The undercut procedure: an algorithm for the envy-free division of indivisible items

@article{Brams2009TheUP,
  title={The undercut procedure: an algorithm for the envy-free division of indivisible items},
  author={Steven J. Brams and D. Marc Kilgour and Christian Klamler},
  journal={Social Choice and Welfare},
  year={2009},
  volume={39},
  pages={615-631}
}
We propose a procedure for dividing a set of indivisible items between two players. We assume that each player’s preference over subsets of items is consistent with a strict ranking of the items, and that neither player has information about the other’s preferences. Our procedure ensures an envy-free division—each player receives a subset of items that it values more than the other player’s complementary subset—given that an envy-free division of “contested items,” which the players would… 

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