Abstract
In many economic, social and political situations individuals carry out activities in groups (coalitions) rather than alone and on their own. Examples range from households and sport clubs to research networks, political parties and trade unions. The underlying game theoretic framework is known as coalition formation.
This survey discusses the notion of core stability in hedonic coalition formation (where each player’s happiness only depends on the other members of his coalition but not on how the remaining players outside his coalition are grouped). We present the central concepts and algorithmic approaches in the area, provide many examples, and pose a number of open problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alkan, A.: Non-existence of stable threesome matchings. Mathematical Social Sciences 16, 207–209 (1988)
Arkin, E.M., Bae, S.W., Efrat, A., Okamoto, K., Mitchell, J.S.B., Polishchuk, V.: Geometric stable roommates. Information Processing Letters 109, 219–224 (2009)
Aziz, H., Brandt, F., Seedig, H.G.: Stable partitions in additively separable hedonic games. In: Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), pp. 183–190 (2001)
Ballester, C.: NP-completeness in hedonic games. Games and Economic Behavior 49, 1–30 (2004)
Banerjee, S., Konishi, H., Sönmez, T.: Core in a simple coalition formation game. Social Choice and Welfare 18, 135–153 (2001)
Barberà , S., Bossert, W., Pattanaik, P.K.: Ranking sets of objects. In: Barberà , S., Hammond, P.J., Seidl, C. (eds.) Handbook of Utility Theory, vol. II, pp. 893–977. Kluwer Academic Publishers (2004)
Biró, P., McDermid, E.: Three-sided stable matchings with cyclic preferences. Algorithmica 58, 5–18 (2010)
Bogomolnaia, A., Jackson, M.O.: The stability of hedonic coalition structures. Games and Economic Behavior 38, 201–230 (2002)
Boros, E., Gurvich, V., Jaslar, S., Krasner, D.: Stable matchings in three-sided systems with cyclic preferences. Discrete Mathematics 289, 1–10 (2004)
de Bruijn, N.G.: Asymptotic Methods in Analysis. North-Holland, Amsterdam (1958)
Cechlárová, K., Hajduková, J.: Computational complexity of stable partitions with B-preferences. International Journal of Game Theory 31, 353–364 (2002)
Cechlárová, K., Hajduková, J.: Stable partitions with W-preferences. Discrete Applied Mathematics 138, 333–347 (2004)
Cechlárová, K., Romero-Medina, A.: Stability in coalition formation games. International Journal of Game Theory 29, 487–494 (2001)
Chebolu, P., Goldberg, L.A., Martin, R.A.: The Complexity of Approximately Counting Stable Matchings. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds.) APPROX and RANDOM 2010. LNCS, vol. 6302, pp. 81–94. Springer, Heidelberg (2010)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press (2001)
Danilov, V.I.: Existence of stable matchings in some three-sided systems. Mathematical Social Sciences 46, 145–148 (2003)
Darmann, A., Elkind, E., Kurz, S., Lang, J., Schauer, J., Woeginger, G.: Group Activity Selection Problem. In: Goldberg, P.W., Guo, M. (eds.) WINE 2012. LNCS, vol. 7695, pp. 156–169. Springer, Heidelberg (2012)
Dimitrov, D., Borm, P., Hendrickx, R., Sung, S.-C.: Simple priorities and core stability in hedonic games. Social Choice and Welfare 26, 421–433 (2006)
Drèze, J., Greenberg, J.: Hedonic coalitions: Optimality and stability. Econometrica 48, 987–1003 (1980)
Eriksson, K., Sjöstrand, J., Strimling, P.: Three-dimensional stable matching with cyclic preferences. Mathematical Social Sciences 52, 77–87 (2006)
Farrell, J., Scotchmer, S.: Partnerships. The Quarterly Journal of Economics 103, 279–297 (1988)
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15 (1962)
Gale, D., Sotomayor, M.A.O.: Some remarks on the stable matching problem. Discrete Applied Mathematics 11, 223–232 (1994)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)
Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press (1989)
Irving, R.W.: An efficient algorithm for the stable roommates problem. Journal of Algorithms 6, 577–595 (1985)
Irving, R.W.: Stable marriage and indifference. Discrete Applied Mathematics 48, 261–272 (1994)
Irving, R.W., Leather, P.: The complexity of counting stable marriages. SIAM Journal on Computing 15, 655–667 (1986)
Irving, R.W., Manlove, D.F.: The stable roommates problem with ties. Journal of Algorithms 43, 85–105 (2002)
Irving, R.W., Manlove, D.F., O’Malley, G.: Stable marriage with ties and bounded length preference lists. Journal of Discrete Algorithms 43, 213–219 (2009)
Knuth, D.E.: Mariages stables et leurs relations avec d’autres problèmes combinatoires [Stable marriage and its relation to other combinatorial problems]. CRM Proceedings and Lecture Notes, vol. 10. Les Presses de l’Université de Montréal (1997)
Manlove, D.F., Irving, R.W., Iwama, K., Miyazaki, S., Morita, Y.: Hard variants of stable marriage. Theoretical Computer Science 276, 261–279 (2002)
Ng, C., Hirschberg, D.S.: Three-dimensional stable matching problems. SIAM Journal on Discrete Mathematics 4, 245–252 (1991)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1994)
Papadimitriou, C.H., Yannakakis, M.: On limited nondeterminism and the complexity of the V-C dimension. Journal of Computer and System Sciences 53, 161–170 (1996)
Ronn, E.: NP-complete stable matching problems. Journal of Algorithms 11, 285–304 (1990)
Roth, A.E., Sotomayor, M.A.O.: Two-Sided Matching. Cambridge University Press (1990)
Shapley, L.S., Scarf, H.: On cores and indivisibility. Journal of Mathematical Economics 1, 23–37 (1974)
Subramanian, A.: A new approach to stable matching problems. SIAM Journal on Computing 23, 671–701 (1994)
Sung, S.-C., Dimitrov, D.: On core membership testing for hedonic coalition formation games. Operations Research Letters 35, 155–158 (2007)
Sung, S.-C., Dimitrov, D.: Computational complexity in additive hedonic games. European Journal of Operational Research 203, 635–639 (2010)
Tamura, A.: Transformation from arbitrary matchings to stable matchings. Journal of Combinatorial Theory A 62, 310–323 (1993)
Wagner, K.: Bounded query classes. SIAM Journal on Computing 19, 833–846 (1990)
Woeginger, G.J.: A hardness result for core stability in additive hedonic games. Mathematical Social Sciences (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Woeginger, G.J. (2013). Core Stability in Hedonic Coalition Formation. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds) SOFSEM 2013: Theory and Practice of Computer Science. SOFSEM 2013. Lecture Notes in Computer Science, vol 7741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35843-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-35843-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35842-5
Online ISBN: 978-3-642-35843-2
eBook Packages: Computer ScienceComputer Science (R0)