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Documents authored by Asano, Takao

Document
DOI: 10.4230/LIPIcs.ISAAC.2021.68
Simple Envy-Free and Truthful Mechanisms for Cake Cutting with a Small Number of Cuts

Authors: Takao Asano

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
For the cake-cutting problem, Alijani, et al. [Reza Alijani et al., 2017; Masoud Seddighin et al., 2019] and Asano and Umeda [Takao Asano and Hiroyuki Umeda, 2020; Takao Asano and Hiroyuki Umeda, 2020] gave envy-free and truthful mechanisms with a small number of cuts, where the desired part of each player’s valuation function is a single interval on a given cake. In this paper, we give envy-free and truthful mechanisms with a small number of cuts, which are much simpler than those proposed by Alijani, et al. [Reza Alijani et al., 2017; Masoud Seddighin et al., 2019] and Asano and Umeda [Takao Asano and Hiroyuki Umeda, 2020; Takao Asano and Hiroyuki Umeda, 2020]. Furthermore, we show that this approach can be applied to the envy-free and truthful mechanism proposed by Chen, et al. [Yiling Chen et al., 2013], where the valuation function of each player is more general and piecewise uniform. Thus, we can obtain an envy-free and truthful mechanism with a small number of cuts even if the valuation function of each player is piecewise uniform, which solves the future problem posed by Alijani, et al. [Reza Alijani et al., 2017; Masoud Seddighin et al., 2019].
Cite as

Takao Asano. Simple Envy-Free and Truthful Mechanisms for Cake Cutting with a Small Number of Cuts. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 68:1-68:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{asano:LIPIcs.ISAAC.2021.68,
  author =	{Asano, Takao},
  title =	{{Simple Envy-Free and Truthful Mechanisms for Cake Cutting with a Small Number of Cuts}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{68:1--68:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.68},
  URN =		{urn:nbn:de:0030-drops-155011},
  doi =		{10.4230/LIPIcs.ISAAC.2021.68},
  annote =	{Keywords: cake-cutting problem, envy-freeness, fairness, truthfulness, mechanism design}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.15
Cake Cutting: An Envy-Free and Truthful Mechanism with a Small Number of Cuts

Authors: Takao Asano and Hiroyuki Umeda

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
The mechanism for the cake-cutting problem based on the expansion process with unlocking proposed by Alijani, Farhadi, Ghodsi, Seddighin, and Tajik [Reza Alijani et al., 2017; Masoud Seddighin et al., 2019] uses a small number of cuts, but is not actually envy-free and truthful, although they claimed that it is envy-free and truthful. In this paper, we consider the same cake-cutting problem and give a new envy-free and truthful mechanism with a small number of cuts, which is not based on their expansion process with unlocking.
Cite as

Takao Asano and Hiroyuki Umeda. Cake Cutting: An Envy-Free and Truthful Mechanism with a Small Number of Cuts. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{asano_et_al:LIPIcs.ISAAC.2020.15,
  author =	{Asano, Takao and Umeda, Hiroyuki},
  title =	{{Cake Cutting: An Envy-Free and Truthful Mechanism with a Small Number of Cuts}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.15},
  URN =		{urn:nbn:de:0030-drops-133599},
  doi =		{10.4230/LIPIcs.ISAAC.2020.15},
  annote =	{Keywords: cake-cutting problem, envy-freeness, fairness, truthfulness, mechanism design}
}
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