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Fully Polynomial-Time Approximation Schemes for Fair Rent Division

Author

Listed:
  • Eshwar Ram Arunachaleswaran

    (Department of Computer and Information Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Siddharth Barman

    (Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560012, India)

  • Nidhi Rathi

    (Department of Mathematics, Indian Institute of Science, Bangalore 560012, India)

Abstract

We study the problem of fair rent division that entails splitting the rent and allocating the rooms of an apartment among agents in a fair manner (i.e., under the imposed rents, no agent has a strictly stronger preference for any other agent’s room). The utility functions specify the cardinal preferences of the agents for the rooms for every possible room rent. Although envy-free solutions are guaranteed to exist under reasonably general utility functions, efficient algorithms for finding them were known only for quasilinear utilities . This work addresses this notable gap and develops a fully polynomial-time approximation scheme for fair rent division with minimal assumptions on the utility functions. Envy-free solutions correspond to equilibria of a two-sided matching market with monetary transfers; hence, this work also provides efficient algorithms for finding approximate equilibria in such markets. We complement the algorithmic results by proving that the fair rent division problem lies in the intersection of the complexity classes polynomial parity arguments on directed graphs and polynomial local search.

Suggested Citation

  • Eshwar Ram Arunachaleswaran & Siddharth Barman & Nidhi Rathi, 2022. "Fully Polynomial-Time Approximation Schemes for Fair Rent Division," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 1970-1998, August.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:3:p:1970-1998
    DOI: 10.1287/moor.2021.1196
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    References listed on IDEAS

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