Rent Division Among Groups

  • Mohammad Ghodsi
  • Mohamad LatifianEmail author
  • Arman Mohammadi
  • Sadra Moradian
  • Masoud Seddighin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)


In this paper, we extend the Rent Sharing problem to the case that every room must be allocated to a group of agents. In the classic Rent Sharing problem, there are n agents and a house with n rooms. The goal is to allocate one room to each agent and assign a rent to each room in a way that no agent envies any other option. Our setting deviates from the classic Rent Sharing problem in a sense that the rent charged to each room must be divided among the members of the resident group.

We define three notions to evaluate fairness, namely, weak envy-freeness, aggregate envy-freeness and strong envy-freeness. We also define three different policies to divide the cost among the group members, namely, equal, proportional, and free cost-sharing policies.

We present several positive and negative results for different combinations of the fairness criteria and rent-division policies. Specifically, when the groups are pre-determined, we propose a strong envy-free solution that allocates the rooms to the agents, with free cost-sharing policy. In addition, for the case that the groups are not pre-determined, we propose a strong envy-free allocation algorithm with equal cost-sharing policy. We leverage our results to obtain an algorithm that determines the maximum total rent along with the proper allocation and rent-division method.


Fairness Envy-freeness Rent sharing House allocation 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mohammad Ghodsi
    • 1
    • 2
  • Mohamad Latifian
    • 1
    Email author
  • Arman Mohammadi
    • 1
  • Sadra Moradian
    • 1
  • Masoud Seddighin
    • 1
  1. 1.Department of Computer EngineeringSharif University of TechnologyTehranIran
  2. 2.School of Computer ScienceInstitute for Research in Fundamental Sciences (IPM)TehranIran

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