Redividing the cake

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Abstract

The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division algorithms that attain various trade-off points between fairness and ownership rights, in various settings differing in the geometric constraints on the allotments: (a) no geometric constraints; (b) connectivity—the cake is a one-dimensional interval and each piece must be a contiguous interval; (c) rectangularity—the cake is a two-dimensional rectangle or rectilinear polygon and the pieces should be rectangles; (d) convexity—the cake is a two-dimensional convex polygon and the pieces should be convex. These re-division algorithms have implications on another problem: the price-of-fairness—the loss of social welfare caused by fairness requirements. Each algorithm implies an upper bound on the price-of-fairness with the respective geometric constraints.

Original languageEnglish
Article number14
JournalAutonomous Agents and Multi-Agent Systems
Volume36
Issue number1
DOIs
StatePublished - Apr 2022

Keywords

  • Cake-cutting
  • Computational geometry
  • Dynamic fair division
  • Land reform
  • Two-dimensional resource allocation

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