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The American Mathematical Monthly Volume 129, 2022 - Issue 5
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Original Articles

Generalized Rental Harmony

Erel Segal-HaleviDepartment of Computer Science, Ariel University, Israel40700Correspondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-7497-5834View further author information
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Pages 403-414 | Received 09 Jul 2020, Accepted 30 Jan 2021, Published online: 13 Apr 2022

References

  • Abdulkadiroğlu, A., Sönmez, T., Ünver, M. U. (2004). Room assignment-rent division: a market approach. Soc. Choice Welf. 22(3): 515–538. DOI: https://doi.org/10.1007/s00355-003-0231-0.
  • Alkan, A., Demange, G., Gale, D. (1991). Fair allocation of indivisible goods and criteria of justice. Econometrica. 59(4): 1023–1039. DOI: https://doi.org/10.2307/2938172.
  • Arunachaleswaran, E. R., Barman, S., Rathi, N. (2019). Fair division with a secretive agent. Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 33. Palo Alto, CA: AAAI Press, pp. 1732–1739. DOI: https://doi.org/10.1609/aaai.v33i01.33011732.
  • Asada, M., Frick, F., Pisharody, V., Polevy, M., Stoner, D., Tsang, L. H., Wellner, Z. (2018). Fair division and generalizations of Sperner- and KKM-type results. SIAM J. Discret. Math. 32(1): 591–610.
  • Azrieli, Y., Shmaya, E. (2014). Rental harmony with roommates. J. Econ. Theory. 153(1): 128–137.
  • Brams, S. J., Kilgour, D. M. (2001). Competitive fair division. J. Political Econ. 109(2): 418–443.
  • Cloutier, J., Nyman, K. L., Su, F. E. (2010). Two-player envy-free multi-cake division. Math. Soc. Sci. 59(1): 26–37.
  • Frick, F., Houston-Edwards, K., Meunier, F. (2019). Achieving rental harmony with a secretive roommate. Amer. Math. Monthly. 126(1): 18–32.
  • Gal, Y. K., Mash, M., Procaccia, A. D., Zick, Y. (2017). Which is the fairest (rent division) of them all? J. ACM. 64(6): 1–22. DOI: https://doi.org/10.1145/3131361.
  • Gale, D. (1960). The Theory of Linear Economic Models. Chicago, IL: Univ. of Chicago Press.
  • Ghodsi, M., Latifian, M., Mohammadi, A., Moradian, S., Seddighin, M. (2018). Rent division among groups. In: Kim, D., Uma, R. N., Zelikovsky, A., eds. Combinatorial Optimization and Applications. Cham: Springer, pp. 577–591.
  • Haake, C.-J., Raith, M. G., Su, F. E. (2002). Bidding for envy-freeness: a procedural approach to n-player fair-division problems. Soc. Choice Welf. 19(4): 723–749. DOI: https://doi.org/10.1007/s003550100149.
  • Hall, P. (1935). On representatives of subsets. In: Gessel, I., Rota, G.-C., eds. Classic Papers in Combinatorics. Boston, MA: Birkhäuser, pp. 58–62.
  • Meunier, F., Su, F. E. (2019). Multilabeled versions of Sperner’s and Fan’s lemmas and applications. SIAM J. Appl. Algebra Geom. 3(3): 391–411.
  • Nyman, K., Su, F. E., Zerbib, S. (2020). Fair division with multiple pieces. Disc. Appl. Math. 283(1): 115–122.
  • Scarf, H. E. (1982). The computation of equilibrium prices: an exposition. In: Arrow, K. J., Intriligator, M. D., Hildenbrand, W., Sonnenschein, H., eds. Handbook of Mathematical Economics, Vol. 2. Amsterdam: North-Holland, pp. 1007–1061.
  • Su, F. E. (1999). Rental harmony: Sperner’s lemma in fair division. Amer. Math. Monthly. 106(10): 930–942.
  • Sung, S. C., Vlach, M. (2004). Competitive envy-free division. Soc. Choice Welf. 23(1): 103–111.
  • Svensson, L.-G. (1983). Large indivisibles: an analysis with respect to price equilibrium and fairness. Econometrica. 151(4): 939–954. DOI: https://doi.org/10.2307/1912044.
  • Velez, R. A. (2016). Fairness and externalities. Theor. Econ. 11(1): 381–410.
  • Velez, R. A. (2018). Equitable rent division. ACM Trans. Econ. Comput. 6(2): 1–25.

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