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On Connected Strongly-Proportional Cake-Cutting

Author

Listed:
  • Zsuzsanna Jank'o
  • Attila Jo'o
  • Erel Segal-Halevi
  • Sheung Man Yuen

Abstract

We investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents. We characterize the existence of an allocation in which every agent receives a contiguous piece worth strictly more than their proportional share, also known as a *strongly-proportional allocation*. The characterization is supplemented with an algorithm that determines the existence of a connected strongly-proportional allocation using at most $n \cdot 2^{n-1}$ queries. We provide a simpler characterization for agents with strictly positive valuations, and show that the number of queries required to determine the existence of a connected strongly-proportional allocation is in $\Theta(n^2)$. Our proofs are constructive and yield a connected strongly-proportional allocation, when it exists, using a similar number of queries.

Suggested Citation

  • Zsuzsanna Jank'o & Attila Jo'o & Erel Segal-Halevi & Sheung Man Yuen, 2023. "On Connected Strongly-Proportional Cake-Cutting," Papers 2312.15326, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2312.15326
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    References listed on IDEAS

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    1. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.
    2. William Thomson, 2007. "Children Crying at Birthday Parties. Why?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 501-521, June.
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