IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2509.20790.html
   My bibliography  Save this paper

B\"orgers's Open Question Resolved

Author

Listed:
  • Siyang Xiong

Abstract

Focusing on stochastic finite-action mechanisms, we study implementation in undominated strategies and iteratively undominated strategies. We establish both possibility and impossibility results that resolve the open question in B\"orgers (1995). Contrary to the conventional understanding that positive results on Nash implementation need separability, quasilinearity, or infinite action sets, we provide -- to our knowledge -- the first positive result beyond those demanding assumptions.

Suggested Citation

  • Siyang Xiong, 2025. "B\"orgers's Open Question Resolved," Papers 2509.20790, arXiv.org.
    • Handle: RePEc:arx:papers:2509.20790
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2509.20790
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404, World Scientific Publishing Co. Pte. Ltd..
    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. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    2. Kunimoto, Takashi & Serrano, Roberto, 2011. "A new necessary condition for implementation in iteratively undominated strategies," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2583-2595.
    3. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404, World Scientific Publishing Co. Pte. Ltd..
    4. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    5. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    6. Chen, Yi-Chun & Sun, Yifei, 2015. "Full implementation in backward induction," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 71-76.
    7. Takashi Kunimoto & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Economics and Statistics Working Papers 4-2020, Singapore Management University, School of Economics.
    8. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    9. , J. & ,, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    10. Kimya, Mert, 2017. "Nash implementation and tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 102(C), pages 138-146.
    11. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    12. Xiong, Siyang, 2023. "Rationalizable implementation of social choice functions: complete characterization," Theoretical Economics, Econometric Society, vol. 18(1), January.
    13. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    14. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
    15. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    16. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
    17. Ritesh Jain & Michele Lombardi & Antonio Penta, 2024. "Strategically robust implementation," Economics Working Papers 1893, Department of Economics and Business, Universitat Pompeu Fabra.
    18. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2021. "Rationalizable implementation in finite mechanisms," Games and Economic Behavior, Elsevier, vol. 129(C), pages 181-197.
    19. Michele Lombardi & Ritesh Jain & Antonio Penta, 2024. "Strategically Robust Implementation," Working Papers 1461, Barcelona School of Economics.
    20. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.

    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:arx:papers:2509.20790. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.