Abstract
A simple example shows that equilibria can fail to exist in second price (Vickrey) and English auctions when there are both common and private components to bidders’ valuations and private information is held on both dimensions. The example shows that equilibrium only exists in the extremes of pure private and pure common values, and that existence in standard models is not robust to a slight perturbation.
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This is a revised version of Jackson (1999), where the implications of the example have been strengthened, and the discussion of its implications for the auctions literature has been updated. I thank Andy Postlewaite for encouraging me to resurrect this paper, Laurent Mathevet for helpful comments on an earlier draft, and Jeroen Swinkels for many valuable discussions of the subject. With fond memories of many long and fascinating discussions about mechanisms and market design, this is dedicated to the memory of Leo Hurwicz: an amazing man and researcher.
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Jackson, M.O. Non-existence of equilibrium in Vickrey, second-price, and English auctions. Rev Econ Design 13, 137–145 (2009). https://doi.org/10.1007/s10058-008-0059-2
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DOI: https://doi.org/10.1007/s10058-008-0059-2
Keywords
- Auction
- Equilibrium existence
- Nonexistence
- Vickrey auction
- Second-price auction
- English auction
- Multi-dimensional information