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Simple fair division of a square

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  • Legut, Jerzy

Abstract

Suppose we are given a cake represented by the unit interval to be divided among agents evaluating the pieces of the cake by nonatomic probability measures. It is known that we can divide the unit interval into contiguous and connected pieces and assign them to the agents in such a way that the values of the pieces are equal according to the individual agents measures. Such division is said to be equitable and simple. In this paper we show that an equitable and simple division also exists in the case of dividing two-dimensional cake represented by the unit square. In this case, by simple division we mean dividing the unit square firstly by horizontal cuts, and then partition the resulting rectangles by vertical cuts. We give a method of obtaining a proportional and simple division of this cake. Furthermore, we prove the existence of proportional, equitable and simple division.

Suggested Citation

  • Legut, Jerzy, 2020. "Simple fair division of a square," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 35-40.
    • Handle: RePEc:eee:mateco:v:86:y:2020:i:c:p:35-40
    DOI: 10.1016/j.jmateco.2019.11.001
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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.
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    5. Jerzy Legut, 2017. "Optimal Fair Division for Measures with Piecewise Linear Density Functions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-12, June.
    6. Legut, J. & Potters, J.A.M. & Tijs, S.H., 1994. "Economies with land : A game theoretical approach," Other publications TiSEM 37ff121d-d79c-4e41-a06a-9, Tilburg University, School of Economics and Management.
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