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Three-sided matching problem with mixed preferences

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Abstract

In this paper, we study the three-sided matching problems with mixed preferences, where three agent sets are U, V and W. We discussed two matching problems with different types of preferences. The first is that each \(u\in U\) has a strict preference over set V, each \(v\in V\) has a strict preference over set W, each \(w\in W\) has a strict preference over set V and each \(w\in W\) has a strict preference over set U. The second is that each \(u\in U\) has a strict preference over set V, each \(v\in V\) has a strict preference over set W and each \(w\in W\) has a strict preference over set \(U\times V=\{(u,v)|u\in U,v\in V \}\). For these two kinds of matching problems, we give the concept of stable matching and the algorithm of solving stable matching respectively. Finally, we discuss the relationship between these two matching problems.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Item Number: 71520107003), the Shanghai Science Committee of China (Item Number: 17495810503), the Gaoyuan Discipline of Shanghai-Environmental Science and Engineering (Resource Recycling Science and Engineering), and the Applied Mathematical Subject of SSPU. We would like to express our heartfelt thanks.

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Authors and Affiliations

  1. Research Center of Resource Recycling Science and Engineering, Shanghai Polytechnic University, Shanghai, 201209, China

    Feng Zhang

  2. Shanghai General Hospital, School of Medicine, Shanghai Jiaotong University, Shanghai, 200080, China

    Liwei Zhong

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  1. Feng Zhang
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  2. Liwei Zhong
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Correspondence to Liwei Zhong.

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Zhang, F., Zhong, L. Three-sided matching problem with mixed preferences. J Comb Optim 42, 928–936 (2021). https://doi.org/10.1007/s10878-019-00501-2

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  • DOI: https://doi.org/10.1007/s10878-019-00501-2

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