 Almost envy-free allocations with connected bundlesVittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci and William S. Zwicker Games and Economic Behavior, 2022, vol. 131, issue C, 197-221 Abstract: We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph. If the graph is a path and the utility functions are monotonic over bundles, we show the existence of EF1 allocations for at most four agents, and the existence of EF2 allocations for any number of agents; our proofs involve discrete analogues of the Stromquist's moving-knife protocol and the Su–Simmons argument based on Sperner's lemma. For identical utilities, we provide a polynomial-time algorithm that computes an EF1 allocation for any number of agents. For the case of two agents, we characterize the class of graphs that guarantee the existence of EF1 allocations as those whose biconnected components are arranged in a path; this property can be checked in linear time. Keywords: Envy-free division; Cake-cutting; Resource allocation; Algorithmic game theory (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:131:y:2022:i:c:p:197-221 DOI: 10.1016/j.geb.2021.11.006 Access Statistics for this article Games and Economic Behavior is currently edited by E. Kalai More articles in Games and Economic Behavior from Elsevier |
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