**Tuesday, 15:45 - 16:10 h, Room: H 3027**

**Takahashi Satoshi**

2-approximation algorithms for the winner determination problem in VCG based single-item multi-unit auctions

**Coauthors: Yoichi Izunaga, Maiko Shigeno, Satoshi Takahashi, Naoki Watanabe**

**Abstract:**

This paper studies the winner determination problem in Vickrey-Clarke-Groves (VCG) based single-item multi-unit auctions: given a set of bids in such an auction, find an allocation of units of an item to bidders that maximizes the seller's revenue. (The seller can keep some units of the item.) This problem is known to be NP-hard. We thus propose two simple 2-approximation algorithms for the problem. One is a linear time algorithm and the other is a greedy algorithm.

Numerical experiments and human subject experiments were conducted to evaluate the computational efficiency and economic efficiency of these approximation algorithms.

Our results are as follows. (1) Approximate ratios of the algorithms are at least 95% in numerical experiments. (2) Under-bidding was observed in human subject experiments although the VCG mechanism theoretically induces bidders to tell their valuation truthfully.

Talk 2 of the contributed session Tue.3.H 3027

**"Applications and algorithms"** [...]

Cluster 7

**"Finance & economics"** [...]