TY - JOUR
T1 - Mark-Choose-Cut Algorithms for Fair and Strongly Fair Division
AU - Shishido, Harunori
AU - Zeng, Dao Zhi
N1 - Funding Information:
The authors are thankful to Prof. S.J. Brams of New York University, Prof. J.B. Barbanel of Union College for beneficial discussions, and three anonymous referees for helpful comments and suggestions. This work was partially supported by the Ministry of Education, Science, Sports and Culture of Japan, Grant-in-Aid for encouragement of young scientists, No. 09780414, which is gratefully acknowledged.
PY - 1999
Y1 - 1999
N2 - This paper proposes a new criterion to evaluate algorithms for cake division by the number of resulting pieces. Then, inspired by the idea of "cut-and-choose", we present "mark-choose-cut" algorithms for fair and strongly fair cake division problems. They are game-theoretic algorithms. The number of resulting pieces is bounded by 2 × 3n-2 + 1 and 4 × 3n-2 + 1, for fair and strongly fair division respectively.
AB - This paper proposes a new criterion to evaluate algorithms for cake division by the number of resulting pieces. Then, inspired by the idea of "cut-and-choose", we present "mark-choose-cut" algorithms for fair and strongly fair cake division problems. They are game-theoretic algorithms. The number of resulting pieces is bounded by 2 × 3n-2 + 1 and 4 × 3n-2 + 1, for fair and strongly fair division respectively.
KW - (Strongly) fair cake division
KW - Entitlement sequence
KW - Mark-choose-cut algorithm
UR - http://www.scopus.com/inward/record.url?scp=0033415102&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033415102&partnerID=8YFLogxK
U2 - 10.1023/A:1008620404353
DO - 10.1023/A:1008620404353
M3 - Article
AN - SCOPUS:0033415102
VL - 8
SP - 125
EP - 137
JO - Group Decision and Negotiation
JF - Group Decision and Negotiation
SN - 0926-2644
IS - 2
ER -