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Fair Division with Subsidy

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Book cover Algorithmic Game Theory (SAGT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11801))

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Abstract

When allocating a set of goods to a set of agents, a classic fairness notion called envy-freeness requires that no agent prefer the allocation of another agent to her own. When the goods are indivisible, this notion is impossible to guarantee, and prior work has focused on its relaxations. However, envy-freeness can be achieved if a third party is willing to subsidize by providing a small amount of money (divisible good), which can be allocated along with the indivisible goods.

In this paper, we study the amount of subsidy needed to achieve envy-freeness for agents with additive valuations, both for a given allocation of indivisible goods and when we can choose the allocation. In the former case, we provide a strongly polynomial time algorithm to minimize subsidy. In the latter case, we provide optimal constructive results for the special cases of binary and identical valuations, and make a conjecture in the general case. Our experiments using real data show that a small amount of subsidy is sufficient in practice.

Full version of this paper is available at www.cs.toronto.edu/~nisarg/papers/subsidy.pdf.

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Notes

  1. 1.

    Note that \({\mathcal {E}}({\mathcal {A}}) \ne \emptyset \) because the allocation maximizing utilitarian welfare is always envy-freeable due to Theorem 1.

  2. 2.

    The leximin rule finds an allocation that maximizes the minimum utility, subject to that maximizes the second minimum utility, and so on.

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Authors and Affiliations

  1. University of Toronto, Toronto, Canada

    Daniel Halpern & Nisarg Shah

Authors
  1. Daniel Halpern
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  2. Nisarg Shah
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Correspondence to Daniel Halpern .

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Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Dimitris Fotakis

  2. Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis

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Halpern, D., Shah, N. (2019). Fair Division with Subsidy. In: Fotakis, D., Markakis, E. (eds) Algorithmic Game Theory. SAGT 2019. Lecture Notes in Computer Science(), vol 11801. Springer, Cham. https://doi.org/10.1007/978-3-030-30473-7_25

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  • DOI: https://doi.org/10.1007/978-3-030-30473-7_25

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-30473-7

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