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Fairness and efficiency in cake-cutting with single-peaked preferences

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  • Bhardwaj, Bhavook
  • Kumar, Rajnish
  • Ortega, Josué

Abstract

We study the cake-cutting problem where agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang and Wu (2019) to obtain envy-free allocations can yield large welfare losses. Using a simplifying assumption, we characterize all Pareto optimal allocations, which have a simple structure: are peak-preserving and non-wasteful. Finally, we provide simple alternative mechanisms that Pareto dominate that of Wang–Wu and achieve envy-freeness or Pareto optimality.

Suggested Citation

  • Bhardwaj, Bhavook & Kumar, Rajnish & Ortega, Josué, 2020. "Fairness and efficiency in cake-cutting with single-peaked preferences," Economics Letters, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:ecolet:v:190:y:2020:i:c:s0165176520300690
    DOI: 10.1016/j.econlet.2020.109064
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    1. Kyropoulou, Maria & Ortega, Josué & Segal-Halevi, Erel, 2022. "Fair cake-cutting in practice," Games and Economic Behavior, Elsevier, vol. 133(C), pages 28-49.
    2. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
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    4. Josué Ortega & Erel Segal-Halevi, 2022. "Obvious manipulations in cake-cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 969-988, November.
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    15. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
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    1. Josué Ortega & Erel Segal-Halevi, 2022. "Obvious manipulations in cake-cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 969-988, November.
    2. Kyropoulou, Maria & Ortega, Josué & Segal-Halevi, Erel, 2022. "Fair cake-cutting in practice," Games and Economic Behavior, Elsevier, vol. 133(C), pages 28-49.

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    More about this item

    Keywords

    Cake-cutting; Fair division; Single-peaked preferences;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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