Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Afacan M (2012) Group robust stability in matching markets. Games Econ Behav 74:394–398

    Article  MathSciNet  MATH  Google Scholar 

  • 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 195–206

  • 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, Berlin

  • Blair C (1988) The lattice structure of the set of pairwise-stable matching with multiple partners. Math Oper Res 13(4):439–457

    Article  Google Scholar 

  • Boros E, Gurvich V, Jaslar S et al (2004) Stable matchings in three-sided systems with cyclic preferences. Discret Math 289(1):1–10

    MathSciNet  MATH  Google Scholar 

  • Chakraborty A, Citanna A, Ostrovsky M (2015) Group stability in matching with interdependent values. Rev Econ Des 19:3–24

    MathSciNet  MATH  Google Scholar 

  • 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 68–83

  • 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 Center

  • Elitzur R, Gavious A (2003) A multi-period game theoretic model of venture capitalists and entrepreneurs. Eur J Oper Res 144(2):440–453

    Article  MathSciNet  MATH  Google Scholar 

  • Eriksson K, Sjöstrand J, Strimling P (2006) Three-dimensional stable matching with cyclic preferences. Math Soc Sci 52(1):77–87

    Article  MathSciNet  MATH  Google Scholar 

  • Farczadi L, Georgiou K, Könemann J (2016) Stable marriage with general preferences. Theory Comput Syst 59(4):683–699

    Article  MathSciNet  MATH  Google Scholar 

  • Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta D, Denton B (2008) Appointment scheduling in health care: challenges and opportunities. IIE Trans 40(9):800–819

    Article  Google Scholar 

  • 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):1–10

    Article  Google Scholar 

  • Irving RW, Manlove DF, Scott S (2000) The hospitals/residents problem with ties. Lect Notes Comput Sci 1851(1):259–271

    Article  MathSciNet  MATH  Google Scholar 

  • Irving RW, Manlove DF, Scoa S (2003) Strong stability in the hospitals/residents problem. Lect Notes Comput Sci 2607(1):439–450

    Article  MathSciNet  MATH  Google Scholar 

  • 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):475–490

    Article  Google Scholar 

  • Kaiser U, Wright J (2006) Price structure in two-sided markets: evidence from the magazine industry. Int J Ind Organ 24(1):1–28

    Article  Google Scholar 

  • Lin HT (2009) A job placement intervention using fuzzy approach for two-way choice. Expert Syst Appl 36(2):2543–2553

    Article  Google Scholar 

  • Ng C, Hirschberg DS (1991) Three-dimensional stabl matching problems. SIAM J Discret Math 4(2):245–252

    Article  MATH  Google Scholar 

  • Roth AE (1986) On the allocation of residents to rural hospitals: a general property of two-sides matching markets. Econometrica 54(2):425–427

    Article  MathSciNet  Google Scholar 

  • Roth A, Sotomayor M (1990) Two-sided matching. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Sarne D, Kraus S (2008) Managing parallel inquiries in agents’ two-sided search. Artif Intell 172(4–5):541–569

    Article  MathSciNet  MATH  Google Scholar 

  • Sukegawa N, Yamamoto Y (2012) Preference profiles determining the proposals in the Gale—Shapley algorithm for stable matching problems. Japan J Indust Appl Math 29:547–560

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shanghai University, Shanghai, 200444, China

    Liwei Zhong & Yanqin Bai

Authors
  1. Liwei Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanqin Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanqin Bai.

Additional information

The study was funded by the National Natural Science Foundation of China (Item Number: 7137112071520107003) as well as the Shanghai Science Committee of China (Item Number: 17495810500). We would like to express our heartfelt thanks.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhong, L., Bai, Y. Three-sided stable matching problem with two of them as cooperative partners. J Comb Optim 37, 286–292 (2019). https://doi.org/10.1007/s10878-017-0224-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-017-0224-z

Keywords

Search

Navigation