IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v88y2020i6p2629-2661.html
   My bibliography  Save this article

Mechanism Design With Aftermarkets: Cutoff Mechanisms

Author

Listed:
  • Piotr Dworczak

Abstract

I study a mechanism design problem in which a designer allocates a single good to one of several agents, and the mechanism is followed by an aftermarket—a post‐mechanism game played between the agent who acquired the good and third‐party market participants. The designer has preferences over final outcomes, but she cannot design the aftermarket. However, she can influence its information structure by publicly disclosing information elicited from the agents by the mechanism. I introduce a class of allocation and disclosure rules, called cutoff rules, that disclose information about the buyer's type only by revealing information about the realization of a random threshold (cutoff) that she had to outbid to win the object. When there is a single agent in the mechanism, I show that the optimal cutoff mechanism offers full privacy to the agent. In contrast, when there are multiple agents, the optimal cutoff mechanism may disclose information about the winner's type; I provide sufficient conditions for optimality of simple designs. I also characterize aftermarkets for which restricting attention to cutoff mechanisms is without loss of generality in a subclass of all feasible mechanisms satisfying additional conditions.

Suggested Citation

  • Piotr Dworczak, 2020. "Mechanism Design With Aftermarkets: Cutoff Mechanisms," Econometrica, Econometric Society, vol. 88(6), pages 2629-2661, November.
    • Handle: RePEc:wly:emetrp:v:88:y:2020:i:6:p:2629-2661
    DOI: 10.3982/ECTA15768
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA15768
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA15768?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. Pavan, Alessandro & Calzolari, Giacomo, 2009. "Sequential contracting with multiple principals," Journal of Economic Theory, Elsevier, vol. 144(2), pages 503-531, March.
    2. Back, Kerry & Liu, Ruomeng & Teguia, Alberto, 2020. "Signaling in OTC Markets: Benefits and Costs of Transparency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 47-75, February.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    4. Goeree, Jacob K., 2003. "Bidding for the future: signaling in auctions with an aftermarket," Journal of Economic Theory, Elsevier, vol. 108(2), pages 345-364, February.
    5. Bergemann, Dirk & Wambach, Achim, 2015. "Sequential information disclosure in auctions," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 1074-1095.
    6. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1996. "How (Not) to Sell Nuclear Weapons," American Economic Review, American Economic Association, vol. 86(4), pages 814-829, September.
    7. Das Varma, Gopal, 2003. "Bidding for a process innovation under alternative modes of competition," International Journal of Industrial Organization, Elsevier, vol. 21(1), pages 15-37, January.
    8. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    9. Hafalir, Isa & Krishna, Vijay, 2009. "Revenue and efficiency effects of resale in first-price auctions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 589-602, September.
    10. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    11. Haile, Philip A., 2003. "Auctions with private uncertainty and resale opportunities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 72-110, January.
    12. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, October.
    13. Engelbrecht-Wiggans, Richard & Kahn, Charles M., 1991. "Protecting the winner : Second-price versus oral auctions," Economics Letters, Elsevier, vol. 35(3), pages 243-248, March.
    14. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    15. Dworczak, Piotr & Zhang, Anthony Lee, 2017. "Implementability, Walrasian equilibria, and efficient matchings," Economics Letters, Elsevier, vol. 153(C), pages 57-60.
    16. Mohammad Akbarpour & Shengwu Li, 2020. "Credible Auctions: A Trilemma," Econometrica, Econometric Society, vol. 88(2), pages 425-467, March.
    17. Matthews, Steven A, 1984. "On the Implementability of Reduced Form Auctions," Econometrica, Econometric Society, vol. 52(6), pages 1519-1522, November.
    18. Kos, Nenad & Messner, Matthias, 2013. "Extremal incentive compatible transfers," Journal of Economic Theory, Elsevier, vol. 148(1), pages 134-164.
    19. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    20. Stephan Lauermann & Gábor Virág, 2012. "Auctions in Markets: Common Outside Options and the Continuation Value Effect," American Economic Journal: Microeconomics, American Economic Association, vol. 4(4), pages 107-130, November.
    21. Zhang, Jun & Wang, Ruqu, 2013. "Optimal mechanism design with resale via bargaining," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2096-2123.
    22. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
    23. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    24. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
    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. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints: A Revision," Discussion Papers 21/05, Department of Economics, University of York.
    3. Xu Lang & Zaifu Yang, 2023. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 23/02, Department of Economics, University of York.
    4. Loertscher, Simon & Marx, Leslie M., 2020. "Asymptotically optimal prior-free clock auctions," Journal of Economic Theory, Elsevier, vol. 187(C).
    5. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    6. Xu Lang, 2022. "Reduced-Form Allocations with Complementarity: A 2-Person Case," Papers 2202.06245, arXiv.org, revised Feb 2022.
    7. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 21/04, Department of Economics, University of York.
    8. Chen, Yi-Chun & Li, Jiangtao, 2018. "Revisiting the foundations of dominant-strategy mechanisms," Journal of Economic Theory, Elsevier, vol. 178(C), pages 294-317.
    9. Goeree, Jacob K. & Kushnir, Alexey, 2016. "Reduced form implementation for environments with value interdependencies," Games and Economic Behavior, Elsevier, vol. 99(C), pages 250-256.
    10. Bernard Lebrun, 2010. "First‐price auctions with resale and with outcomes robust to bid disclosure," RAND Journal of Economics, RAND Corporation, vol. 41(1), pages 165-178, March.
    11. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
    12. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2021. "A Theory of Auctions with Endogenous Valuations," Journal of Political Economy, University of Chicago Press, vol. 129(4), pages 1011-1051.
    13. Onur A. Koska & Ilke Onur & Frank Stähler, 2018. "The scope of auctions in the presence of downstream interactions and information externalities," Journal of Economics, Springer, vol. 125(2), pages 107-136, October.
    14. Rey, Patrick & Salant, David, 2017. "Allocating essential inputs," TSE Working Papers 17-820, Toulouse School of Economics (TSE), revised Jun 2019.
    15. Xu Lang, 2023. "A Belief-Based Characterization of Reduced-Form Auctions," Papers 2307.04070, arXiv.org.
    16. Erya Yang, 2021. "Reduced-form mechanism design and ex post fairness constraints," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 269-293, October.
    17. Xu Lang, 2022. "Reduced-form budget allocation with multiple public alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 335-359, August.
    18. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    19. Marek Pycia & Peter Troyan, 2023. "A Theory of Simplicity in Games and Mechanism Design," Econometrica, Econometric Society, vol. 91(4), pages 1495-1526, July.
    20. Hernando-Veciana, Ángel & Michelucci, Fabio, 2014. "On the optimality of not allocating," Economics Letters, Elsevier, vol. 125(2), pages 233-235.

    More about this item

    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:wly:emetrp:v:88:y:2020:i:6:p:2629-2661. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.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.