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Simple Envy-Free and Truthful Mechanisms for Cake Cutting with a Small Number of Cuts

Author Takao Asano

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Takao Asano
  • Chuo University, Tokyo, Japan

Acknowledgements

The author would like to thank Professor Shigeo Tsujii of Chuo University.

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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) https://doi.org/10.4230/LIPIcs.ISAAC.2021.68

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].

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • cake-cutting problem
  • envy-freeness
  • fairness
  • truthfulness
  • mechanism design

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