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Meta-Envy-Free Cake-Cutting Protocols

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Mathematical Foundations of Computer Science 2010 (MFCS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6281))

Abstract

This paper discusses cake-cutting protocols when the cake is a heterogeneous good that is represented by an interval in the real line. We propose a new desirable property, the meta-envy-freeness of cake-cutting, which has not been formally considered before. Though envy-freeness was considered to be one of the most important desirable properties, envy-freeness does not prevent envy about role assignment in the protocols. We define meta-envy-freeness that formalizes this kind of envy. We show that current envy-free cake-cutting protocols do not satisfy meta-envy-freeness. Formerly proposed properties such as strong envy-free, exact, and equitable do not directly consider this type of envy and these properties are very difficult to realize. This paper then shows meta-envy-free cake-cutting protocols for two and three party cases.

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Author information

Authors and Affiliations

  1. NTT Communication Science Laboratories, 3-1 Morinosato-Wakamitya, Atsugi, Kanagawa, 243-0198, Japan

    Yoshifumi Manabe

  2. NTT Information Sharing Platform Laboratories, 3-9-11, Midori-cho, Musashino-shi, 180-8585, Japan

    Tatsuaki Okamoto

Authors
  1. Yoshifumi Manabe
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  2. Tatsuaki Okamoto
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Editor information

Editors and Affiliations

  1. Falculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

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Manabe, Y., Okamoto, T. (2010). Meta-Envy-Free Cake-Cutting Protocols. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_44

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  • DOI: https://doi.org/10.1007/978-3-642-15155-2_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15154-5

  • Online ISBN: 978-3-642-15155-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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