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Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm

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  • Brams, Steven J.
  • Kilgour, D. Marc
  • Klamler, Christian

Abstract

Many procedures have been suggested for the venerable problem of dividing a set of indivisible items between two players. We propose a new algorithm (AL), related to one proposed by Brams and Taylor (BT), which requires only that the players strictly rank items from best to worst. Unlike BT, in which any item named by both players in the same round goes into a “contested pile,” AL may reduce, or even eliminate, the contested pile, allocating additional or more preferred items to the players. The allocation(s) that AL yields are Pareto-optimal, envy-free, and maximal; as the number of items (assumed even) increases, the probability that AL allocates all the items appears to approach infinity if all possible rankings are equiprobable. Although AL is potentially manipulable, strategizing under it would be difficult in practice.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47400.

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Date of creation: Jun 2013
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Handle: RePEc:pra:mprapa:47400

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Keywords: Two-person fair division; indivisible items; envy-freeness; efficiency; algorithm;

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  1. Brams,S.L. & Kaplan,T.R., 2002. "Dividing the indivisible : procedures for allocating cabinet ministries to political parties in a parliamentary system," Working Papers, Bielefeld University, Center for Mathematical Economics 340, Bielefeld University, Center for Mathematical Economics.
  2. Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2009. "The undercut procedure: an algorithm for the envy-free division of indivisible items," MPRA Paper 12774, University Library of Munich, Germany.
  3. Dorothea Herreiner & Clemens Puppe, 2002. "A simple procedure for finding equitable allocations of indivisible goods," Social Choice and Welfare, Springer, Springer, vol. 19(2), pages 415-430, April.
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