TY - JOUR

T1 - Resource-monotonicity and population-monotonicity in connected cake-cutting

AU - Segal-Halevi, Erel

AU - Sziklai, Balázs R.

N1 - Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/9

Y1 - 2018/9

N2 - In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way —giving each agent a piece with a value of at least 1∕n of the total. In many applications, such as dividing a land-estate or a time-interval, it is also important that the pieces are connected. We propose two additional requirements: resource-monotonicity (RM) and population-monotonicity (PM). When either the cake or the set of agents grows or shrinks and the cake is re-divided using the same rule, the utility of all remaining agents must change in the same direction. Classic cake-cutting protocols are neither RM nor PM. Moreover, we prove that no Pareto-optimal proportional division rule can be either RM or PM. Motivated by this negative result, we search for division rules that are weakly-Pareto-optimal — no other division is strictly better for all agents. We present two such rules. The relative-equitable rule, which assigns the maximum possible relative value equal for all agents, is proportional and PM. The so-called rightmost mark rule, which is an improved version of the Cut and Choose protocol, is proportional and RM for two agents.

AB - In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way —giving each agent a piece with a value of at least 1∕n of the total. In many applications, such as dividing a land-estate or a time-interval, it is also important that the pieces are connected. We propose two additional requirements: resource-monotonicity (RM) and population-monotonicity (PM). When either the cake or the set of agents grows or shrinks and the cake is re-divided using the same rule, the utility of all remaining agents must change in the same direction. Classic cake-cutting protocols are neither RM nor PM. Moreover, we prove that no Pareto-optimal proportional division rule can be either RM or PM. Motivated by this negative result, we search for division rules that are weakly-Pareto-optimal — no other division is strictly better for all agents. We present two such rules. The relative-equitable rule, which assigns the maximum possible relative value equal for all agents, is proportional and PM. The so-called rightmost mark rule, which is an improved version of the Cut and Choose protocol, is proportional and RM for two agents.

UR - http://www.scopus.com/inward/record.url?scp=85050889214&partnerID=8YFLogxK

U2 - 10.1016/j.mathsocsci.2018.07.001

DO - 10.1016/j.mathsocsci.2018.07.001

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AN - SCOPUS:85050889214

SN - 0165-4896

VL - 95

SP - 19

EP - 30

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

ER -