Abstract
We consider the two-sided stable matching setting in which there may be uncertainty about the agents’ preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model — in which for each agent, there is a probability distribution over linear preferences, (2) compact indifference model — for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model — there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists. We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.
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- 1.
We note that the complexity of all problems that we study are the same for complete and incomplete lists, where non-listed agents are deemed unacceptable—see Proposition 2 in the full version of the paper [1].
References
Aziz, H., Biró, P., Gaspers, S., de Haan, R., Mattei, N., Rastegari, B.: Stable matching with uncertain linear preferences. Technical Report 1607.02917, Cornell University Library. http://arxiv.org/abs/1607.02917
Drummond, J., Boutilier, C.: Preference elicitation and interview minimization in stable matchings. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, pp. 645–653 (2014)
Ehlers, L., Massó, J.: Matching markets under (in)complete information. J. Econ. Theor. 157, 295–314 (2015)
Gusfield, D., Irving, R.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)
Halldórsson, M.M., Iwama, K., Miyazaki, S., Yanagisawa, H.: Improved approximation results for the stable marriage problem. ACM Trans. Algorithms 3(3), 30 (2007)
Hazon, N., Aumann, Y., Kraus, S., Wooldridge, M.: On the evaluation of electionoutcomes under uncertainty. Artif. Intell. 189, 1–18 (2012)
Irving, R.: Stable marriage and indifference. Discrete Appl. Math. 48, 261–272 (1994)
Li, Y., Conitzer, V.: Cooperative game solution concepts that maximize stability under noise. In: AAAI, pp. 979–985 (2015)
Manlove, D.: Algorithmics of Matching Under Preferences. World Scientific Publishing Company, Hackensack (2013)
Rastegari, B., Condon, A., Immorlica, N., Irving, R., Leyton-Brown, K.: Reasoning about optimal stable matching under partial information. In: Proceedings of the ACM Conference on Electronic Commerce (EC), pp. 431–448. ACM (2014)
Roth, A.E., Sotomayor, M.A.O.: Two-Sided Matching: A Study in Game Theoretic Modelling and Analysis. Cambridge University Press, Cambridge (1990)
Welsh, D.J.A., Merino, C.: The Potts model and the Tutte polynomial. J. Math. Phys. 41(3), 1127–1152 (2000)
Acknowledgments
Biró is supported by the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3) and the Hungarian Scientific Research Fund, OTKA, Grant No. K108673. Rastegari was supported EPSRC grant EP/K010042/1 at the time of the submission. De Haan is supported by the Austrian Science Fund (FWF), project P26200. The authors gratefully acknowledge the support from European Cooperation in Science and Technology (COST) action IC1205. Serge Gaspers is the recipient of an Australian Research Council (ARC) Future Fellowship (FT140100048) and acknowledges support under the ARC’s Discovery Projects funding scheme (DP150101134). Data61/CSIRO (formerly, NICTA) is funded by the Australian Government through the Department of Communications and the ARC through the ICT Centre of Excellence Program.
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Aziz, H., Biró, P., Gaspers, S., de Haan, R., Mattei, N., Rastegari, B. (2016). Stable Matching with Uncertain Linear Preferences. In: Gairing, M., Savani, R. (eds) Algorithmic Game Theory. SAGT 2016. Lecture Notes in Computer Science(), vol 9928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53354-3_16
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DOI: https://doi.org/10.1007/978-3-662-53354-3_16
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