Multi-item Vickrey-English-Dutch auctions

Assuming that bidders wish to acquire at most one item, this paper defines a polynomial time multi-item auction that locates the VCG prices in a finite number of iterations for any given starting prices. This auction is called the Vickrey-English-Dutch auction and it contains the Vickrey-English auction [Sankaran, J.K., 1994. On a dynamic auction mechanism for a bilateral assignment problem. Math. Soc. Sci. 28, 143-150] and the Vickrey-Dutch auction [Mishra, D., Parkes, D., 2009. Multi-item Vickrey-Dutch auctions. Games Econ. Behav. 66, 326-347] as special cases. By means of numerical experiments, it is showed that when the auctioneer knows the biddersʼ value distributions, the Vickrey-English-Dutch auction is weakly faster than the Vickrey-English auction and the Vickrey-Dutch auction in 89 percent and 99 percent, respectively, of the investigated problems. A greedy version of the Vickrey-English-Dutch auction is demonstrated to perform even better in the simulation studies.