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Pricing Problems with Buyer Preselection

Authors Vittorio Bilò, Michele Flammini, Gianpiero Monaco, Luca Moscardelli

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Vittorio Bilò
  • Univ. of Salento, Lecce, Italy
Michele Flammini
  • GSSI Institute, L'Aquila, Italy & Univ. of L'Aquila, L'Aquila, Italy
Gianpiero Monaco
  • Univ. of L'Aquila, L'Aquila Italy
Luca Moscardelli
  • Univ. of Chieti-Pescara, Pescara, Italy

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Vittorio Bilò, Michele Flammini, Gianpiero Monaco, and Luca Moscardelli. Pricing Problems with Buyer Preselection. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.MFCS.2018.47

Abstract

We investigate the problem of preselecting a subset of buyers participating in a market so as to optimize the performance of stable outcomes. We consider four scenarios arising from the combination of two stability notions, item and bundle envy-freeness, with the two classical objective functions, i.e., the social welfare and the seller's revenue. When adopting the notion of item envy-freeness, we prove that, for both the two objective functions, the problem cannot be approximated within n^(1-epsilon) for any epsilon >0, and provide tight or nearly tight approximation algorithms. We also prove that maximizing the seller's revenue is NP-hard even for a single buyer, thus closing an open question. Under bundle envy-freeness, instead, we show how to transform in polynomial time any stable outcome for a market involving only a subset of buyers to a stable one for the whole market without worsening its performance, both for the social welfare and the seller's revenue. Finally, we consider multi-unit markets, where all items are of the same type and are assigned the same price. For this specific case, we show that buyer preselection can improve the performance of stable outcomes in all of the four considered scenarios, and we design corresponding approximation algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational pricing and auctions
Keywords
  • Pricing problems
  • Envy-freeness
  • Revenue maximization
  • Social Welfare maximization

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Related Versions

  • A two-page extended abstract [V. Bilò et al., 2018] of a preliminary version of this paper appeared in the proceedings of AAMAS 2018.

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