechanism to be second-best efficient. This set includes mechanisms that destroy the good at certain profiles. For domains comprising two individuals we provide an explicit characterization of the family of second-best efficient mechanisms.

Suggested Citation

  • Athanasiou, Efthymios, 2013. "A Solomonic solution to the problem of assigning a private indivisible good," Games and Economic Behavior, Elsevier, vol. 82(C), pages 369-387.
    • Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:369-387
    DOI: 10.1016/j.geb.2013.07.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613001097
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2013.07.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Conan Mukherjee, 2014. "Fair and group strategy-proof good allocation with money," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 289-311, February.
    3. de Clippel, Geoffroy & Naroditskiy, Victor & Polukarov, Maria & Greenwald, Amy & Jennings, Nicholas R., 2014. "Destroy to save," Games and Economic Behavior, Elsevier, vol. 86(C), pages 392-404.
      • Geoffroy de Clippel & Louis Putterman & Victor Naroditskiy & Maria Polukarov & Amy Greenwald & Nicholas R. Jennings, 2012. "Destroy to Save," Working Papers 2012-9, Brown University, Department of Economics.
    4. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    5. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, vol. 47(5), pages 1137-1144, September.
    6. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
    7. Moulin, Hervé, 2009. "Almost budget-balanced VCG mechanisms to assign multiple objects," Journal of Economic Theory, Elsevier, vol. 144(1), pages 96-119, January.
    8. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    9. Maniquet, François & Sprumont, Yves, 2010. "Sharing the cost of a public good: An incentive-constrained axiomatic approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 275-302, January.
    10. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    11. Bailey, Martin J, 1997. "The Demand Revealing Process: To Distribute the Surplus," Public Choice, Springer, vol. 91(2), pages 107-126, April.
    12. Schummer, James, 2000. "Eliciting Preferences to Assign Positions and Compensation," Games and Economic Behavior, Elsevier, vol. 30(2), pages 293-318, February.
    13. Murat Atlamaz & Duygu Yengin, 2008. "Fair Groves mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 573-587, December.
    14. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    15. Olszewski, Wojciech, 2004. "Coalition strategy-proof mechanisms for provision of excludable public goods," Games and Economic Behavior, Elsevier, vol. 46(1), pages 88-114, January.
    16. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
    17. Guo, Mingyu & Conitzer, Vincent, 2009. "Worst-case optimal redistribution of VCG payments in multi-unit auctions," Games and Economic Behavior, Elsevier, vol. 67(1), pages 69-98, September.
    18. Hervé Moulin, 1994. "Serial Cost-Sharing of Excludable Public Goods," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 305-325.
    19. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    20. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Efthymios Athanasiou & Giacomo Valletta, 2021. "Undominated mechanisms and the provision of a pure public good in two agent economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 763-795, November.
    2. Drexl, Moritz & Kleiner, Andreas, 2015. "Optimal private good allocation: The case for a balanced budget," Games and Economic Behavior, Elsevier, vol. 94(C), pages 169-181.
    3. Athanasiou, Efthymios & Valletta, Giacomo, 2021. "Binary public decisions and undominated mechanisms," Journal of Economic Theory, Elsevier, vol. 198(C).
    4. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "Asymmetrically fair rules for an indivisible good problem with a budget constraint," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 603-633, October.
    5. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
    6. Ranojoy Basu & Conan Mukherjee, 2024. "Characterization of maxmed mechanisms for multiple objects," Review of Economic Design, Springer;Society for Economic Design, vol. 28(2), pages 313-330, June.
    7. Athanasiou, E. & Dey, S. & Valletta, G., 2012. "On sharing the benefits of communication," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. C. Gizem Korpeoglu, 2018. "Allocation of an indivisible object on the full preference domain: axiomatic characterizations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 41-53, April.
    9. Efthymios Athanasiou & Santanu Dey & Giacomo Valletta, 2016. "Groves mechanisms and communication externalities," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 1-37, March.
    10. Mukherjee, Conan, 2015. "On Axioms Underlying Use of Reserve Price," Working Papers 2015:7, Lund University, Department of Economics, revised 14 Apr 2015.

    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. Kazuhiko Hashimoto, 2015. "Strategy-Proof Rule in Probabilistic Allocation Problem of an Indivisible Good and Money," ISER Discussion Paper 0931, Institute of Social and Economic Research, Osaka University.
    2. Duygu Yengin, 2017. "No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 81-108, January.
    3. , & ,, 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.
    4. Athanasiou, E. & Dey, S. & Valletta, G., 2012. "On sharing the benefits of communication," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Efthymios Athanasiou & Santanu Dey & Giacomo Valletta, 2016. "Groves mechanisms and communication externalities," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 1-37, March.
    6. Shao, Ran & Zhou, Lin, 2016. "Optimal allocation of an indivisible good," Games and Economic Behavior, Elsevier, vol. 100(C), pages 95-112.
    7. Yi, Jianxin & Li, Yong, 2016. "A general impossibility theorem and its application to individual rights," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 79-86.
    8. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
    9. 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.
    10. 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.
    11. , & , & ,, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    12. Yi, Jianxin & Wang, Hefei & Li, Yong, 2018. "Designing efficient and incentive compatible mechanisms is almost impossible in quasi-linear environments," Economics Letters, Elsevier, vol. 173(C), pages 113-117.
    13. Ranojoy Basu & Conan Mukherjee, 2024. "Characterization of maxmed mechanisms for multiple objects," Review of Economic Design, Springer;Society for Economic Design, vol. 28(2), pages 313-330, June.
    14. Nath, Swaprava & Sandholm, Tuomas, 2019. "Efficiency and budget balance in general quasi-linear domains," Games and Economic Behavior, Elsevier, vol. 113(C), pages 673-693.
    15. Quadir, Abdul, 2017. "Spanning tree auctions: A complete characterization," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 1-8.
    16. Blumrosen, Liad & Solan, Eilon, 2023. "Selling spectrum in the presence of shared networks: The case of the Israeli 5G auction," Telecommunications Policy, Elsevier, vol. 47(2).
    17. 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.
    18. 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.
    19. Efthymios Athanasiou & Giacomo Valletta, 2021. "Undominated mechanisms and the provision of a pure public good in two agent economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 763-795, November.
    20. Eric Maskin, 2004. "The Unity of Auction Theory: Paul Milgrom's Masterclass," Economics Working Papers 0044, Institute for Advanced Study, School of Social Science.

    More about this item

    Keywords

    Indivisible private good; Quasi-linear preferences; Strategy-Proofness; Vickrey–Clarke–Groves mechanism;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

    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:eee:gamebe:v:82:y:2013:i:c:p:369-387. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.