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arXiv · 1310.0038

The Unit-Demand Envy-Free Pricing Problem

Cristina G. Fernandes·Carlos E. Ferreira·Álvaro J. P. Franco·Rafael C. S. Schouery
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Abstract

We consider the unit-demand envy-free pricing problem, which is a unit-demand auction where each bidder receives an item that maximizes his utility, and the goal is to maximize the auctioneer's profit. This problem is NP-hard and unlikely to be in APX. We present four new MIP formulations for it and experimentally compare them to a previous one due to Shioda, Tunçel, and Myklebust. We describe three models to generate different random instances for general unit-demand auctions, that we designed for the computational experiments. Each model has a nice economic interpretation. Aiming approximation results, we consider the variant of the problem where the item prices are restricted to be chosen from a geometric series, and prove that an optimal solution for this variant has value that is a fraction (depending on the series used) of the optimal value of the original problem. So this variant is also unlikely to be in APX.

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Cristina G. Fernandes, Carlos E. Ferreira, Álvaro J. P. Franco, Rafael C. S. Schouery. 2013-09-30. The Unit-Demand Envy-Free Pricing Problem. https://arxiv.org/abs/1310.0038

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