Stable and Fair Random Allocations in a Two-Sided Discrete-Concave Market

Kenzo Imamura and Yasushi Kawase

Papers from arXiv.org

Abstract: We study random allocations in two-sided many-to-many matching markets with ties, where random tie-breaking can violate ex ante stability and fairness. We show that, when valuations are discrete concave (M$^\natural$-concave), stable and fair fractional allocations always exist and form a distributive lattice under the induced preference orders. Every such allocation can be implemented as a lottery over stable deterministic allocations that simultaneously gives every agent the highest expected utility compatible with her fractional bundle. Since cardinal utilities are difficult to elicit, we then ask what ordinal preferences over deterministic outcomes can identify. The set of stable and fair fractional allocations is the same for all M$^\natural$-concave valuations consistent with the same ordinal preferences, although utility-preserving lotteries may differ across them. No such dependence arises for additive valuations under matroid constraints, where every implementing lottery is ex post stable and utility-preserving under every consistent cardinal representation.

Date: 2026-06, Revised 2026-09
New Economics Papers: this item is included in nep-dcm, nep-des and nep-mic
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