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Resource-monotonicity and population-monotonicity in connected cake-cutting.
- Source :
-
Mathematical Social Sciences . Sep2018, Vol. 95, p19-30. 12p. - Publication Year :
- 2018
-
Abstract
- Abstract 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PROPORTIONAL control systems
*COMPUTER network protocols
*MONOTONIC functions
Subjects
Details
- Language :
- English
- ISSN :
- 01654896
- Volume :
- 95
- Database :
- Academic Search Index
- Journal :
- Mathematical Social Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 131631253
- Full Text :
- https://doi.org/10.1016/j.mathsocsci.2018.07.001