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Equitable rent division

Author

Listed:
  • Rodrigo A. Velez

    (Texas A&M University, Department of Economics)

Abstract

How should a group of roommates allocate the rooms and contributions to rent in the house they lease? Economists have provided partial answers to this question in a literature that spans the least forty years. Unfortunately, these results were developed in a non-linear fashion, which obscures them to the non-specialist. Recently, computer scientists have developed an interest in this particular problem and have advanced from an algorithmic complexity perspective. Remarkably, an online application, Spliddit.org (Goldman and Procaccia, 2014), has been deployed, gathering thousands of users around the world and sparking new questions about the optimal way to provide recommendations. With this new interest gaining traction in computer science, there is an evident need for a coherent development of the results in economics literature. This paper does so. In particular, we build connections among results that were seemingly unrelated and considerably simplify their development, fill in non-trivial gaps, and identify open questions. Our focus is on incentives issues, the area in which we believe economists have more to contribute in this discussion.

Suggested Citation

  • Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    • Handle: RePEc:txm:wpaper:20170818-001
    as

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    File URL: https://pvsessions.tamu.edu/RePEc/velezeqrent.pdf
    File Function: First version, 2017
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    References listed on IDEAS

    as
    1. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    2. Rodrigo A. Velez, 2017. "Sharing an increase of the rent fairly," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 59-80, January.
    3. Fujinaka, Yuji & Wakayama, Takuma, 2015. "Maximal manipulation of envy-free solutions in economies with indivisible goods and money," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 165-185.
    4. Gabrielle Demange & Ahmet Alkan & David Gale, 1991. "Fair Allocation of Indivisible Goods and Money and Criteria of Justice," Post-Print halshs-00670945, HAL.
    5. Tommy ANDERSSON & Lars EHLERS, 2013. "An Algorithm for Identifying Agent-k-Linked Allocations in Economies with Indivisibilities," Cahiers de recherche 17-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-1767, November.
    7. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 201-215.
    8. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    9. Varian, Hal R., 1976. "Two problems in the theory of fairness," Journal of Public Economics, Elsevier, vol. 5(3-4), pages 249-260.
    10. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    11. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    12. Velez, Rodrigo A., 2015. "Sincere and sophisticated players in an equal-income market," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1114-1129.
    13. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 209-222, March.
    14. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    15. , & , & ,, 2014. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, vol. 9(3), September.
    16. Velez, Rodrigo A., 2016. "Fairness and externalities," Theoretical Economics, Econometric Society, vol. 11(1), January.
    17. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    18. Velez, Rodrigo A. & Thomson, William, 2012. "Let them cheat!," Games and Economic Behavior, Elsevier, vol. 75(2), pages 948-963.
    19. William Thomson, 1984. "The Manipulability of Resource Allocation Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 447-460.
    20. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    21. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
    22. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
    23. Alkan, Ahmet, 1994. "Monotonicity and Envyfree Assignments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(4), pages 605-616, May.
    24. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2014. "Least manipulable Envy-free rules in economies with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 43-49.
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    Cited by:

    1. Tommy Andersson & Lars Ehlers, 2022. "An algorithm for identifying least manipulable envy‐free and budget‐balanced allocations in economies with indivisibilities," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 50-60, March.
    2. Rodrigo A. Velez, 2020. "A polynomial algorithm for maxmin and minmax envy-free rent division on a soft budget," Papers 2002.02966, arXiv.org.
    3. Rodrigo A. Velez, 2019. "Expressive mechanisms for equitable rent division on a budget," Papers 1902.02935, arXiv.org, revised Apr 2020.

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    2. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    3. Rodrigo A. Velez, 2019. "Expressive mechanisms for equitable rent division on a budget," Papers 1902.02935, arXiv.org, revised Apr 2020.
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    6. Velez, Rodrigo A., 2015. "Sincere and sophisticated players in an equal-income market," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1114-1129.
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    9. Tommy ANDERSSON & Lars EHLERS, 2013. "An Algorithm for Identifying Agent-k-Linked Allocations in Economies with Indivisibilities," Cahiers de recherche 17-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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    20. Velez, Rodrigo A., 2016. "Fairness and externalities," Theoretical Economics, Econometric Society, vol. 11(1), January.

    More about this item

    Keywords

    inequity aversion; general equilibrium;

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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