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Fairness and Efficiency in Cake-Cutting with Single-Peaked Preferences

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  • Bhavook Bhardwaj
  • Rajnish Kumar
  • Josue Ortega

Abstract

We study the cake-cutting problem when agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang-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 which achieve envy-freeness or Pareto optimality.

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  • Bhavook Bhardwaj & Rajnish Kumar & Josue Ortega, 2020. "Fairness and Efficiency in Cake-Cutting with Single-Peaked Preferences," Papers 2002.03174, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:2002.03174
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    References listed on IDEAS

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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. Ortega, Josué, 2018. "Social integration in two-sided matching markets," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 119-126.
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    4. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, April.
    5. Erel Segal-Halevi & Balázs R. Sziklai, 2019. "Monotonicity and competitive equilibrium in cake-cutting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 363-401, September.
    6. 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.
    7. Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
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    9. Ortega, Josué, 2019. "The losses from integration in matching markets can be large," Economics Letters, Elsevier, vol. 174(C), pages 48-51.
    10. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
    11. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
    12. Yan Long, 2019. "Strategy-proof group selection under single-peaked preferences over group size," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 579-608, October.
    13. 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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    15. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
    16. Fedor Sandomirskiy & Erel Segal-Halevi, 2019. "Efficient Fair Division with Minimal Sharing," Papers 1908.01669, arXiv.org, revised Apr 2022.
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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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    JEL classification:

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

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