Multi-Item Vickery-English-Dutch Auctions

Assuming that bidders wish to acquire at most one item, this paper defines a polynomial time multiitem 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 (J.K. Sankaran, Math. Soc. Sci. 28:143–150, 1994) and the Vickrey-Dutch auction (D. Mishra and D. Parkes, Games Econ. Behav. 66:326–347, 2009) as special cases. Several properties of this iterative auction are provided. It is, for example, demonstrated that the number of iterations from the starting prices to the VCG prices can be calculated using a measure based on the Chebyshev metric. By means of numerical experiments, it is showed that when the auctioneer knows the bidders' 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. In fact, it follows the theoretically shortest path in 63 percent of the investigated problems.