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Envy-freeness in house allocation problems

Author

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  • Gan, Jiarui
  • Suksompong, Warut
  • Voudouris, Alexandros A.

Abstract

We consider the house allocation problem, where m houses are to be assigned to n agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor.

Suggested Citation

  • Gan, Jiarui & Suksompong, Warut & Voudouris, Alexandros A., 2019. "Envy-freeness in house allocation problems," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 104-106.
    • Handle: RePEc:eee:matsoc:v:101:y:2019:i:c:p:104-106
    DOI: 10.1016/j.mathsocsci.2019.07.005
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    References listed on IDEAS

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    1. Zhou, Lin, 1990. "On a conjecture by gale about one-sided matching problems," Journal of Economic Theory, Elsevier, vol. 52(1), pages 123-135, October.
    2. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    3. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
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    Cited by:

    1. Takehiro Ito & Yuni Iwamasa & Naonori Kakimura & Naoyuki Kamiyama & Yusuke Kobayashi & Yuta Nozaki & Yoshio Okamoto & Kenta Ozeki, 2022. "Reforming an Envy-Free Matching," Papers 2207.02641, arXiv.org.
    2. Pasin Manurangsi & Warut Suksompong, 2020. "Closing Gaps in Asymptotic Fair Division," Papers 2004.05563, arXiv.org.

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