IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Bilateral k+1-price auctions with asymmetric shares and values

  • Wasser, Cédric

We study a sealed-bid auction between two bidders with asymmetric independent private values. The two bidders own asymmetric shares in a partnership. The higher bidder buys the lower bidderʼs shares at a per-unit price that is a convex combination of the two bids. The weight of the lower bid is denoted by k∈[0,1]. We partially characterize equilibrium strategies and show that they are closely related to equilibrium strategies of two well-studied mechanisms: the double auction between a buyer and a seller and the first-price auction between two buyers (or two sellers). Combining results from those two branches of the literature enables us to prove equilibrium existence. Moreover, we find that there is a continuum of equilibria if k∈(0,1) whereas the equilibrium is unique if k∈{0,1}. Our approach also suggests a procedure for numerical simulations.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0899825613001176
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 82 (2013)
Issue (Month): C ()
Pages: 350-368

as
in new window

Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:350-368
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Sudipto Dasgupta & Kevin Tsui, 2004. "Auctions with cross-shareholdings," Economic Theory, Springer, vol. 24(1), pages 163-194, 07.
  2. Emiel Maasland & Sander Onderstal, 2003. "Auctions with Financial Externalities," Working Papers 2003.30, Fondazione Eni Enrico Mattei.
  3. Maxim Engers & Brian McManus, 2007. "Charity Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 953-994, 08.
  4. Peter Cramton & Robert Gibbons & Paul Klemperer, 1987. "Dissolving a Partnership Efficiently," Papers of Peter Cramton 87econ, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
  5. Kittsteiner, T. & De Frutos & M-A, 2004. "Efficient Partnership Dissolution under Buy/Sell Clauses," Econometric Society 2004 Latin American Meetings 314, Econometric Society.
  6. Jacob K. Goeree & Emiel Maasland & Sander Onderstal & John L. Turner, 2005. "How (Not) to Raise Money," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 897-926, August.
  7. Kittsteiner, Thomas, 2000. "Partnerships and Double Auctions with Interdependent Valuations," Sonderforschungsbereich 504 Publications 01-15, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  8. Athanassoglou, Stergios & Brams, Steven J. & Sethuraman, Jay, 2010. "A note on the inefficiency of bidding over the price of a share," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 191-195, November.
  9. Preston McAfee, R., 1992. "Amicable divorce: Dissolving a partnership with simple mechanisms," Journal of Economic Theory, Elsevier, vol. 56(2), pages 266-293, April.
  10. Jeremy Bulow & Ming Huang & Paul Klemperer, 1999. "Toeholds and Takeovers," Finance 9903005, EconWPA.
  11. Stefano Galavotti & Nozomu Muto & Daisuke Oyama, 2011. "On efficient partnership dissolution under ex post individual rationality," Economic Theory, Springer, vol. 48(1), pages 87-123, September.
  12. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-42, February.
  13. Chillemi, Ottorino, 2005. "Cross-owned firms competing in auctions," Games and Economic Behavior, Elsevier, vol. 51(1), pages 1-19, April.
  14. Moldovanu, Benny & Fieseler, Karsten & Kittsteiner, Thomas, 1999. "Partnerships, Lemons and Efficient Trade," Sonderforschungsbereich 504 Publications 01-18, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  15. de Frutos, M. Angeles, 2000. "Asymmetric Price-Benefits Auctions," Games and Economic Behavior, Elsevier, vol. 33(1), pages 48-71, October.
  16. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
  17. Engelbrecht-Wiggans Richard, 1994. "Auctions with Price-Proportional Benefits to Bidders," Games and Economic Behavior, Elsevier, vol. 6(3), pages 339-346, May.
  18. Lu, Jingfeng, 2012. "Optimal auctions with asymmetric financial externalities," Games and Economic Behavior, Elsevier, vol. 74(2), pages 561-575.
  19. Olivier, Bos, 2011. "Charitable asymmetric bidders," MPRA Paper 31877, University Library of Munich, Germany.
  20. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
  21. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
  22. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  23. Williams, Steven R., 1987. "Efficient performance in two agent bargaining," Journal of Economic Theory, Elsevier, vol. 41(1), pages 154-172, February.
  24. Leininger, W. & Linhart, P. B. & Radner, R., 1989. "Equilibria of the sealed-bid mechanism for bargaining with incomplete information," Journal of Economic Theory, Elsevier, vol. 48(1), pages 63-106, June.
  25. Fibich, Gadi & Gavish, Nir, 2011. "Numerical simulations of asymmetric first-price auctions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 479-495.
  26. Roger B. Myerson & Mark A. Satterthwaite, 1981. "Efficient Mechanisms for Bilateral Trading," Discussion Papers 469S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  27. Burkart, Mike, 1995. " Initial Shareholdings and Overbidding in Takeover Contests," Journal of Finance, American Finance Association, vol. 50(5), pages 1491-1515, December.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:350-368. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.