IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v126y2023icp1-12.html
   My bibliography  Save this article

Sensitivity of fair prices in assignment markets

Author

Listed:
  • Solymosi, Tamás

Abstract

It is well known that in assignment markets competitive prices always exist, but no price mechanism is strategy-proof for all agents. We investigate the extent a single agent can influence three special competitive price vectors by misreporting his/her reservation values. We provide an exact formula how the minimum, the maximum, and the fair competitive price vectors change, and show that at the fair prices no agent can gain more than half of the deviation from the true values. We also derive the analogous results for the corresponding core payoffs of the associated assignment game via graph-theoretic characterizations of the two side-optimal core payoffs.

Suggested Citation

  • Solymosi, Tamás, 2023. "Sensitivity of fair prices in assignment markets," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 1-12.
    • Handle: RePEc:eee:matsoc:v:126:y:2023:i:c:p:1-12
    DOI: 10.1016/j.mathsocsci.2023.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489623000781
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2023.09.003?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. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    2. David Pérez-Castrillo & Marilda Sotomayor, 2017. "The outcome of competitive equilibrium rules in buyer–seller markets when the agents play strategically," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 99-119, June.
    3. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    4. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
    5. 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.
    6. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    7. David Pérez-Castrillo & Marilda Sotomayor, 2013. "Two Folk Manipulability Theorems in the General One-to-one Two-sided Matching Markets with Money," Working Papers 681, Barcelona School of Economics.
    8. Caplin, Andrew & Leahy, John, 2014. "A graph theoretic approach to markets for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 112-122.
    9. van den Brink, René & Núñez, Marina & Robles, Francisco, 2021. "Valuation monotonicity, fairness and stability in assignment problems," Journal of Economic Theory, Elsevier, vol. 195(C).
    10. Tijs, S., 1981. "Bounds for the core of a game and the t-value," Other publications TiSEM ebc650eb-f25e-4802-ba0b-2, Tilburg University, School of Economics and Management.
    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. Yu Zhou & Shigehiro Serizawa, 2019. "Minimum price equilibrium in the assignment market," ISER Discussion Paper 1047, Institute of Social and Economic Research, Osaka University.
    2. Zhou, Yu & Serizawa, Shigehiro, 2023. "Multi-object auction design beyond quasi-linearity: Leading examples," Games and Economic Behavior, Elsevier, vol. 140(C), pages 210-228.
    3. Yu Zhou & Shigehiro Serizawa, 2020. "Serial Vickrey Mechanism," ISER Discussion Paper 1095, Institute of Social and Economic Research, Osaka University.
    4. Andersson, Tommy & Erlanson, Albin, 2013. "Multi-item Vickrey–English–Dutch auctions," Games and Economic Behavior, Elsevier, vol. 81(C), pages 116-129.
    5. Andersson, Tommy & Andersson, Christer & Andersson, Ola, 2010. "Sealed Bid Auctions vs. Ascending Bid Auctions: An Experimental Study," Working Papers 2010:17, Lund University, Department of Economics.
    6. , & ,, 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.
    7. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    8. Yu Zhou & Shigehiro Serizawa, 2016. "Strategy-Proofness and Efficiency for Non-quasi-linear Common-Tiered-Object Preferences: Characterization of Minimum Price Rule," ISER Discussion Paper 0971, Institute of Social and Economic Research, Osaka University.
    9. Caplin, Andrew & Leahy, John, 2020. "Comparative statics in markets for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 80-94.
    10. David Pérez-Castrillo & Marilda Sotomayor, 2013. "Two Folk Manipulability Theorems In The General One-To-Two-Sided Matching Markets With Money," Working Papers, Department of Economics 2013_01, University of São Paulo (FEA-USP).
    11. 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.
    12. Andersson, Tommy & Gudmundsson, Jens & Talman, Dolf & Yang, Zaifu, 2014. "A competitive partnership formation process," Games and Economic Behavior, Elsevier, vol. 86(C), pages 165-177.
    13. Andersson, Tommy & Andersson, Christer & Talman, Adolphus Johannes Jan, 2010. "Sets in Excess Demand in Ascending Auctions with Unit-Demand Bidders," Working Papers 2010:15, Lund University, Department of Economics, revised 28 Jun 2012.
    14. T. Andersson & C. Andersson & A. Talman, 2013. "Sets in excess demand in simple ascending auctions with unit-demand bidders," Annals of Operations Research, Springer, vol. 211(1), pages 27-36, December.
    15. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," ISER Discussion Paper 1001, Institute of Social and Economic Research, Osaka University.
    16. Tierney, Ryan, 2019. "The problem of multiple commons: A market design approach," Games and Economic Behavior, Elsevier, vol. 114(C), pages 1-27.
    17. Ingebretsen Carlson, Jim, 2016. "An Auction with Approximated Bidder Preferences - When an Auction has to be Quick," Working Papers 2016:12, Lund University, Department of Economics.
    18. Sotomayor, Marilda, 2007. "Core structure and comparative statics in a hybrid matching market," Games and Economic Behavior, Elsevier, vol. 60(2), pages 357-380, August.
    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. Tommy Andersson & Christer Andersson, 2012. "Properties of the DGS-Auction Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 113-133, February.

    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:matsoc:v:126:y:2023:i:c:p:1-12. 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/505565 .

    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.