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Optimal equity auction with interdependent valuations

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  • Wang, Dazhong
  • Xu, Xinyi

Abstract

This study considers a seller using an equity auction to sell an indivisible asset for which bidders have interdependent valuations. First, we introduce bidders’ conditional virtual valuations for this setting, and identify sufficient conditions for conditional virtual valuations’ monotonicity and single-crossing property. Then, we characterize the optimal equity mechanism, which is ex post incentive compatible and individually rational. In general symmetric case, English equity auction or two-round sealed bid equity auction with an endogenous take-it-or-leave-it contract can implement the optimal ex post equity auction; in asymmetric case, English auction with an endogenous discriminatory equity contract could be constructed for the implementation of the optimal ex post equity auction under certain conditions.

Suggested Citation

  • Wang, Dazhong & Xu, Xinyi, 2022. "Optimal equity auction with interdependent valuations," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    • Handle: RePEc:eee:mateco:v:100:y:2022:i:c:s0304406821001701
    DOI: 10.1016/j.jmateco.2021.102623
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    1. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-194, March.
    2. Ilya Segal, 2003. "Optimal Pricing Mechanisms with Unknown Demand," American Economic Review, American Economic Association, vol. 93(3), pages 509-529, June.
    3. Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, vol. 55(1), pages 69-94, January.
    4. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-1090, October.
    5. Hansen, Robert G, 1985. "Auctions with Contingent Payments," American Economic Review, American Economic Association, vol. 75(4), pages 862-865, September.
    6. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    7. John G. Riley, 1988. "Ex Post Information in Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(3), pages 409-429.
    8. 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.
    9. Dubra, Juan & Echenique, Federico & Manelli, Alejandro M., 2009. "English auctions and the Stolper-Samuelson theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 825-849, March.
    10. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    11. 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.
    12. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    13. Luciano De Castro, 2010. "Affiliation, Equilibrium Existence and Revenue Ranking of Auctions," Discussion Papers 1530, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    15. Birulin, Oleksii & Izmalkov, Sergei, 2011. "On efficiency of the English auction," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1398-1417, July.
    16. Perry, Motty & Wolfstetter, Elmar & Zamir, Shmuel, 2000. "A Sealed-Bid Auction That Matches the English Auction," Games and Economic Behavior, Elsevier, vol. 33(2), pages 265-273, November.
    17. 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.
    18. Hernando-Veciana, Angel & Michelucci, Fabio, 2018. "Inefficient rushes in auctions," Theoretical Economics, Econometric Society, vol. 13(1), January.
    19. Liu, Tingjun & Bernhardt, Dan, 2019. "Optimal equity auctions with two-dimensional types," Journal of Economic Theory, Elsevier, vol. 184(C).
    20. Gregor Andrade & Mark Mitchell & Erik Stafford, 2001. "New Evidence and Perspectives on Mergers," Journal of Economic Perspectives, American Economic Association, vol. 15(2), pages 103-120, Spring.
    21. Sandro Brusco & Giuseppe Lopomo & David T. Robinson & S. Viswanathan, 2007. "Efficient Mechanisms For Mergers And Acquisitions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 995-1035, August.
    22. Motty Perry & Philip J. Reny, 2002. "An Efficient Auction," Econometrica, Econometric Society, vol. 70(3), pages 1199-1212, May.
    23. Kenneth Hendricks & Joris Pinkse & Robert H. Porter, 2003. "Empirical Implications of Equilibrium Bidding in First-Price, Symmetric, Common Value Auctions," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 115-145.
    24. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    25. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
    26. Liu, Tingjun, 2016. "Optimal equity auctions with heterogeneous bidders," Journal of Economic Theory, Elsevier, vol. 166(C), pages 94-123.
    27. Alexander S. Gorbenko & Andrey Malenko, 2014. "Strategic and Financial Bidders in Takeover Auctions," Journal of Finance, American Finance Association, vol. 69(6), pages 2513-2555, December.
    28. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    29. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
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