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Winner determination in geometrical combinatorial auctions

Author

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

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.

Suggested Citation

  • Vangerven, Bart & Goossens, Dries R. & Spieksma, Frits C.R., 2017. "Winner determination in geometrical combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 258(1), pages 254-263.
  • Handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:254-263
    DOI: 10.1016/j.ejor.2016.08.037
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    References listed on IDEAS

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    1. Babaioff, Moshe & Blumrosen, Liad, 2008. "Computationally-feasible truthful auctions for convex bundles," Games and Economic Behavior, Elsevier, vol. 63(2), pages 588-620, July.
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    6. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    7. Tobias Scheffel & Georg Ziegler & Martin Bichler, 2012. "On the impact of package selection in combinatorial auctions: an experimental study in the context of spectrum auction design," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 667-692, December.
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