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Approximation algorithms for the selling with preference

Author

Listed:
  • Pan Li

    (Hebei University)

  • Qiang Hua

    (Hebei University)

  • Zhijun Hu

    (Guizhou University)

  • Hing-Fung Ting

    (The University of Hong Kong)

  • Yong Zhang

    (Chinese Academy of Sciences)

Abstract

We consider the market mechanism to sell two types of products, A and B, to a set of buyers $$I=\{1, 2, \ldots , n\}$$ I = { 1 , 2 , … , n } . The amounts of products are $$m_A$$ m A and $$m_B$$ m B respectively. Each buyer i has his information including the budget, the preference and the utility function. On collecting the information from all buyers, the market maker determines the price of each product and allocates some amount of product to each buyer. The objective of the market maker is designing a mechanism to maximize the total utility of the buyers in satisfying the semi market equilibrium. In this paper, we show that this problem is NP-hard and give an iterative algorithm with the approximation ratio 1.5. Moreover, we introduce a PTAS for the problem, which is an ( $$1+\epsilon $$ 1 + ϵ )-approximation algorithm with the running time $$O(2^{1/\epsilon }+n\log n)$$ O ( 2 1 / ϵ + n log n ) for any positive $$\epsilon $$ ϵ .

Suggested Citation

  • Pan Li & Qiang Hua & Zhijun Hu & Hing-Fung Ting & Yong Zhang, 2020. "Approximation algorithms for the selling with preference," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 366-378, August.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:2:d:10.1007_s10878-020-00602-3
    DOI: 10.1007/s10878-020-00602-3
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    References listed on IDEAS

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    1. Yukun Cheng & Xiaotie Deng & Dominik Scheder, 2018. "Recent studies of agent incentives in internet resource allocation and pricing," 4OR, Springer, vol. 16(3), pages 231-260, September.
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