IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v8y2020i2d10.1007_s40505-020-00184-7.html
   My bibliography  Save this article

On group strategyproof and optimal object allocation

Author

Listed:
  • Conan Mukherjee

    (Indian Institute of Management Calcutta)

Abstract

We consider a two-agent, single indivisible object allocation problem. We focus on continuous mechanisms that satisfy agent sovereignty, and investigate implications of group strategyproofness. In particular, we provide an explicit characterization of the strategyproof mechanisms and show that there are non-affine maximizer mechanisms that do not belong to the class characterized by Roberts (North-Holland, 1979). Further, we show that there are no budget-balanced strategyproof mechanisms. Also, we obtain an impossibility for existence of strong group strategyproof mechanism. We find that this impossibility goes away upon relaxing our notion of group strategyproofness, and consequently, present a class of weak group strategyproof mechanisms. Finally, we completely characterize the class of feasible strategyproof mechanisms satisfying individual rationality, and show that there are no optimal strategyproof expected revenue maximizing mechanisms under a general class of well behaved type distributions.

Suggested Citation

  • Conan Mukherjee, 2020. "On group strategyproof and optimal object allocation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 289-304, October.
    • Handle: RePEc:spr:etbull:v:8:y:2020:i:2:d:10.1007_s40505-020-00184-7
    DOI: 10.1007/s40505-020-00184-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-020-00184-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40505-020-00184-7?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. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
    2. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 511-533.
    3. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Domains, ranges and strategy-proofness: the case of single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 335-352, July.
    4. 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.
    5. Thierry Marchant & Debasis Mishra, 2015. "Mechanism design with two alternatives in quasi-linear environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 433-455, February.
    6. Conan Mukherjee, 2013. "Weak group strategy-proof and queue-efficient mechanisms for the queueing problem with multiple machines," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 131-163, February.
    7. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    8. 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.
    9. 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.
    10. Shigehiro Serizawa, 2006. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 305-331, April.
    11. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    12. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
    13. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    14. , & , A., 2007. "Efficiency in repeated trade with hidden valuations," Theoretical Economics, Econometric Society, vol. 2(3), September.
    15. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2016. "Group Strategy-Proofness in Private Good Economies," American Economic Review, American Economic Association, vol. 106(4), pages 1073-1099, April.
    16. Kentaro Hatsumi & Shigehiro Serizawa, 2009. "Coalitionally strategy-proof rules in allotment economies with homogeneous indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 423-447, September.
    17. Hagerty, Kathleen M. & Rogerson, William P., 1987. "Robust trading mechanisms," Journal of Economic Theory, Elsevier, vol. 42(1), pages 94-107, June.
    18. De, Parikshit & Mitra, Manipushpak, 2019. "Balanced implementability of sequencing rules," Games and Economic Behavior, Elsevier, vol. 118(C), pages 342-353.
    19. Kentaro Hatsumi & Shigehiro Serizawa, 2007. "Coalitionally Strategy-Proof Rules in Allotment Economies of Homogeneous Indivisible Goods," ISER Discussion Paper 0686, Institute of Social and Economic Research, Osaka University, revised Feb 2009.
    20. Shao, Ran & Zhou, Lin, 2016. "Optimal allocation of an indivisible good," Games and Economic Behavior, Elsevier, vol. 100(C), pages 95-112.
    21. Mitra, Manipushpak & Mutuswami, Suresh, 2011. "Group strategyproofness in queueing models," Games and Economic Behavior, Elsevier, vol. 72(1), pages 242-254, May.
    22. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    23. Debasis Mishra & Abdul Quadir, 2014. "Non-bossy single object auctions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 93-110, April.
    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. Hagen, Martin, 2023. "Collusion-proof mechanisms for multi-unit procurement," Games and Economic Behavior, Elsevier, vol. 138(C), pages 281-298.
    2. Sreoshi Banerjee & Parikshit De & Manipushpak Mitra, 2024. "Generalized welfare lower bounds and strategyproofness in sequencing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 323-357, September.

    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. Hagen, Martin, 2023. "Collusion-proof mechanisms for multi-unit procurement," Games and Economic Behavior, Elsevier, vol. 138(C), pages 281-298.
    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. William Thomson, 2016. "Non-bossiness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 665-696, October.
    4. Kiho Yoon, 2021. "Robust double auction mechanisms," Papers 2102.00669, arXiv.org, revised May 2022.
    5. 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.
    6. Kiho Yoon, 2018. "Optimal robust allocation of private goods," Discussion Paper Series 1803, Institute of Economic Research, Korea University.
    7. Conan Mukherjee, 2013. "Weak group strategy-proof and queue-efficient mechanisms for the queueing problem with multiple machines," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 131-163, February.
    8. Long, Yan & Mishra, Debasis & Sharma, Tridib, 2017. "Balanced ranking mechanisms," Games and Economic Behavior, Elsevier, vol. 105(C), pages 9-39.
    9. Raghavan, Madhav, 2020. "Influence in private-goods allocation," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 14-28.
    10. Moulin, Hervé, 2017. "One dimensional mechanism design," Theoretical Economics, Econometric Society, vol. 12(2), May.
    11. Shao, Ran & Zhou, Lin, 2016. "Voting and optimal provision of a public good," Journal of Public Economics, Elsevier, vol. 134(C), pages 35-41.
    12. Thierry Marchant & Debasis Mishra, 2015. "Mechanism design with two alternatives in quasi-linear environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 433-455, February.
    13. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    14. 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).
    15. 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.
    16. Yan Long, 2020. "Optimal budget-balanced ranking mechanisms to assign identical objects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 467-502, September.
    17. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2017. "Reordering an existing queue," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 65-87, June.
    18. Juarez, Ruben, 2013. "Group strategyproof cost sharing: The role of indifferences," Games and Economic Behavior, Elsevier, vol. 82(C), pages 218-239.
    19. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2014. "Egalitarian equivalence and strategyproofness in the queueing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 425-442, June.
    20. Marek Pycia & Peter Troyan, 2023. "A Theory of Simplicity in Games and Mechanism Design," Econometrica, Econometric Society, vol. 91(4), pages 1495-1526, July.

    More about this item

    Keywords

    Group strategyproofness; Budget balance; Optimal mechanism;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    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:spr:etbull:v:8:y:2020:i:2:d:10.1007_s40505-020-00184-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.