K-price Auctions: Revenue Inequalities, Utility Equivalence, and Competition in Auction Design†

This paper discusses revenue inequalities, utility equivalence, and a model of competition in auction design in symmetric equilibrium of k-price auctions, k ≥ 1, all in the setup of symmetric independent-private-value auctions. Our recommendation to organizers of auctions is to conduct k-price auctions, k ≥ 3 in environments in which buyers are risk-seeking. The recommendation is given both for, a setup in which each organizer is a monopolist, and for one of oligopolistic competition. 1.Introduction. Here we discuss the relevant literature and describe our main results. Every definition and theorem depends on particular assumptions. For simplicity we do not describe these (relatively common) assumptions in the introduction. A reader who wishes to quote our theorems should read the precise †First version (titled “Internet Auctions”): October 1997. This version was split to Monderer and Tennenholtz (2000), and to the manuscript: ”Internet Auctions: Are They Gamblers’ Attraction?”. The current version is a newer version of the later one with a new title. We are thankful for useful comments from the participants of the CS-economics seminar at Stanford University, the participants of the economics seminars at Tel-Aviv University, Mannheim University, and the University of Bonn, and the participants of the computer science seminar at the Weizmann Institute. We would also like to thank Haim Reisman, Yoav Shoham, Doron Sonsino, Hal Varian, and specially Shlomit Hon-Snir for helpful comments and discussions. Part of this research was supported by the Technion Fund for the Promotion of Research.