STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES

Maria Silvia Pini, Francesca Rossi, Kristen Brent Venable, Toby Walsh

2011

Abstract

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or more generally to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here we consider stable marriage problems with weighted preferences: each man (resp., woman) provides a score for each woman (resp., man). Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations it is more natural to express scores (to model, for example, profits or costs) rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages which are stable and/or optimal according to these notions. While expressivity greatly increases by adopting weighted preferences, we show that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.

References

  1. Arrow, K., Sen, A., and Suzumura, K. (2002). Handbook of Social Choice and Welfare. North Holland, Elsevier.
  2. Bistarelli, S., Foley, S. N., O'Sullivan, B., and Santini, F. (2008). From marriages to coalitions: A soft csp approach. In CSCLP, pages 1-15.
  3. Bistarelli, S., Montanari, U., and Rossi, F. (1997). Semiring-based constraint solving and optimization. Journal of the ACM, 44(2):201-236.
  4. Gale, D. and Shapley, L. S. (1962). College admissions and the stability of marriage. Amer. Math. Monthly, 69:9- 14.
  5. Gelain, M., Pini, M. S., Rossi, F., Venable, K. B., and Walsh, T. (2010a). Male optimal and unique stable marriages with partially ordered preferences. In Proc. CARE 2009/2010. Springer LNAI 6066.
  6. Gelain, M., Pini, M. S., Rossi, F., Venable, K. B., and Walsh, T. (2010b). Male optimality and uniqueness in stable marriage problems with partial orders - Extended abstract. In Proc. AAMAS'10.
  7. Gusfield, D. (1987). Three fast algorithms for four problems in stable marriage. SIAM J. Comput., 16(1):111-128.
  8. Gusfield, D. and Irving, R. W. (1989). The Stable Marriage Problem: Structure and Algorithms. MIT Press, Boston, Mass.
  9. Halldorsson, M., Irving, R. W., Iwama, K., Manlove, D., Miyazaki, S., Morita, Y., and Scott, S. (2003). Approximability results for stable marriage problems with ties. Theor. Comput. Sci, 306(1-3):431-447.
  10. Irving, R. W. (1994). Stable marriage and indifference. Discrete Applied Mathematics, 48:261-272.
  11. Irving, R. W. (1998). Matching medical students to pairs of hospitals: a new variation on an old theme. In Proc. ESA'98, volume 1461 of LNCS, pages 381-392. Springer-Verlag.
  12. Irving, R. W., Leather, P., and Gusfield, D. (1987). An efficient algorithm for the “optimal” stable marriage. J. ACM, 34(3):532-543.
  13. Liebowitz, J. and Simien, J. (2005). Computational efficiencies for multi-agents: a look at a multi-agent system for sailor assignment. Electonic government: an International Journal, 2(4):384-402.
  14. Manlove, D. (2002). The structure of stable marriage with indifference. Discrete Applied Mathematics, 122(1- 3):167-181.
  15. Pini, M. S., Rossi, F., Venable, K. B., and Walsh, T. (2009). Manipulation and gender neutrality in stable marriage procedures. In Proc. AAMAS'09, volume 1, pages 665-672.
  16. Pini, M. S., Rossi, F., Venable, K. B., and Walsh, T. (2010a). Manipulation complexity and gender neutrality in stable marriage procedures. Jornal of Autonomous Agents and Multi-Agent Systems.
  17. Pini, M. S., Rossi, F., Venable, K. B., and Walsh, T. (2010b). Stable marriage problems with quantitative preferences. In Informal Proc. of COMSOC'10 - Third International Workshop on Computational Social Choice.
  18. Roth, A. E. (1984). The evolution of the labor market for medical interns and residents: a case study in game theory. Journal of Political Economy, 92:991-1016.
  19. Roth, A. E. (2008). Deferred acceptance algorithms: History, theory, practice, and open questions. International Journal of Game Theory, Special Issue in Honor of David Gale on his 85th birthday, 36:537- 569.
  20. Teo, C.-P., Sethuraman, J., and Tan, W.-P. (2001). Galeshapley stable marriage problem revisited: Strategic issues and applications. Manage. Sci., 47(9):1252- 1267.
  21. Tesfatsion, L. (1998). Gale-shapley matching in an evolutionary trade network game. Economic Report, 43.
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Paper Citation


in Harvard Style

Pini M., Rossi F., Venable K. and Walsh T. (2011). STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES . In Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8425-41-6, pages 45-53. DOI: 10.5220/0003144200450053


in Bibtex Style

@conference{icaart11,
author={Maria Silvia Pini and Francesca Rossi and Kristen Brent Venable and Toby Walsh},
title={STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES},
booktitle={Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2011},
pages={45-53},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003144200450053},
isbn={978-989-8425-41-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - STABILITY IN MATCHING PROBLEMS WITH WEIGHTED PREFERENCES
SN - 978-989-8425-41-6
AU - Pini M.
AU - Rossi F.
AU - Venable K.
AU - Walsh T.
PY - 2011
SP - 45
EP - 53
DO - 10.5220/0003144200450053