Winner determination in geometrical combinatorial auctions

Bart Vangerven, Dries R. Goossens and Frits C.R. Spieksma

European Journal of Operational Research, 2017, vol. 258, issue 1, 254-263

Abstract: We consider auctions of items that can be arranged in rows. Examples of such a setting appear in allocating pieces of land for real estate development, or seats in a theater or stadium. The objective is, given bids on subsets of items, to find a subset of bids that maximizes auction revenue (often referred to as the winner determination problem). We describe a dynamic programing algorithm which, for a k-row problem with connected and gap-free bids, solves the winner determination problem in polynomial time. We study the complexity for bids in a grid, complementing known results in literature. Additionally, we study variants of the geometrical winner determination setting. We provide a NP-hardness proof for the 2-row setting with gap-free bids. Finally, we extend this dynamic programing algorithm to solve the case where bidders submit connected, but not necessarily gap-free bids in a 2-row and a 3-row problem.

Keywords: Auctions; Dynamic programing; Winner determination problem; Complexity; Rows (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:258:y:2017:i:1:p:254-263

DOI: 10.1016/j.ejor.2016.08.037

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