Almost Envy-Free Allocations with Connected Bundles

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Tác giả: Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, William S Zwicker

Ngôn ngữ: eng

Ký hiệu phân loại: 027.4 *Public libraries

Thông tin xuất bản: 2018

Mô tả vật lý:

Bộ sưu tập: Metadata

ID: 162172

 Comment: Accepted journal versionWe 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.
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