IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v58y2022i1d10.1007_s00355-021-01351-w.html
   My bibliography  Save this article

Optimal revenue-sharing mechanisms with seller commitment to ex-post effort

Author

Listed:
  • Xun Chen

    (Sun Yat-sen University)

  • Shanmin Li

    (Sun Yat-sen University)

  • Dazhong Wang

    (Nanjing University)

Abstract

This study considers the characterization and implementation of the optimal revenue-sharing mechanism when the seller’s ex-post effort affects the final outcome. In the optimal revenue-sharing mechanism with the seller’s full commitment to effort exertion, the seller commits to the first-best effort. Under the regularity condition guaranteed by the assumption of log-concave density, the optimal mechanism selects the bidder with the highest type, provided that the associated virtual surplus with the seller’s commitment to the first-best effort is positive. A first-price share auction with an appropriate reserve share and an effort commitment scheme can implement the optimal revenue-sharing mechanism. However, a second-price share auction might fail for implementation, such as in a case with two bidders and a uniform type distribution. Lastly, we introduce a sealed-bid share auction called the first-second price share auction, which can implement the optimal mechanism in dominant strategy.

Suggested Citation

  • Xun Chen & Shanmin Li & Dazhong Wang, 2022. "Optimal revenue-sharing mechanisms with seller commitment to ex-post effort," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 141-159, January.
    • Handle: RePEc:spr:sochwe:v:58:y:2022:i:1:d:10.1007_s00355-021-01351-w
    DOI: 10.1007/s00355-021-01351-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-021-01351-w
    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/s00355-021-01351-w?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. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Byoung Jun & Elmar Wolfstetter, 2014. "Security bid auctions for agency contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 18(4), pages 289-319, December.
    3. Tingjun Liu & Dan Bernhardt, 2021. "Rent Extraction with Securities Plus Cash," Journal of Finance, American Finance Association, vol. 76(4), pages 1869-1912, August.
    4. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    5. Peter M. DeMarzo & Ilan Kremer & Andrzej Skrzypacz, 2005. "Bidding with Securities: Auctions and Security Design," American Economic Review, American Economic Association, vol. 95(4), pages 936-959, September.
    6. Sun, Wuqin & Wang, Dazhong & Zhang, Yue, 2018. "Optimal profit sharing mechanisms with type-dependent outside options," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 57-66.
    7. Shimon Kogan & John Morgan, 2010. "Securities Auctions under Moral Hazard: An Experimental Study," Review of Finance, European Finance Association, vol. 14(3), pages 477-520.
    8. Riordan, Michael H. & Sappington, David E. M., 1988. "Optimal contracts with public ex post information," Journal of Economic Theory, Elsevier, vol. 45(1), pages 189-199, June.
    9. Liu, Tingjun, 2016. "Optimal equity auctions with heterogeneous bidders," Journal of Economic Theory, Elsevier, vol. 166(C), pages 94-123.
    10. Liu, Tingjun & Bernhardt, Dan, 2019. "Optimal equity auctions with two-dimensional types," Journal of Economic Theory, Elsevier, vol. 184(C).
    11. Bester, Helmut & Strausz, Roland, 2001. "Contracting with Imperfect Commitment and the Revelation Principle: The Single Agent Case," Econometrica, Econometric Society, vol. 69(4), pages 1077-1098, July.
    12. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    13. Dixit, Avinash K, 1987. "Strategic Behavior in Contests," American Economic Review, American Economic Association, vol. 77(5), pages 891-898, December.
    14. Skrzypacz, Andrzej, 2013. "Auctions with contingent payments — An overview," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 666-675.
    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. Sun, Wuqin & Wang, Dazhong & Zhang, Yue, 2018. "Optimal profit sharing mechanisms with type-dependent outside options," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 57-66.
    2. Wong, Tak-Yuen & Wong, Ho-Po Crystal, 2023. "Securities auctions with pre-project information management," International Journal of Industrial Organization, Elsevier, vol. 88(C).
    3. Wang, Dazhong & Xu, Xinyi, 2022. "Optimal equity auction with interdependent valuations," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    4. Liu, Tingjun & Bernhardt, Dan, 2019. "Optimal equity auctions with two-dimensional types," Journal of Economic Theory, Elsevier, vol. 184(C).
    5. Hernandez-Chanto, Allan & Fioriti, Andres, 2019. "Bidding securities in projects with negative externalities," European Economic Review, Elsevier, vol. 118(C), pages 14-36.
    6. Liu, Tingjun, 2016. "Optimal equity auctions with heterogeneous bidders," Journal of Economic Theory, Elsevier, vol. 166(C), pages 94-123.
    7. Zachary Breig & Allan Hernández-Chanto & Declan Hunt, 2022. "Experimental Auctions with Securities," Discussion Papers Series 657, School of Economics, University of Queensland, Australia.
    8. Jyh-Bang Jou & Charlene Tan Lee, 2023. "Design of the contingent royalty rate as related to the type of investment," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-25, December.
    9. Pan, Lijun & Wang, Dazhong, 2021. "The broker-optimal bilateral trading mechanisms with linear contracts," Economics Letters, Elsevier, vol. 208(C).
    10. Wang, Dazhong & Xu, Xinyi & Zeng, Xianjie, 2023. "Comparisons of standard royalty auctions with seller post-auction effort," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    11. Andrés Fioriti & Allan Hernandez-Chanto, 2022. "Leveling the Playing Field for Risk-Averse Agents in Security-Bid Auctions," Management Science, INFORMS, vol. 68(7), pages 5441-5463, July.
    12. Di Corato, Luca & Dosi, Cesare & Moretto, Michele, 2015. "Multidimensional auctions for long-term procurement contracts under the threat of early exit: the case of conservation auctions," Working Paper Series 2015:6, Swedish University of Agricultural Sciences, Department Economics.
    13. Bernhardt, Dan & Liu, Tingjun & Sogo, Takeharu, 2020. "Costly auction entry, royalty payments, and the optimality of asymmetric designs," Journal of Economic Theory, Elsevier, vol. 188(C).
    14. Tingjun Liu & Dan Bernhardt, 2021. "Rent Extraction with Securities Plus Cash," Journal of Finance, American Finance Association, vol. 76(4), pages 1869-1912, August.
    15. Sogo, Takeharu, 2017. "Effects of seller’s information disclosure in equity auctions requiring post-auction investment," International Journal of Industrial Organization, Elsevier, vol. 55(C), pages 166-181.
    16. Takeharu Sogo & Dan Bernhardt & Tingjun Liu, 2016. "Endogenous Entry to Security-Bid Auctions," American Economic Review, American Economic Association, vol. 106(11), pages 3577-3589, November.
    17. Byoung Jun & Elmar Wolfstetter, 2014. "Security bid auctions for agency contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 18(4), pages 289-319, December.
    18. Wang, Dazhong & Xu, Xinyi & Zeng, Xianjie, 2022. "Bid signaling in first-price royalty auction," Economics Letters, Elsevier, vol. 216(C).
    19. Di Corato, Luca & Dosi, Cesare & Moretto, Michele, 2018. "Multidimensional auctions for long-term procurement contracts with early-exit options: The case of conservation contracts," European Journal of Operational Research, Elsevier, vol. 267(1), pages 368-380.
    20. Diego Carrasco-Novoa & Allan Hernández-Chanto, 2022. "Competing Sellers in Security-Bid Auctions under Risk-Averse Bidders," Discussion Papers Series 655, School of Economics, University of Queensland, Australia.

    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:spr:sochwe:v:58:y:2022:i:1:d:10.1007_s00355-021-01351-w. 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.