Abstract
We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences.
This research was supported by NSF Grant CCFā1217980.
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Notes
- 1.
The algorithm of Erdil and Ergin proceeds in two phases. In the first phase, ties are broken arbitrarily and the deferred acceptance algorithm is used to obtain a weakly stable matching. In the second phase, a sequence of Pareto-improvements are applied until a Pareto-stable matching is reached. In App. A in the full version of [7], we show that this algorithm does not provide a strategyproof mechanism.
- 2.
A stable mechanism can be strategyproof only for the side having unit demand, namely the students [20].
References
AbdulkadiroĒ§lu, A., Pathak, P.A., Roth, A.E.: Strategy-proofness versus efficiency in matching with indifferences: redesigning the NYC high school match. Am. Econ. Rev. 99, 1954ā1978 (2009)
Chen, N.: On computing Pareto stable assignments. In: Proceedings of the 29th International Symposium on Theoretical Aspects of Computer Science, pp. 384ā395 (2012)
Chen, N., Ghosh, A.: Algorithms for Pareto stable assignment. In: Proceedings of the Third International Workshop on Computational Social Choice, pp. 343ā354 (2010)
Crawford, V.P., Knoer, E.M.: Job matching with heterogeneous firms and workers. Econometrica 49, 437ā450 (1981)
Demange, G., Gale, D.: The strategy structure of two-sided matching markets. Econometrica 53, 873ā888 (1985)
DomaniƧ, N.O., Lam, C.K., Plaxton, C.G.: Group strategyproof Pareto-stable marriage with indifferences via the generalized assignment game, July 2017. https://arxiv.org/abs/1707.01496
DomaniƧ, N.O., Lam, C.K., Plaxton, C.G.: Strategyproof Pareto-stable mechanisms for two-sided matching with indifferences. In: Fourth International Workshop on Matching under Preferences, April 2017. https://arxiv.org/abs/1703.10598
Dubins, L.E., Freedman, D.A.: Machiavelli and the Gale-Shapley algorithm. Am. Math. Mon. 88, 485ā494 (1981)
DĆ¼tting, P., Henzinger, M., Weber, I.: An expressive mechanism for auctions on the web. ACM Trans. Econ. Comput. 4, 1:1ā1:34 (2015)
Erdil, A., Ergin, H.: Whatās the matter with tie-breaking? Improving efficiency in school choice. Am. Econ. Rev. 98, 669ā689 (2008)
Erdil, A., Ergin, H.: Two-sided matching with indifferences (2015). working paper
Eriksson, K., Karlander, J.: Stable matching in a common generalization of the marriage and assignment models. Discrete Math. 217, 135ā156 (2000)
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 69, 9ā15 (1962)
Irving, R.W.: Stable marriage and indifference. Discrete Appl. Math. 48, 261ā272 (1994)
Kamiyama, N.: A new approach to the Pareto stable matching problem. Math. Oper. Res. 39, 851ā862 (2014)
Kesten, O.: School choice with consent. Q. J. Econ. 125, 1297ā1348 (2010)
Knuth, D.: Marriages Stables. Montreal University Press, Montreal (1976)
Quinzii, M.: Core and competitive equilibria with indivisibilities. Int. J. Game Theory 13, 41ā60 (1984)
Roth, A.E.: The economics of matching: stability and incentives. Math. Oper. Res. 7, 617ā628 (1982)
Roth, A.E.: The college admissions problem is not equivalent to the marriage problem. J. Econ. Theory 36, 277ā288 (1985)
Roth, A.E., Sotomayor, M.: Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis. Cambridge University Press, New York (1990)
Shapley, L.S., Shubik, M.: The assignment game I: the core. Int. J. Game Theory 1, 111ā130 (1971)
Sotomayor, M.: Existence of stable outcomes and the lattice property for a unified matching market. Math. Soc. Sci. 39, 119ā132 (2000)
Sotomayor, M.: The Pareto-stability concept is a natural solution concept for discrete matching markets with indifferences. Int. J. Game Theory 40, 631ā644 (2011)
Zhou, L.: On a conjecture by gale about one-sided matching problems. J. Econ. Theory 52, 123ā135 (1990)
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DomaniƧ, N.O., Lam, CK., Plaxton, C.G. (2017). Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game. In: BilĆ², V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_22
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