IDEAS home Printed from https://ideas.repec.org/a/spr/eurjco/v6y2018i4d10.1007_s13675-018-0106-x.html
   My bibliography  Save this article

Robust bilateral trade with discrete types

Author

Listed:
  • Kamyar Kargar

    (Bilkent University)

  • Halil Ibrahim Bayrak

    (Bilkent University)

  • Mustafa Çelebi Pinar

    (Bilkent University)

Abstract

Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and $$\phi $$ ϕ -divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:eurjco:v:6:y:2018:i:4:d:10.1007_s13675-018-0106-x
    DOI: 10.1007/s13675-018-0106-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13675-018-0106-x
    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/s13675-018-0106-x?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. , & , & ,, 2006. "Optimal auctions with ambiguity," Theoretical Economics, Econometric Society, vol. 1(4), pages 411-438, December.
    2. Çağıl Koçyiğit & Halil I. Bayrak & Mustafa Ç. Pınar, 2018. "Robust auction design under multiple priors by linear and integer programming," Annals of Operations Research, Springer, vol. 260(1), pages 233-253, January.
    3. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    4. 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.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    7. 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.
    8. Aharon Ben-Tal & Dimitris Bertsimas & David B. Brown, 2010. "A Soft Robust Model for Optimization Under Ambiguity," Operations Research, INFORMS, vol. 58(4-part-2), pages 1220-1234, August.
    9. 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).
    10. Hagerty, Kathleen M. & Rogerson, William P., 1987. "Robust trading mechanisms," Journal of Economic Theory, Elsevier, vol. 42(1), pages 94-107, June.
    11. Bayrak, Halil I. & Pınar, Mustafa Ç., 2016. "Generalized second price auction is optimal for discrete types," Economics Letters, Elsevier, vol. 141(C), pages 35-38.
    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. Arie M. C. A. Koster & Michael Poss, 2018. "Special issue on: robust combinatorial optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 207-209, 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. Mustafa Ç. Pınar, 2018. "Robust trading mechanisms over 0/1 polytopes," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 845-860, October.
    2. Hagen, Martin, 2019. "Collusion-proof and fair auctions," Economics Letters, Elsevier, vol. 185(C).
    3. Sosung Baik & Sung-Ha Hwang, 2021. "Auction design with ambiguity: Optimality of the first-price and all-pay auctions," Papers 2110.08563, arXiv.org.
    4. Song, Yangwei, 2018. "Efficient Implementation with Interdependent Valuations and Maxmin Agents," Rationality and Competition Discussion Paper Series 92, CRC TRR 190 Rationality and Competition.
    5. Song, Yangwei, 2022. "Approximate Bayesian Implementation and Exact Maxmin Implementation: An Equivalence," Rationality and Competition Discussion Paper Series 362, CRC TRR 190 Rationality and Competition.
    6. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    7. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.
    8. 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).
    9. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    10. Rohit Lamba, 2022. "Efficiency with(out) intermediation in repeated bilateral trade," Papers 2202.04201, arXiv.org.
    11. Guo, Huiyi, 2019. "Mechanism design with ambiguous transfers: An analysis in finite dimensional naive type spaces," Journal of Economic Theory, Elsevier, vol. 183(C), pages 76-105.
    12. 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.
    13. De Castro, Luciano & Yannelis, Nicholas C., 2018. "Uncertainty, efficiency and incentive compatibility: Ambiguity solves the conflict between efficiency and incentive compatibility," Journal of Economic Theory, Elsevier, vol. 177(C), pages 678-707.
    14. Song, Yangwei, 2023. "Approximate Bayesian implementation and exact maxmin implementation: An equivalence," Games and Economic Behavior, Elsevier, vol. 139(C), pages 56-87.
    15. Kocherlakota, Narayana R. & Song, Yangwei, 2019. "Public goods with ambiguity in large economies," Journal of Economic Theory, Elsevier, vol. 182(C), pages 218-246.
    16. Kneeland, Terri, 2022. "Mechanism design with level-k types: Theory and an application to bilateral trade," Journal of Economic Theory, Elsevier, vol. 201(C).
    17. Song, Yangwei, 2018. "Efficient implementation with interdependent valuations and maxmin agents," Journal of Economic Theory, Elsevier, vol. 176(C), pages 693-726.
    18. Bodoh-Creed, Aaron L., 2012. "Ambiguous beliefs and mechanism design," Games and Economic Behavior, Elsevier, vol. 75(2), pages 518-537.
    19. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    20. Kos, Nenad & Messner, Matthias, 2013. "Extremal incentive compatible transfers," Journal of Economic Theory, Elsevier, vol. 148(1), pages 134-164.

    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:eurjco:v:6:y:2018:i:4:d:10.1007_s13675-018-0106-x. 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.