Maximin Envy-Free Division of Indivisible Items

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

    Research output: Contribution to journalArticlepeer-review


    Assume that two players have strict rankings over an even number of indivisible items. We propose two algorithms to find balanced allocations of these items that are maximin—maximize the minimum rank of the items that the players receive—and are envy-free and Pareto-optimal, if such allocations exist. To determine whether an envy-free allocation exists, we introduce a simple condition on preference profiles; in fact, our condition guarantees the existence of a maximin, envy-free, and Pareto-optimal allocation. Although not strategy-proof, our algorithms would be difficult to manipulate unless a player has complete information about its opponent’s ranking. We assess the applicability of the algorithms to real-world problems, such as allocating marital property in a divorce or assigning people to committees or projects.

    Original languageEnglish (US)
    Pages (from-to)115-131
    Number of pages17
    JournalGroup Decision and Negotiation
    Issue number1
    StatePublished - Jan 1 2017


    • Allocation of indivisible items
    • Envy-freeness
    • Fair division
    • Maximin

    ASJC Scopus subject areas

    • General Decision Sciences
    • Arts and Humanities (miscellaneous)
    • General Social Sciences
    • Strategy and Management
    • Management of Technology and Innovation


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