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Two Algorithms for Additive and Fair Division of Mixed Manna

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KI 2020: Advances in Artificial Intelligence (KI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12325))

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Abstract

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property (EFX) and three new and related properties (EFX\(_0\), EFX\(^3\) and EF1\(^3\)) in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1\(^3\) allocation. With \(-\alpha /0/\alpha \) utilities, this algorithm returns an EFX\(^3\) and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With \(-\alpha /0/\beta \) utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.

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Author information

Authors and Affiliations

  1. Technical University Berlin, Berlin, Germany

    Martin Aleksandrov & Toby Walsh

Authors
  1. Martin Aleksandrov
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  2. Toby Walsh
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Corresponding author

Correspondence to Martin Aleksandrov .

Editor information

Editors and Affiliations

  1. Universität Bamberg, Bamberg, Germany

    Ute Schmid

  2. Örebro University, Örebro, Sweden

    Franziska Klügl

  3. Universität Bamberg, Bamberg, Germany

    Diedrich Wolter

A A Complete Version of Algorithm 1

A A Complete Version of Algorithm 1

For reasons of space, we presented a short version of Algorithm 1 in the main text. We present in here a complete version of it.

figure d

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Aleksandrov, M., Walsh, T. (2020). Two Algorithms for Additive and Fair Division of Mixed Manna. In: Schmid, U., Klügl, F., Wolter, D. (eds) KI 2020: Advances in Artificial Intelligence. KI 2020. Lecture Notes in Computer Science(), vol 12325. Springer, Cham. https://doi.org/10.1007/978-3-030-58285-2_1

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  • DOI: https://doi.org/10.1007/978-3-030-58285-2_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58284-5

  • Online ISBN: 978-3-030-58285-2

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