 Resource-monotonicity and population-monotonicity in connected cake-cuttingErel Segal-Halevi and Balázs Sziklai Mathematical Social Sciences, 2018, vol. 95, issue C, 19-30 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. Date: 2018 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:95:y:2018:i:c:p:19-30 DOI: 10.1016/j.mathsocsci.2018.07.001 Access Statistics for this article Mathematical Social Sciences is currently edited by J.-F. Laslier More articles in Mathematical Social Sciences from Elsevier |
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