arXiv subjects

R. Pablo Arribillaga

Publications and source records attributed to R. Pablo Arribillaga.

13 recordsLinked to original sources

arXiv2026

The Large and Likely Inefficiency of Stable Matching Mechanisms

We prove that any stable matching mechanism suffers from systematic inefficiency of striking magnitude: in large random markets, any stable allocation is Pareto-inefficient with high probability, and almost all students can simultaneously improve their placements without harming anyone else. We establish this result by showing that the envy digraph generated by the student-proposing Deferred Acceptance mechanism contains a unique giant strongly connected component, implying that nearly all students are improvable via trading cycles. Finally, we show that every maximal cycle packing covers almost all students, revealing a surprising asymptotic equivalence among all efficient mechanisms that Pareto-dominate DA.

econ.TH↗

arXiv2026

Sharing the proceeds from a hierarchical venture when agents have needs

We consider a setting in which a set of agents are hierarchically organized for a joint venture. They each generate revenues for the joint venture and have individual needs to cover. The aim is to distribute aggregate revenues appropriately. We characterize a family of need-adjusted geometric rules where the net revenue (after covering needs) "bubbles up" in the hierarchy, as well as a need-adjusted serial rule in which the net revenue is equally shared among each agent and his predecessors in the hierarchy.

econ.TH↗

arXiv2026

Justifiable Priority Violations

Addressing the large inefficiencies generated by the Deferred Acceptance (DA) mechanism requires priority violations, but which ones are justifiable? The leading approach is to ask individuals if they consent to waive their priority ex-ante. We develop an alternative question-free solution, in which a priority violation is justifiable whenever the affected student either (i) directly benefits from the improvement, or (ii) is unimprovable under any assignment that Pareto-dominates DA. This endogenous justifiability criterion permits improvements unattainable by the leading consent-based mechanism under any consent structure. We provide a ``just below cutoffs'' mechanism that always finds a strongly justifiable matching whenever DA's outcome is inefficient, and build on it to construct a polynomial-time algorithm that expands justifiable improvements iteratively, converging to a DA improvement that cannot be Pareto-improved by any justifiable matching without strictly expanding the beneficiary set. Finally, we prove theoretically that both the ex-ante consent and the endogenous justifiability frameworks have important limitations in reaching Pareto-efficient outcomes, and use simulations to quantify how binding these constraints are in practice.

econ.TH↗

arXiv2026

The Distribution of Envy in Matching Markets

We study the distribution of envy in random matching markets under the Deferred Acceptance (DA) algorithm. Using tools from applied probability, we compute the expected number of proposing agents whom nobody envies and those who envy nobody. We obtain an exact finite-market expression for the former, based on a connection with the coupon collector problem, and asymptotic bounds for the latter. To put these quantities into perspective, we compare them to their counterparts under Random Serial Dictatorship (RSD): while RSD assigns a constant fraction of agents to their top choice, both DA and RSD leave exactly $H_n$ proposing agents unenvied in expectation. Our results show that these clearly unimprovable proposing agents constitute a vanishing fraction of the market.

econ.TH↗

arXiv2025

Non-obvious manipulability in division problems with general preferences

In problems involving the allocation of a single non-disposable commodity, we study rules defined on a general domain of preferences requiring only that each preference exhibit a unique global maximum. Our focus is on rules that satisfy a relaxed form of strategy-proofness, known as non-obvious manipulability. We show that the combination of efficiency and non-obvious manipulability leads to impossibility results, whereas weakening efficiency to unanimity gives rise to a large family of well-behaved non-obviously manipulable rules.

econ.TH↗

arXiv2025

What Pareto-Efficiency Adjustments Cannot Fix

The Deferred Acceptance (DA) algorithm is stable and strategy-proof, but can produce outcomes that are Pareto-inefficient for students, and thus several alternative mechanisms have been proposed to correct this inefficiency. However, we show that these mechanisms cannot correct DA's rank-inefficiency and inequality, because these shortcomings can arise even in cases where DA is Pareto-efficient. We also examine students' segregation in settings with advantaged and marginalized students. We prove that the demographic composition of every school is perfectly preserved under any Pareto-efficient mechanism that dominates DA, and consequently fully segregated schools under DA maintain their extreme homogeneity.

econ.TH↗

arXiv2025

Regret-free truth-telling voting rules

We study the ability of different classes of voting rules to induce agents to report their preferences truthfully, if agents want to avoid regret. First, we show that regret-free truth-telling is equivalent to strategy-proofness among tops-only rules. Then, we focus on three important families of (non-tops-only) voting methods: maxmin, scoring, and Condorcet consistent ones. We prove positive and negative results for both neutral and anonymous versions of maxmin and scoring rules. In several instances we provide necessary and sufficient conditions. We also show that Condorcet consistent rules that satisfy a mild monotonicity requirement are not regret-free truth-telling. Successive elimination rules fail to be regret-free truth-telling despite not satisfying the monotonicity condition. Lastly, we provide two characterizations for the case of three alternatives and two agents.

econ.TH↗

arXiv2025

A Note on Obvious Manipulations of Quantile Stable Mechanisms

In two-sided matching markets with contracts, quantile (or generalized median) stable mechanisms represent an interesting class that produces stable allocations which can be viewed as compromises between both sides of the market. These mechanisms balance the competing priorities of the parties while maintaining stability. This paper explores obvious manipulations of quantile stable mechanisms. Unfortunately, we get that any quantile stable mechanism different to the doctor-proposal DA is obviously manipulable. Our findings highlight the trade-offs between robustness to manipulation and other desirable properties, such as equity, in the design of stable matching mechanisms.

econ.TH↗

arXiv2024

Obvious manipulations, consistency, and the uniform rule

In the problem of fully allocating an infinitely divisible commodity among agents whose preferences are single-peaked, we show that the uniform rule is the only allocation rule that satisfies efficiency, the equal division guarantee, consistency, and non-obvious manipulability.

econ.TH↗

arXiv2024

Obvious Manipulations in Matching without and with Contracts

This paper explores many-to-one matching models, both with and without contracts, where doctors' preferences are private and hospitals' preferences are public and substitutable. It is known that any stable-dominating mechanism --which is either stable or individually rational and Pareto-dominates (from the doctors' perspective) a stable mechanism--, is susceptible to manipulation by doctors. Our study focuses on \textit{obvious manipulations} and identifies stable-dominating mechanisms that prevent them. Without contracts, we show that more efficient mechanisms are less likely to be obviously manipulable and that any stable-dominating mechanism is not obviously manipulable. However, with contracts, none of these results hold. While we demonstrate that the Doctor-Proposing Deferred Acceptance (DA) Mechanism remains not obviously manipulable, we show that the Hospital-Proposing DA Mechanism and any efficient mechanism that Pareto-dominates the Doctor-Proposing DA Mechanism become (very) obviously manipulable, in the model with contracts.

econ.TH↗

arXiv2024

Obvious Strategy-proofness with Respect to a Partition

We define and study obvious strategy-proofness with respect to a partition of the set of agents. It encompasses strategy-proofness as a special case when the partition is the coarsest one and obvious strategy-proofness when the partition is the finest. For any partition, it falls between these two extremes. We establish two general properties of this new notion and apply it to the simple anonymous voting problem with two alternatives and strict preferences.

econ.TH↗

arXiv2024

Not obviously manipulable allotment rules

In the problem of allocating a single non-disposable commodity among agents whose preferences are single-peaked, we study a weakening of strategy-proofness called not obvious manipulability (NOM). If agents are cognitively limited, then NOM is sufficient to describe their strategic behavior. We characterize a large family of own-peak-only rules that satisfy efficiency, NOM, and a minimal fairness condition. We call these rules "simple". In economies with excess demand, simple rules fully satiate agents whose peak amount is less than or equal to equal division and assign, to each remaining agent, an amount between equal division and his peak. In economies with excess supply, simple rules are defined symmetrically. These rules can be thought of as a two-step procedure that involves solving a claims problem. We also show that the single-plateaued domain is maximal for the characterizing properties of simple rules. Therefore, even though replacing strategy-proofness with NOM greatly expands the family of admissible rules, the maximal domain of preferences involved remains basically unaltered.

econ.TH↗

arXiv2022

Obvious manipulations of tops-only voting rules

In a voting problem with a finite set of alternatives to choose from, we study the manipulation of tops-only rules. Since all non-dictatorial (onto) voting rules are manipulable when there are more than two alternatives and all preferences are allowed, we look for rules in which manipulations are not obvious. First, we show that a rule does not have obvious manipulations if and only if when an agent vetoes an alternative it can do so with any preference that does not have such alternative in the top. Second, we focus on two classes of tops-only rules: (i) (generalized) median voter schemes, and (ii) voting by committees. For each class, we identify which rules do not have obvious manipulations on the universal domain of preferences.

econ.TH↗