Impact of Dependence Among Valuations on Expected Revenue in Auctions

SYNOPTIC ABSTRACT

This work studies the dependence and asymmetry among valuations in sealed-bid auctions with private valuations. In the framework of valuations with Archimedean copulas, it is found that a stronger positive dependence stochastically enhances the final price and lowers the winner’s expected rent in the two-bidder, second-price auction, and the degree of positive dependence has an opposite impact on the final price in the first-price auction. In the context of multiple bidders with valuations having proportional reversed hazards, reducing the asymmetry among negatively dependent valuations is proved to enhance the final price in the second-price auction, and a stronger (weaker) positive dependence along with less (more) asymmetry on valuations is showed to stochastically lower (increase) the final price in the first-price auction.

Key Words and Phrases::

• Archimedean copula
• Kendall’s tau
• majorization
• superadditive