Journal of Combinatorial Optimization

, Volume 37, Issue 1, pp 286–292 | Cite as

Three-sided stable matching problem with two of them as cooperative partners

  • Liwei Zhong
  • Yanqin BaiEmail author


In this paper, three-sided stable matching problem is discussed, in which two sets, \(V_1\) and \(V_2\) are cooperative partners, and the agent of the other set U has a strict preference to the agents of set \(V_1\) and set \(V_2\) respectively. On the other side, the agents of set \(V_1\) and set \(V_2\) have a strict preference to the agent of set U . About this three-sided matching problem, this paper gives the definition of stable matching, proves that the problem must have a stable matching, and gives an algorithm that can obtain a stable matching.


Three-sided matching Stable matching Algorithm 


  1. Afacan M (2012) Group robust stability in matching markets. Games Econ Behav 74:394–398MathSciNetCrossRefzbMATHGoogle Scholar
  2. Aziz H, Biró P, Gaspers S et al (2016) Stable matching with uncertain linear preferences. In: International symposium on algorithmic game theory. Springer, Berlin, pp 195–206Google Scholar
  3. Biró P, Manlove DF, McBride I (2014) The hospitals/residents problem with couples: complexity and integer programming models, In: Proceedings of SEA’14: the 8th symposium on experimental algorithms, lecture notes in computer science vol 8504: 10C21, Springer, BerlinGoogle Scholar
  4. Blair C (1988) The lattice structure of the set of pairwise-stable matching with multiple partners. Math Oper Res 13(4):439–457CrossRefGoogle Scholar
  5. Boros E, Gurvich V, Jaslar S et al (2004) Stable matchings in three-sided systems with cyclic preferences. Discret Math 289(1):1–10MathSciNetzbMATHGoogle Scholar
  6. Chakraborty A, Citanna A, Ostrovsky M (2015) Group stability in matching with interdependent values. Rev Econ Des 19:3–24MathSciNetzbMATHGoogle Scholar
  7. De Clercq S, Schockaert S, De Cock M et al (2013) Modeling stable matching problems with answer set programming. In: International workshop on rules and rule markup languages for the semantic web. Springer, Berlin, pp 68–83Google Scholar
  8. Eggleston K (2010)‘Kan Bing Nan, Kan Bing Gui’: challenges for China’s healthcare system thirty years into reform. Growing Pains: tensions and opportunities in Chinas transformation. Stanford: Walter H. Shorenstein Asia-Pacific Research CenterGoogle Scholar
  9. Elitzur R, Gavious A (2003) A multi-period game theoretic model of venture capitalists and entrepreneurs. Eur J Oper Res 144(2):440–453MathSciNetCrossRefzbMATHGoogle Scholar
  10. Eriksson K, Sjöstrand J, Strimling P (2006) Three-dimensional stable matching with cyclic preferences. Math Soc Sci 52(1):77–87MathSciNetCrossRefzbMATHGoogle Scholar
  11. Farczadi L, Georgiou K, Könemann J (2016) Stable marriage with general preferences. Theory Comput Syst 59(4):683–699MathSciNetCrossRefzbMATHGoogle Scholar
  12. Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15MathSciNetCrossRefzbMATHGoogle Scholar
  13. Gupta D, Denton B (2008) Appointment scheduling in health care: challenges and opportunities. IIE Trans 40(9):800–819CrossRefGoogle Scholar
  14. Huang DK, Chiu HN, Yeh RH et al (2009) A fuzzy multi-criteria decision making approach for solving a bi-objective personnel assignment problem. Comput Ind Eng 56(1):1–10CrossRefGoogle Scholar
  15. Irving RW, Manlove DF, Scott S (2000) The hospitals/residents problem with ties. Lect Notes Comput Sci 1851(1):259–271MathSciNetCrossRefzbMATHGoogle Scholar
  16. Irving RW, Manlove DF, Scoa S (2003) Strong stability in the hospitals/residents problem. Lect Notes Comput Sci 2607(1):439–450MathSciNetCrossRefzbMATHGoogle Scholar
  17. Janssen M, Verbraeck A (2008) Comparing the strengths and weaknesses of internet-based matching mechanisms for the transport market. Transp Res Part E Logist Transp Rev 44(3):475–490CrossRefGoogle Scholar
  18. Kaiser U, Wright J (2006) Price structure in two-sided markets: evidence from the magazine industry. Int J Ind Organ 24(1):1–28CrossRefGoogle Scholar
  19. Lin HT (2009) A job placement intervention using fuzzy approach for two-way choice. Expert Syst Appl 36(2):2543–2553CrossRefGoogle Scholar
  20. Ng C, Hirschberg DS (1991) Three-dimensional stabl matching problems. SIAM J Discret Math 4(2):245–252CrossRefzbMATHGoogle Scholar
  21. Roth AE (1986) On the allocation of residents to rural hospitals: a general property of two-sides matching markets. Econometrica 54(2):425–427MathSciNetCrossRefGoogle Scholar
  22. Roth A, Sotomayor M (1990) Two-sided matching. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  23. Sarne D, Kraus S (2008) Managing parallel inquiries in agents’ two-sided search. Artif Intell 172(4–5):541–569MathSciNetCrossRefzbMATHGoogle Scholar
  24. Sukegawa N, Yamamoto Y (2012) Preference profiles determining the proposals in the Gale—Shapley algorithm for stable matching problems. Japan J Indust Appl Math 29:547–560MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Shanghai UniversityShanghaiChina

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