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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    5. 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.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Avinash Dixit, 2008. "Strategic Behavior in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 431-438, Springer.
    8. Skrzypacz, Andrzej, 2013. "Auctions with contingent payments — An overview," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 666-675.
    9. Tingjun Liu & Dan Bernhardt, 2021. "Rent Extraction with Securities Plus Cash," Journal of Finance, American Finance Association, vol. 76(4), pages 1869-1912, August.
    10. 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.
    11. Liu, Tingjun & Bernhardt, Dan, 2019. "Optimal equity auctions with two-dimensional types," Journal of Economic Theory, Elsevier, vol. 184(C).
    12. 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.
    13. 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.
    14. Liu, Tingjun, 2016. "Optimal equity auctions with heterogeneous bidders," Journal of Economic Theory, Elsevier, vol. 166(C), pages 94-123.
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