Abstract
Stable matching studies how to pair members of two sets with the objective to achieve a matching that satisfies all participating agents based on their preferences. In this research, we consider the case of matching in a social network where agents are not fully connected. We propose the concept of D-neighbourhood associated with connective costs to investigate the matching quality in four types of well-used networks. A matching algorithm is proposed based on the classical Gale-Shapley algorithm under constraints of network topology. Through experimental studies, we find that the matching outcomes in scale-free networks yield the best average utility with least connective costs comparing to other structured networks. This research provides insights for understanding matching behavior in social networks like marriage, trade, partnership, online social and job search.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences for the theory of stable allocations and the practice of market design.
- 2.
Preferential attachment can be regarded as a positive feedback in a network, more connected a node is, the more likely it is to receive new links.
References
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Dijkstra, E.W.: A note on two problems in connection with graphs. Numerische Math. 1(1), 269–271 (1959)
Erdös, P., Rényi, A.: On random graphs. Publicationes Math. 6(4), 290–297 (1959)
Gale, D.: College admissions and the stability of marriage. Am. Math. Mon. 69(5), 9–15 (2013)
Gale, D., Sotomayor, M.: Some remarks on the stable matching problem. Discrete Appl. Math. 11(3), 223–232 (1985)
Gomez-Gardenes, J., Moreno, Y.: From scale-free to Erdos-Renyi networks. Phys. Rev. E 73(5), 056124 (2006)
Jackson, M.O.: Allocation rules for network games. Games Econ. Behav. 51(1), 128–154 (2005)
Jackson, M.O., Watts, A.: The evolution of social and economic networks. J. Econ. Theory 106(2), 265–295 (2002)
Kitsak, M., et al.: Betweenness centrality of fractal, nonfractal scale-free model networks, tests on real networks. Phys. Rev. E 75, 056115 (2007)
Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87(19), 198701 (2001)
Li, Z., Qin, Z.: Impact of social network structure on social welfare and inequality. In: Pedrycz, W., Chen, S.-M. (eds.) Social Networks: A Framework of Computational Intelligence. SCI, vol. 526, pp. 123–144. Springer, Switzerland (2014)
Li, Z., Chang, Y.-H., Maheswaran, R.: Graph formation effects on social welfare and inequality in a networked resource game. In: Greenberg, A.M., Kennedy, W.G., Bos, N.D. (eds.) SBP 2013. LNCS, vol. 7812, pp. 221–230. Springer, Heidelberg (2013)
Liu, Q., et al.: Stable matching with incomplete information. Econometrica 82(2), 541–587 (2014)
Moldovanu, B.: Two-sided matching-A study in game-theoretic modeling and analysis (Book Review). J. Econ. (1992)
Nisan, N., et al.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
Roth, A.E., Sotomayor, M.A.O.: A Study in Game-theoretic Modeling and Analysis. Cambridge University Press, Cambridge (2006)
Shoham, Y.: Computer science and game theory. Commun. ACM 51(8), 74–79 (2008)
Strogatz, S.H.: Exploring complex networks. Nature 410(2), 24–27 (2001)
Wang, X., Jiang, Y.: The influence of the randomness on average path length. Adv. Mat. Res. 87(19), 198701 (2011)
Acknowledgement
This work is supported by the National Science Foundation of China Nos. 61305047 and 61401012.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Ling, Y., Wan, T., Qin, Z. (2016). Stable Matching in Structured Networks. In: Ohwada, H., Yoshida, K. (eds) Knowledge Management and Acquisition for Intelligent Systems . PKAW 2016. Lecture Notes in Computer Science(), vol 9806. Springer, Cham. https://doi.org/10.1007/978-3-319-42706-5_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-42706-5_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42705-8
Online ISBN: 978-3-319-42706-5
eBook Packages: Computer ScienceComputer Science (R0)