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On (Coalitional) Exchange-Stable Matching

Part of the Lecture Notes in Computer Science book series (LNISA,volume 12885)


We study , which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a given Stable Marriage or Stable Roommates instance is called if it does not admit any , that is, a subset S of agents in which everyone prefers the partner of some other agent in S. The matching is if it does not admit any , that is, an exchange-blocking coalition of size two.

We investigate the computational and parameterized complexity of the Coalitional Exchange-Stable Marriage (resp. Coalitional Exchange Roommates) problem, which is to decide whether a Stable Marriage (resp. Stable Roommates) instance admits a coalitional exchange-stable matching. Our findings resolve an open question and confirm the conjecture of Cechlárová and Manlove [Discrete Applied Mathematics, 2005] that Coalitional Exchange-Stable Marriage is NP-hard even for complete preferences without ties. We also study bounded-length preference lists and a local-search variant of deciding whether a given matching can reach an exchange-stable one after at most k  , where a swap is defined as exchanging the partners of the two agents in an exchange-blocking pair .

JC was supported by the WWTF research project (VRG18-012). MS was supported by the Alexander von Humboldt Foundation.

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  1. Abizada, A.: Exchange-stability in roommate problems. Rev. Econ. Des. 23, 3–12 (2019).

  2. Abraham, D.J., Manlove, D.F.: Pareto optimality in the roommates problem. Technical report, University of Glasgow, Department of Computing Science (2004). tR-2004-182

    Google Scholar 

  3. Alcalde, J.: Exchange-proofness or divorce-proofness? Stability in one-sided matching markets. Econ. Des. 1, 275–287 (1995)

    Google Scholar 

  4. Aziz, H., Goldwaser, A.: Coalitional exchange stable matchings in marriage and roommate market. In: Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2017), pp. 1475–1477 (2017). extended Abstract

    Google Scholar 

  5. Biró, P., Norman, G.: Analysis of stochastic matching markets. Int. J. Game Theory 42(4), 1021–1040 (2012).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Bodlaender, H.L., Hanaka, T., Jaffke, L., Ono, H., Otachi, Y., van der Zanden, T.C.: Hedonic seat arrangement problems. In: Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2020), pp. 1777–1779 (2020). extended Abstract

    Google Scholar 

  7. Bodlaender, H.L., Hanaka, T., Jaffke, L., Ono, H., Otachi, Y., van der Zanden, T.C.: Hedonic seat arrangement problems. Technical report, arXiv:2002.10898 (cs.GT) (2020)

  8. Bredereck, R., Chen, J., Finnendahl, U.P., Niedermeier, R.: Stable roommate with narcissistic, single-peaked, and single-crossing preferences. Auton. Agent. Multi-Agent Syst. 34(53), 1–29 (2020)

    MATH  Google Scholar 

  9. Cechlárová, K.: On the complexity of exchange-stable roommates. Discret. Appl. Math. 116(3), 279–287 (2002)

    CrossRef  MathSciNet  Google Scholar 

  10. Cechlárová, K., Manlove, D.F.: The exchange-stable marriage problem. Discret. Appl. Math. 152(1–3), 109–122 (2005)

    CrossRef  MathSciNet  Google Scholar 

  11. Chen, J.: Reaching stable marriage via divorces is hard. Technical report, arXiv:1906.12274(cs.GT) (2020)

  12. Chen, J., Chmurovic, A., Jogl, F., Sorge, M.: On (coalitional) exchange-stable matching. Technical report, arXiv:2105.05725(cs.GT) (2021)

  13. Cygan, M., et al.: Lower bounds for kernelization. In: Parameterized Algorithms, pp. 523–555. Springer, Cham (2015).

    CrossRef  Google Scholar 

  14. Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 120(5), 386–391 (1962)

    CrossRef  MathSciNet  Google Scholar 

  15. Irving, R.W.: Stable matching problems with exchange restrictions. J. Comb. Optim. 16(4), 344–360 (2008)

    CrossRef  MathSciNet  Google Scholar 

  16. Knuth, D.: Mariages Stables. Les Presses de L’Université de Montréal (1976)

    Google Scholar 

  17. McDermid, E., Cheng, C.T., Suzuki, I.: Hardness results on the man-exchange stable marriage problem with short preference lists. Inf. Process. Lett. 101(1), 13–19 (2007)

    CrossRef  MathSciNet  Google Scholar 

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Correspondence to Jiehua Chen or Manuel Sorge .

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Chen, J., Chmurovic, A., Jogl, F., Sorge, M. (2021). On (Coalitional) Exchange-Stable Matching. In: Caragiannis, I., Hansen, K.A. (eds) Algorithmic Game Theory. SAGT 2021. Lecture Notes in Computer Science(), vol 12885. Springer, Cham.

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