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Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

  • Nevzat Onur DomaniçEmail author
  • Chi-Kit LamEmail author
  • C. Gregory PlaxtonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10504)

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.

References

  1. 1.
    Abdulkadiroǧlu, 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, 1954–1978 (2009)CrossRefGoogle Scholar
  2. 2.
    Chen, N.: On computing Pareto stable assignments. In: Proceedings of the 29th International Symposium on Theoretical Aspects of Computer Science, pp. 384–395 (2012)Google Scholar
  3. 3.
    Chen, N., Ghosh, A.: Algorithms for Pareto stable assignment. In: Proceedings of the Third International Workshop on Computational Social Choice, pp. 343–354 (2010)Google Scholar
  4. 4.
    Crawford, V.P., Knoer, E.M.: Job matching with heterogeneous firms and workers. Econometrica 49, 437–450 (1981)CrossRefGoogle Scholar
  5. 5.
    Demange, G., Gale, D.: The strategy structure of two-sided matching markets. Econometrica 53, 873–888 (1985)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Domaniç, 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
  7. 7.
    Domaniç, 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
  8. 8.
    Dubins, L.E., Freedman, D.A.: Machiavelli and the Gale-Shapley algorithm. Am. Math. Mon. 88, 485–494 (1981)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Dütting, P., Henzinger, M., Weber, I.: An expressive mechanism for auctions on the web. ACM Trans. Econ. Comput. 4, 1:1–1:34 (2015)MathSciNetGoogle Scholar
  10. 10.
    Erdil, A., Ergin, H.: What’s the matter with tie-breaking? Improving efficiency in school choice. Am. Econ. Rev. 98, 669–689 (2008)CrossRefGoogle Scholar
  11. 11.
    Erdil, A., Ergin, H.: Two-sided matching with indifferences (2015). working paperGoogle Scholar
  12. 12.
    Eriksson, K., Karlander, J.: Stable matching in a common generalization of the marriage and assignment models. Discrete Math. 217, 135–156 (2000)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon. 69, 9–15 (1962)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Irving, R.W.: Stable marriage and indifference. Discrete Appl. Math. 48, 261–272 (1994)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kamiyama, N.: A new approach to the Pareto stable matching problem. Math. Oper. Res. 39, 851–862 (2014)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Kesten, O.: School choice with consent. Q. J. Econ. 125, 1297–1348 (2010)CrossRefGoogle Scholar
  17. 17.
    Knuth, D.: Marriages Stables. Montreal University Press, Montreal (1976)Google Scholar
  18. 18.
    Quinzii, M.: Core and competitive equilibria with indivisibilities. Int. J. Game Theory 13, 41–60 (1984)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Roth, A.E.: The economics of matching: stability and incentives. Math. Oper. Res. 7, 617–628 (1982)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Roth, A.E.: The college admissions problem is not equivalent to the marriage problem. J. Econ. Theory 36, 277–288 (1985)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Roth, A.E., Sotomayor, M.: Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis. Cambridge University Press, New York (1990)CrossRefGoogle Scholar
  22. 22.
    Shapley, L.S., Shubik, M.: The assignment game I: the core. Int. J. Game Theory 1, 111–130 (1971)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Sotomayor, M.: Existence of stable outcomes and the lattice property for a unified matching market. Math. Soc. Sci. 39, 119–132 (2000)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Sotomayor, M.: The Pareto-stability concept is a natural solution concept for discrete matching markets with indifferences. Int. J. Game Theory 40, 631–644 (2011)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zhou, L.: On a conjecture by gale about one-sided matching problems. J. Econ. Theory 52, 123–135 (1990)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Texas at AustinAustinUSA

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