Linear Programming and Vickrey Auctions
Professor Rakesh Vohra
John L. and Helen Kellogg Professor of Managerial
Ecomonics and Decision Science
Kellogg School of Management
Northwestern University
The Vickrey sealed bid auction occupies a central place in auction theory
because of its efficiency and incentive properties. Implementing the
auction requires the auctioneer to solve $n+1$ optimization problems,
where $n$ is the number of bidders.
In this talk we survey various environments (some old and some new)
where the payments bidders make under the Vickrey auction correspond
to dual variables in certain linear programs.
Thus, in these environments, at most two optimization problems must
be solved to determine the Vickrey outcome. Furthermore, primal-dual
algorithms for some of these linear programs give rise to ascending
auctions that implement the Vickrey outcome.
Based on joint work with:Sushil Bikhchandani, Sven de Vries, James Schummer