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Fair Division with Money and Prices

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  • Anna Bogomolnaia
  • Herve Moulin

Abstract

We divide efficiently a pile of indivisible goods in common property, using cash transfers to ensure fairness among agents with utility linear in money. We compare three cognitively feasible and privacy preserving division rules in terms of the guarantees (worst case utility) they offer to the participants. In the first version of Divide & Choose to n agents, they bid for the role of Divider then everyone bids on the shares of the Divider's partition. In the second version each agent announces a partition and they all bid to select the most efficient one. In the Bid & Sell rule the agents bid for the role of Seller: with two agents the smallest bid defines the Seller who then charges any price constrained only by her winning bid. Both rules reward subadditive utilities and penalise superadditive ones, and B&S more so than both D&C-s. B&S is also better placed to collect a larger share of the surplus when agents play safe.

Suggested Citation

  • Anna Bogomolnaia & Herve Moulin, 2022. "Fair Division with Money and Prices," Papers 2202.08117, arXiv.org, revised Jul 2025.
    • Handle: RePEc:arx:papers:2202.08117
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    References listed on IDEAS

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    Cited by:

    1. Dall’Aglio, Marco, 2023. "Fair division of goods in the shadow of market values," European Journal of Operational Research, Elsevier, vol. 307(2), pages 785-801.

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