Issue: 2018/Vol.28/No.1, Pages 95-115
AN APPROXIMATION ALGORITHM FOR MULTI-UNIT AUCTIONS: NUMERICAL AND SUBJECT EXPERIMENTS
Satoshi Takahashi
, Yoichi Izunaga, Naoki Watanabe
Cite as: S. Takahashi, Y. Izunaga, N. Watanabe. An approximation algorithm for multi-unit auctions: numerical and subject experiments. Operations Research and Decisions 2018: 28(1), 95-115. DOI 10.5277/ord180105
Abstract
In multi-unit auctions for a single item, the Vickrey–Clarke–Groves mechanism (VCG) attains allocative efficiency but suffers from its computational complexity. Takahashi and Shigeno thus proposed a greedy based approximation algorithm (GBA). In a subject experiment there was truly a difference in efficiency rate but no significant difference in seller’s revenue between GBA and VCG. It is not clear in theory whether each bidder will submit his or her true unit valuations in GBA. We show, however, that in a subject experiment there was no significant difference in the number of bids that obey “almost” truth-telling between GBA and VCG. As for individual bidding behavior, GBA and VCG show a sharp contrast when a human bidder competes against machine bidders; underbidding was observed in GBA, while overbidding was observed in VCG. Some results in a numerical experiment are also provided prior to reporting those observations.
Keywords: multi-unit auctions, approximation algorithm, experiment
Received: 12 November 2018 Accepted: 13 April 2018