arXiv subjects

Kenzo Imamura

Publications and source records attributed to Kenzo Imamura.

6 recordsLinked to original sources

arXiv2026

Cores of $3$-distant convex games

Convex cooperative games have a nonempty core and admit an efficient construction of core allocations. However, economically natural local frictions may violate convexity. We study the core of $3$-distant convex games, which permit violations of convexity only between closely related coalitions. Although the core of such a game may be empty, we establish a simple necessary and sufficient condition for its nonemptiness. We also develop a strongly polynomial-time combinatorial algorithm for finding a core allocation whenever one exists. Finally, we demonstrate the applicability of the framework to oligopolistic competition with merger synergies and profit allocation of joint production with complementary inputs.

cs.GT↗

arXiv2026

Overlapping Reserves without a Common Priority: Theory and an Application to School Choice in Chile

We study matching markets with overlapping reserves governed by heterogeneous priorities. When applicants qualify for multiple reserves, how they are routed can affect reserve utilization and which applicants are admitted. We introduce classify-and-rank choice rules that yield strategy-proof deferred acceptance mechanisms satisfying maximum reserve utilization and priority-respect. We axiomatically characterize our mechanism's admission outcomes for any given classification and reserve order. With two reserve categories, we provide a foundation for the reserve order and establish its distributional implications for access across eligibility groups. Using nine cycles of Chilean school admissions, which feature such reserves, we document reserve-utilization failures under the deployed mechanism and show that their frequency depends sharply on the reserve order. We show how our mechanism can be adapted to Chile's institutional setting to prevent such failures. Under this alternative mechanism, the reserve order generates a distributional pattern across eligibility groups, consistent with our theory.

econ.TH↗

arXiv2026

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

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.

econ.TH↗

arXiv2026

A Note on Assortativeness Measures

Chiappori et al. (2025) study several indices of assortativeness in matching, including the aggregate likelihood ratio and the odds ratio. We provide a counterexample showing that their axiomatization of the aggregate likelihood ratio is not valid as stated. We identify the exact class of indices characterized by the axioms in Chiappori et al. (2025). We then show that the axiomatization of the aggregate likelihood ratio can be recovered by adding new axioms. In addition, we point out errors in the axiomatizations of other measures in Chiappori et al. (2025). Finally, we offer a generalization of the odds ratio from two-type markets to multi-type markets.

econ.TH↗

arXiv2025

Properties of Path-Independent Choice Correspondences and Their Applications to Efficient and Stable Matchings

Choice correspondences are crucial in decision-making, especially when faced with indifferences or ties. While tie-breaking can transform a choice correspondence into a choice function, it often introduces inefficiencies. This paper introduces a novel notion of path-independence (PI) for choice correspondences, extending the existing concept of PI for choice functions. Intuitively, a choice correspondence is PI if any consistent tie-breaking produces a PI choice function. This new notion yields several important properties. First, PI choice correspondences are rationalizabile, meaning they can be represented as the maximization of a utility function. This extends a core feature of PI in choice functions. Second, we demonstrate that the set of choices selected by a PI choice correspondence for any subset forms a generalized matroid. This property reveals that PI choice correspondences exhibit a nice structural property. Third, we establish that choice correspondences rationalized by ordinally concave functions inherently satisfy the PI condition. This aligns with recent findings that a choice function satisfies PI if and only if it can be rationalized by an ordinally concave function. Building on these theoretical foundations, we explore stable and efficient matchings under PI choice correspondences. Specifically, we investigate constrained efficient matchings, which are efficient (for one side of the market) within the set of stable matchings. Under responsive choice correspondences, such matchings are characterized by cycles. However, this cycle-based characterization fails in more general settings. We demonstrate that when the choice correspondence of each school satisfies both PI and monotonicity conditions, a similar cycle-based characterization is restored. These findings provide new insights into the matching theory and its practical applications.

cs.GT↗

arXiv2022

Market Design with Deferred Acceptance: A Recipe for Policymaking

We introduce a method to derive from a characterization of institutional choice rules (or priority rules), a characterization of the Gale-Shapley deferred-acceptance (DA) matching rule based on these choice rules. We apply our method to school choice in Chile, where we design choice rules for schools that are uniquely compatible with the School Inclusion Law and derive a set of matching properties, compatible with the law, that characterizes the DA rule based on the designed choice rules. Our method provides a recipe for establishing such results and can help policymakers decide on which allocation rule to use in practice.

econ.TH↗