Skip to main content
SpringerLink
Log in

Hedonic games related to many-to-one matching problems

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

We consider the existence problem of stable matchings in many-to-one matching problems. Unlike other approaches which use algorithmic techniques to give necessary and sufficient conditions, we adopt a game theoretic point of view. We first associate, with each many-to-one matching problem, a hedonic game to take advantage of recent results guaranteeing the existence of core-partitions for that class of games, to build up our conditions. The main result states that a many-to-one matching problem, with no restrictions on individual preferences, has stable* matchings if and only if a related hedonic game is pivotally balanced. In the case that the preferences in the matching problem are substitutable, the notions of stability and stability* coincide.

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

  • Banerjee S, Konishi H, Sonmez T (2001) Core in a simple coalition formation game. Soc Choice Welf 18: 135–153

    Article  Google Scholar 

  • Bogomolnaia A, Jackson M (2002) The stability of hedonic coalition structures. Games Econ Behav 38: 201–230

    Article  Google Scholar 

  • Dimitrov D, Lazarova E (2008) Coalitional matchings. Nota di Laboro 45.2008, Fundazione Eni Enrico Mattei

  • Echenique F, Oviedo J (2004) Core many-to-one matchings by fixed point methods. J Econ Theory 115: 358–376

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Iehlé V (2007) The core-partition of a hedonic game. Math Soc Sci 54: 176–185

    Article  Google Scholar 

  • Pápai S (2004) Unique stability in simple coalition formation games. Games Econ Behav 48: 337–354

    Article  Google Scholar 

  • Roth A, Sotomayor M (1990) Two-sided matching: a study in game-theoretic modelling and analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Shapley L (1967) On balanced sets and cores. Nav Res Logist Q 14: 453–460

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Matemática Aplicada San Luis (UNSL-CONICET), Av. Ejército de los Andes 950, 5700, San Luis, Argentina

    Juan Carlos Cesco

  2. Departamento de Matemática (U.N. San Luis), Chacabuco y Pedernera, 5700, San Luis, Argentina

    Juan Carlos Cesco

Authors
  1. Juan Carlos Cesco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Carlos Cesco.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cesco, J.C. Hedonic games related to many-to-one matching problems. Soc Choice Welf 39, 737–749 (2012). https://doi.org/10.1007/s00355-011-0559-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-011-0559-9

Keywords

Search

Navigation