IDEAS home Printed from https://ideas.repec.org/p/unm/umagsb/2013025.html
   My bibliography  Save this paper

The bilateral trade model in a discrete setting

Author

Listed:
  • Flesch, J.

    (Quantitative Economics)

  • Schröder, M.J.W.

    (Quantitative Economics)

  • Vermeulen, A.J.

    (Quantitative Economics)

Abstract

We consider a bilateral trade model in which both players have a finite number of possible valuations. The seller's valuation and the buyer's valuation for the object are private information, but the independent beliefs about these valuations are common knowledge. In this setting, we provide a characterization of the set of interim individually rational-implementable trading rules, analogous to the result of Myerson and Satterthwaite [1983]. Thereafter, we derive necessary conditions for incentive compatible and ex post individually rational direct mechanisms. For the special class of corner mechanisms with discrete uniform beliefs, we characterize the set of ex post individually rational-implementable trading rules. In this context it is also shown that ex post efficiency can only be achieved if the number of different valuations is small. The maximal number of different valuations for which efficiency is still possible depends on the prior probability distribution of valuations.

Suggested Citation

  • Flesch, J. & Schröder, M.J.W. & Vermeulen, A.J., 2013. "The bilateral trade model in a discrete setting," Research Memorandum 025, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2013025
    DOI: 10.26481/umagsb.2013025
    as

    Download full text from publisher

    File URL: https://cris.maastrichtuniversity.nl/ws/files/1682576/guid-4dd6c6c5-4587-4dba-9019-3594f3105a08-ASSET1.0.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.26481/umagsb.2013025?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
    ---><---

    References listed on IDEAS

    as
    1. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-1090, October.
    2. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    3. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    4. Hagerty, Kathleen M. & Rogerson, William P., 1987. "Robust trading mechanisms," Journal of Economic Theory, Elsevier, vol. 42(1), pages 94-107, June.
    5. Matsuo, Toshihide, 1989. "On incentive compatible, individually rational, and ex post efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 49(1), pages 189-194, October.
    6. Gresik, Thomas A., 1991. "Efficient bilateral trade with statistically dependent beliefs," Journal of Economic Theory, Elsevier, vol. 53(1), pages 199-205, February.
    7. Thomas A. Gresik & Mark A. Satterthwaite, 1983. "The Number of Traders Required to Make a Market Competitive: The Beginnings of a Theory," Discussion Papers 551, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Gresik, Thomas A., 1991. "Ex ante efficient, ex post individually rational trade," Journal of Economic Theory, Elsevier, vol. 53(1), pages 131-145, February.
    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. Kamyar Kargar & Halil Ibrahim Bayrak & Mustafa Çelebi Pinar, 2018. "Robust bilateral trade with discrete types," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 367-393, December.

    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. Flesch, János & Schröder, Marc & Vermeulen, Dries, 2016. "Implementable and ex-post IR rules in bilateral trading with discrete values," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 68-75.
    2. Olivier Compte & Philippe Jehiel, 2009. "Veto Constraint in Mechanism Design: Inefficiency with Correlated Types," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 182-206, February.
    3. Crawford, Vincent P., 2021. "Efficient mechanisms for level-k bilateral trading," Games and Economic Behavior, Elsevier, vol. 127(C), pages 80-101.
    4. Saran, Rene, 2011. "Bilateral trading with naive traders," Games and Economic Behavior, Elsevier, vol. 72(2), pages 544-557, June.
    5. Rohit Lamba, 2022. "Efficiency with(out) intermediation in repeated bilateral trade," Papers 2202.04201, arXiv.org.
    6. Kneeland, Terri, 2022. "Mechanism design with level-k types: Theory and an application to bilateral trade," Journal of Economic Theory, Elsevier, vol. 201(C).
    7. Simon Loertscher & Andras Niedermayer, 2012. "Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation," Department of Economics - Working Papers Series 1162, The University of Melbourne.
    8. Gottardi, Piero & Mezzetti, Claudio, 2020. "Mediation Design," The Warwick Economics Research Paper Series (TWERPS) 1248, University of Warwick, Department of Economics.
    9. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225, Elsevier.
    10. Steven J. Brams & Todd R. Kaplan & D. Marc Kilgour, 2015. "A Simple Bargaining Mechanism that Elicits Truthful Reservation Prices," Group Decision and Negotiation, Springer, vol. 24(3), pages 401-413, May.
    11. William P. Barnett & Daniel A. Levinthal, 2017. "Special Issue Introduction: Evolutionary Logics of Strategy and Organization," Strategy Science, INFORMS, vol. 2(1), pages 1-1, March.
    12. Blumrosen, Liad & Dobzinski, Shahar, 2021. "(Almost) efficient mechanisms for bilateral trading," Games and Economic Behavior, Elsevier, vol. 130(C), pages 369-383.
    13. Stefano Galavotti, 2008. "On Efficient Trading Mechanisms with Ex-Post Individually Rational Traders," Working Papers 161, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    14. Kadan, Ohad, 2007. "Equilibrium in the two-player, k-double auction with affiliated private values," Journal of Economic Theory, Elsevier, vol. 135(1), pages 495-513, July.
    15. Loertscher, Simon & Marx, Leslie M., 2020. "Asymptotically optimal prior-free clock auctions," Journal of Economic Theory, Elsevier, vol. 187(C).
    16. Soumendu Sarkar, 2022. "Strategyproof and Budget Balanced Mechanisms for Assembly," Working papers 320, Centre for Development Economics, Delhi School of Economics.
    17. Bichler, Martin & Kohring, Nils & Oberlechner, Matthias & Pieroth, Fabian R., 2023. "Learning equilibrium in bilateral bargaining games," European Journal of Operational Research, Elsevier, vol. 311(2), pages 660-678.
    18. Peter Cramton, 1985. "Sequential Bargaining Mechanisms," Papers of Peter Cramton 85roth, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
    19. Luyi Yang & Laurens Debo & Varun Gupta, 2017. "Trading Time in a Congested Environment," Management Science, INFORMS, vol. 63(7), pages 2377-2395, July.
    20. Thomas A. Gresik & Mark A. Satterthwaite, 1985. "The Rate at Which a Simple Market Becomes Efficient as the Number of Traders Increases: An Asymptotic Result for Optimal Trading Mechanisms," Discussion Papers 641, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

    More about this item

    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:unm:umagsb:2013025. 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: Andrea Willems or Leonne Portz (email available below). General contact details of provider: https://edirc.repec.org/data/meteonl.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.