Analysis and design for multi-unit online auctions

Abstract

By incorporating platform fees and bidders’ stochastic arrival process into the analysis of the multi-unit Vickrey auctions, we examine the performance of the two popular selling mechanisms (posted price and auction) on the Internet, characterize and derive the closed-form solution for the optimal lot-sizing policies. We show that the seller prefers auctions rather than posted price selling only when the valuation dispersion and the Web traffic are both sufficiently large. The theory also implies that there is no dominant selling mechanism. Since it is not always beneficial for the seller to auction more goods in a single auction, we further derive the optimal number of auction the seller should run and the optimal number of units to be sold in each auction. Moreover, we consider how to reconcile the conflict interests between the seller and the auction platform in single period and multi-period auctions respectively. Our main results indicate that, to decrease the listing fees, increase commission ratio and shorten the auction duration are all helpful for the platform to coordinate its interests with that of the seller.