Debasis Mishra
ABSTRACT
de Vries et al. [3] show that if valuation function of each buyer satisfies gross substitutes condition, then we can design primal-dual auctions that implement the Vickrey-Clarke-Groves (VCG) outcome. But they require prices in these auctions to be non-linear and non-anonymous. In this note, we show that such a requirement is necessary. This means, if valuation function of each buyer satisfies gross substitutes, then there does not exist a primal-dual auction which will always converge to the VCG outcome if prices in the auction are (i) linear and non-anonymous, OR (ii) non-linear and anonymous.
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Cross Ref
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Index Terms
- Simple primal-dual auctions are not possible
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