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Existence and Optimality of Envy-Free random allocations

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  • Anna Vakarova

Abstract

I provide a unified framework to establish the existence of a weak Pareto efficient, envy-free allocation in general settings: random allocations are probability measures on a compact metric space, and preferences of agents are represented by continuous, concave utility function on the space of probability measures. The generality of my setting nests the existence results for small spaces with indivisibles -- the list of prominent applications includes the school assignment problem and the house allocation problem. The technique developed to prove the existence also applies to allocation problems with divisibles, like fair cake-cutting or land-division problems. Here I also show that even when agents' preferences are not atomless, the allocation in question can be represented as a probability measure over partitions with finite support. Last but not least, I apply the existence result to new allocation problems that no existing framework encompasses. These include allocation of indivisible goods or services over time and allocation of differentiated goods.

Suggested Citation

  • Anna Vakarova, 2026. "Existence and Optimality of Envy-Free random allocations," Papers 2605.28263, arXiv.org.
    • Handle: RePEc:arx:papers:2605.28263
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    References listed on IDEAS

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    1. Federico Echenique & Antonio Miralles & Jun Zhang, 2019. "Fairness and efficiency for probabilistic allocations with participation constraints," Papers 1908.04336, arXiv.org, revised May 2020.
    2. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    3. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
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