2026-07-24T01:14:28Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15501 2024-03-06T10:55:27Z ddc:004 open_access

Simple Envy-Free and Truthful Mechanisms for Cake Cutting with a Small Number of Cuts Asano, Takao cake-cutting problem envy-freeness fairness truthfulness mechanism design 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]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Takao Asano 2021 Is Part Of LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2021.68 urn:nbn:de:0030-drops-155011 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.68 eng https://creativecommons.org/licenses/by/4.0/legalcode