TY - JOUR
T1 - Three Persons, Two Cuts
T2 - A New Cake-Cutting Algorithm
AU - Brams, Steven J.
AU - Landweber, Peter S.
N1 - Publisher Copyright:
© 2022 Mathematical Association of America.
PY - 2022
Y1 - 2022
N2 - Summary: We describe a 3-person, 2-cut envy-free cake-cutting algorithm, inspired by a continuous moving-knife procedure, that does not require that the players continuously move knifes across the cake. By having the players submit their value functions over the cake to a referee—rather than move knives according to these functions—the referee can ensure that the division is not only envy-free but also maximin. In addition, the referee can use the value functions to find a maximally equitable division, whereby the players receive equally valued shares that are maximal, but this allocation may not be envy-free.
AB - Summary: We describe a 3-person, 2-cut envy-free cake-cutting algorithm, inspired by a continuous moving-knife procedure, that does not require that the players continuously move knifes across the cake. By having the players submit their value functions over the cake to a referee—rather than move knives according to these functions—the referee can ensure that the division is not only envy-free but also maximin. In addition, the referee can use the value functions to find a maximally equitable division, whereby the players receive equally valued shares that are maximal, but this allocation may not be envy-free.
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U2 - 10.1080/0025570X.2022.2023300
DO - 10.1080/0025570X.2022.2023300
M3 - Article
AN - SCOPUS:85123780457
SN - 0025-570X
VL - 95
SP - 110
EP - 122
JO - Mathematics Magazine
JF - Mathematics Magazine
IS - 2
ER -