arXiv subjects

Péter Biró

Publications and source records attributed to Péter Biró.

At least 19 recordsLinked to original sources

arXiv2026

Smart Lotteries in School Choice: Ex-ante Pareto-Improvement with Ex-post Stability

In school choice, students typically have strict preferences over the schools while the schools have coarse priorities over the students based on their distance and their enrolled siblings. The outcome of a centralized admission mechanism is then usually obtained by the Deferred Acceptance (DA) algorithm with random tie-breaking. Therefore, every outcome of this mechanism that occurs with a positive probability is a stable solution for the coarse priorities. This implies a probabilistic assignment, specifying the admission probability for each student-school pair. In this paper, we propose a new efficiency-improving stable 'smart lottery' mechanism. We aim to improve the probabilistic assignment ex-ante in a stochastic dominance sense, while ensuring that the improved random matching is still ex-post stable, meaning that it can be decomposed into stable matchings regarding the original coarse priorities. Therefore, this smart lottery mechanism can provide a clear Pareto-improvement in expectation for any cardinal utilities compared to the standard DA with lottery solution, without sacrificing the stability of the final outcome. We show that although the underlying computational problem is NP-hard, we can solve the problem in practice by using column generation. Our computational results show that the welfare gains by our mechanism are substantially larger than the expected gains by standard methods that realize efficiency improvements after ties have already been broken. Additionally, we illustrate for real-world school choice data of Ghent (Belgium) that, while not theoretically guaranteed, our mechanism can Pareto-improve upon methods that improve upon DA but violate ex-post stability, such as Efficiency-Adjusted Deferred Acceptance.

cs.GT↗

arXiv2026

Ex-post Stability under Two-Sided Matching: Complexity and Characterization

A probabilistic approach to the stable matching problem has been identified as an important research area with several important open problems. When considering random matchings, ex-post stability is a fundamental stability concept. A prominent open problem is characterizing ex-post stability and establishing its computational complexity. We investigate the computational complexity of testing ex-post stability. Our central result is that when either side has ties in the preferences/priorities, testing ex-post stability is NP-complete. The result even holds if both sides have dichotomous preferences. On the positive side, we give an algorithm using an integer programming approach, that can determine a decomposition with a maximum probability of being weakly stable. We also consider stronger versions of ex-post stability (in particular robust ex-post stability and ex-post strong stability) and prove that they can be tested in polynomial time.

cs.GT↗

arXiv2025

Computing Balanced Solutions for Large International Kidney Exchange Schemes When Cycle Length Is Unbounded

In kidney exchange programmes (KEP) patients may swap their incompatible donors leading to cycles of kidney transplants. Nowadays, countries try to merge their national patient-donor pools leading to international KEPs (IKEPs). As shown in the literature, long-term stability of an IKEP can be achieved through a credit-based system. In each round, every country is prescribed a "fair" initial allocation of kidney transplants. The initial allocation, which we obtain by using solution concepts from cooperative game theory, is adjusted by incorporating credits from the previous round, yielding the target allocation. The goal is to find, in each round, an optimal solution that closely approximates this target allocation. There is a known polynomial-time algorithm for finding an optimal solution that lexicographically minimizes the country deviations from the target allocation if only $2$-cycles (matchings) are permitted. In practice, kidney swaps along longer cycles may be performed. However, the problem of computing optimal solutions for maximum cycle length $\ell$ is NP-hard for every $\ell\geq 3$. This situation changes back to polynomial time once we allow unbounded cycle length. However, in contrast to the case where $\ell=2$, we show that for $\ell=\infty$, lexicographical minimization is only polynomial-time solvable under additional conditions (assuming P $\neq$ NP). Nevertheless, the fact that the optimal solutions themselves can be computed in polynomial time if $\ell=\infty$ still enables us to perform a large scale experimental study for showing how stability and total social welfare are affected when we set $\ell=\infty$ instead of $\ell=2$.

cs.GT↗

arXiv2025

Stable Hypergraph Matching in Unimodular Hypergraphs

We study the NP-hard Stable Hypergraph Matching (SHM) problem and its generalization allowing capacities, the Stable Hypergraph $b$-Matching (SH$b$M) problem, and investigate their computational properties under various structural constraints. Our study is motivated by the fact that Scarf's Lemma (Scarf, 1967) together with a result of Lovász (1972) guarantees the existence of a stable matching whenever the underlying hypergraph is normal. Furthermore, if the hypergraph is unimodular (i.e., its incidence matrix is totally unimodular), then even a stable $b$-matching is guaranteed to exist. However, no polynomial-time algorithm is known for finding a stable matching or $b$-matching in unimodular hypergraphs. We identify subclasses of unimodular hypergraphs where SHM and SH$b$M are tractable such as laminar hypergraphs or so-called subpath hypergraphs with bounded-size hyperedges; for the latter case, even a maximum-weight stable $b$-matching can be found efficiently. We complement our algorithms by showing that optimizing over stable matchings is NP-hard even in laminar hypergraphs. As a practically important special case of SH$b$M for unimodular hypergraphs, we investigate a tripartite stable matching problem with students, schools, and companies as agents, called the University Dual Admission problem, which models real-world scenarios in higher education admissions. Finally, we examine a superclass of subpath hypergraphs that are normal but necessarily not unimodular, namely subtree hypergraphs where hyperedges correspond to subtrees of a tree. We establish that for such hypergraphs, stable matchings can be found in polynomial time but, in the setting with capacities, finding a stable $b$-matching is NP-hard.

cs.GT↗

arXiv2024

Partitioned Matching Games for International Kidney Exchange

We introduce partitioned matching games as a suitable model for international kidney exchange programmes, where in each round the total number of available kidney transplants needs to be distributed amongst the participating countries in a "fair" way. A partitioned matching game $(N,v)$ is defined on a graph $G=(V,E)$ with an edge weighting $w$ and a partition $V=V_1 \cup \dots \cup V_n$. The player set is $N = \{1, \dots, n\}$, and player $p \in N$ owns the vertices in $V_p$. The value $v(S)$ of a coalition $S \subseteq N$ is the maximum weight of a matching in the subgraph of $G$ induced by the vertices owned by the players in $S$. If $|V_p|=1$ for all $p\in N$, then we obtain the classical matching game. Let $c=\max\{|V_p| \; |\; 1\leq p\leq n\}$ be the width of $(N,v)$. We prove that checking core non-emptiness is polynomial-time solvable if $c\leq 2$ but co-NP-hard if $c\leq 3$. We do this via pinpointing a relationship with the known class of $b$-matching games and completing the complexity classification on testing core non-emptiness for $b$-matching games. With respect to our application, we prove a number of complexity results on choosing, out of possibly many optimal solutions, one that leads to a kidney transplant distribution that is as close as possible to some prescribed fair distribution.

cs.GT↗

arXiv2024

The core of housing markets from an agent's perspective: Is it worth sprucing up your home?

We study housing markets as introduced by Shapley and Scarf (1974). We investigate the computational complexity of various questions regarding the situation of an agent $a$ in a housing market $H$: we show that it is $\mathsf{NP}$-hard to find an allocation in the core of $H$ where (i) $a$ receives a certain house, (ii) $a$ does not receive a certain house, or (iii) $a$ receives a house other than her own. We prove that the core of housing markets respects improvement in the following sense: given an allocation in the core of $H$ where agent $a$ receives a house $h$, if the value of the house owned by $a$ increases, then the resulting housing market admits an allocation in its core in which $a$ receives either $h$, or a house that $a$ prefers to $h$; moreover, such an allocation can be found efficiently. We further show an analogous result in the Stable Roommates setting by proving that stable matchings in a one-sided market also respect improvement.

cs.GT↗

arXiv2023

How to measure consumer's inconsistency in sensory testing?

Standard methods, standard test conditions and the use of good sensory practices are key elements of sensory testing. However, while compliance assessment by trained and expert assessors is well developed, few information is available on testing consumer consistency. Therefore, we aim to answer the following research questions: What type of metrics can be used to characterise (in)consistent evaluation? How to rank assessors and attributes' evaluations based on (in)consistency? Who can be considered an (in)consistent assessor? What is the difference between consistent and inconsistent assessors' evaluations and use of scale? What is the impact of consistent and inconsistent assessors' evaluations on the overall liking estimate? The proposed detection of (in)consistency requires evaluations on two connected scales. We reveal how assessors and attributes can be ranked according to the level of inconsistency, as well as how inconsistent assessors can be identified. The suggested approach is illustrated by data from sensory tests of biscuits enriched with three pollens at different levels. Future consumer tests are recommended to account for possible inconsistent evaluations.

stat.AP↗

arXiv2023

The Complexity of Matching Games: A Survey

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an overview of matching games and extensions, such as $b$-matching games and partitioned matching games; the latter originating from the emerging area of international kidney exchange. In this survey we focus on computational complexity aspects of various game-theoretical solution concepts, such as the core, nucleolus and Shapley value, when the input is restricted to a matching game or one if its variants.

cs.GT↗

arXiv2023

Computing Balanced Solutions for Large International Kidney Exchange Schemes

To overcome incompatibility issues, kidney patients may swap their donors. In international kidney exchange programmes (IKEPs), countries merge their national patient-donor pools. We consider a recently introduced credit system. In each round, countries are given an initial ``fair'' allocation of the total number of kidney transplants. This allocation is adjusted by a credit function yielding a target allocation. The goal is to find a solution that approaches the target allocation as closely as possible, to ensure long-term stability of the international pool. As solutions, we use maximum matchings that lexicographically minimize the country deviations from the target allocation. We perform, for the first time, a computational study for a {\it large} number of countries. For the initial allocations we use two easy-to-compute solution concepts, the benefit value and the contribution value, and four classical but hard-to-compute concepts, the Shapley value, nucleolus, Banzhaf value and tau value. By using state-of-the-art software we show that the latter four concepts are now within reach for IKEPs of up to fifteen countries. Our experiments show that using lexicographically minimal maximum matchings instead of ones that only minimize the largest deviation from the target allocation (as previously done) may make an IKEP up to 54% more balanced.

cs.GT↗

arXiv2022

The Large Core of College Admission Markets: Theory and Evidence

We study stable allocations in college admissions markets where students can attend the same college under different financial terms. The deferred acceptance algorithm identifies a stable allocation where funding is allocated based on merit. While merit-based stable allocations assign the same students to college, non-merit-based stable allocations may differ in the number of students assigned to college. In large markets, this possibility requires heterogeneity in applicants' sensitivity to financial terms. In Hungary, where such heterogeneity is present, a non-merit-based stable allocation would increase the number of assigned applicants by 1.9%, and affect 8.3% of the applicants relative to any merit-based stable allocation. These findings contrast sharply with findings from the matching (without contracts) literature.

econ.TH↗

arXiv2022

The efficacy of tournament designs

Tournaments are a widely used mechanism to rank alternatives in a noisy environment. This paper investigates a fundamental issue of economics in tournament design: what is the best usage of limited resources, that is, how should the alternatives be compared pairwise to best approximate their true but latent ranking. We consider various formats including knockout tournaments, multi-stage championships consisting of round-robin groups followed by single elimination, and the Swiss-system. They are evaluated via Monte-Carlo simulations under six different assumptions on winning probabilities. Comparing the same pair of alternatives multiple times turns out to be an inefficacious policy. While seeding can increase the efficacy of the knockout and group-based designs, its influence remains marginal unless one has an unrealistically good estimation on the true ranking of the players. The Swiss-system is found to be the most accurate among all these tournament formats, especially in its ability to rank all participants. A possible explanation is that it does not eliminate a player after a single loss, while it takes the history of the comparisons into account. The results can be especially interesting for emerging esports, where the tournament designs are not yet solidified.

stat.AP↗

arXiv2022

Strong core and Pareto-optimal solutions for the multiple partners matching problem under lexicographic preferences

In a multiple partners matching problem the agents can have multiple partners up to their capacities. In this paper we consider both the two-sided many-to-many stable matching problem and the one-sided stable fixtures problem under lexicographic preferences. We study strong core and Pareto-optimal solutions for this setting from a computational point of view. First we provide an example to show that the strong core can be empty even under these severe restrictions for many-to-many problems, and that deciding the non-emptiness of the strong core is NP-hard. We also show that for a given matching checking Pareto-optimality and the strong core properties are co-NP-complete problems for the many-to-many problem, and deciding the existence of a complete Pareto-optimal matching is also NP-hard for the fixtures problem. On the positive side, we give efficient algorithms for finding a near feasible strong core solution, where the capacities are only violated by at most one unit for each agent, and also for finding a half-matching in the strong core of fractional matchings. These polynomial time algorithms are based on the Top Trading Cycle algorithm. Finally, we also show that finding a maximum size matching that is Pareto-optimal can be done efficiently for many-to-many problems, which is in contrast with the hardness result for the fixtures problem.

cs.GT↗

arXiv2022

Understanding hesitancy with revealed preferences across COVID-19 vaccine types

Many countries have secured larger quantities of COVID-19 vaccines than their populace is willing to take. This abundance and variety of vaccines created a historical moment to understand vaccine hesitancy better. Never before were more types of vaccines available for an illness and the intensity of vaccine-related public discourse is unprecedented. Yet, the heterogeneity of hesitancy by vaccine types has been neglected so far, even though factual or believed vaccine characteristics and patient attributes are known to influence acceptance. We address this problem by analysing acceptance and assessment of five vaccine types using information collected with a nationally representative survey at the end of the third wave of the COVID-19 pandemic in Hungary, where a unique portfolio of vaccines were available to the public in large quantities. Our special case enables us to quantify revealed preferences across vaccine types since one could evaluate a vaccine unacceptable and even could reject an assigned vaccine to wait for another type. We find that the source of information that respondents trust characterizes their attitudes towards vaccine types differently and leads to divergent vaccine hesitancy. Believers of conspiracy theories were significantly more likely to evaluate the mRNA vaccines (Pfizer and Moderna) unacceptable while those who follow the advice of politicians evaluate vector-based (AstraZeneca and Sputnik) or whole-virus vaccines (Sinopharm) acceptable with higher likelihood. We illustrate that the rejection of non-desired and re-selection of preferred vaccines fragments the population by the mRNA versus other type of vaccines while it generally improves the assessment of the received vaccine. These results highlight that greater variance of available vaccine types and individual free choice are desirable conditions that can widen the acceptance of vaccines in societies.

econ.GN↗

arXiv2021

Online voluntary mentoring: Optimising the assignment of students and mentors

After the closure of the schools in Hungary from March 2020 due to the pandemic, many students were left at home with no or not enough parental help for studying, and in the meantime some people had more free time and willingness to help others in need during the lockdown. In this paper we describe the optimisation aspects of a joint NGO project for allocating voluntary mentors to students using a web-based coordination mechanism. The goal of the project has been to form optimal pairs and study groups by taking into the preferences and the constraints of the participants. In this paper we present the optimisation concept, and the integer programming techniques used for solving the allocation problems. Furthermore, we conducted computation simulations on real and generated data for evaluate the performance of this dynamic matching scheme under different parameter settings.

cs.GT↗

arXiv2021

Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange

In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. In this paper we show that in the case of strict preferences the unique strong core allocation (or competitive allocation) respects improvement: if an agent's object becomes more attractive for some other agents, then the agent's allotment in the unique strong core allocation weakly improves. We obtain a general result in case of ties in the preferences and provide new integer programming formulations for computing (strong) core and competitive allocations. Finally, we conduct computer simulations to compare the game-theoretical solutions with maximum size and maximum weight exchanges for markets that resemble the pools of kidney exchange programmes.

econ.TH↗

arXiv2020

Novel Integer Programming models for the stable kidney exchange problem

Kidney exchange programs (KEP's) represent an additional possibility of transplant for patients suffering from end stage kidney disease. If a patient has a willing living donor with whom the patient is not compatible, the pair patient--donor can join a pool of incompatible pairs and, if compatibility between patient and donor in two our more pairs exists, organs can be exchanged between them. The problem can be modeled as an integer program that, in general, aims at finding the pairs that should be selected for transplant such that maximum number of transplants is performed. In this paper we consider that for each patient there may exist a preference order over the organs that he/she can receive, since a patient may be compatible with several donors but may have a better fit over some than over others. Under this setting, the aim is to find the maximum cardinality stable exchange, a solution where no blocking cycle exists. For this purpose we propose three novel integer programming models based on the well-known edge and cycle formulations. These formulations are adjusted for both finding stable and strongly stable exchanges under strict preferences and for the case when ties in preferences may exist. Furthermore, we study a situation when the stability requirement can be relaxed by addressing the trade-off between maximum cardinality versus number of blocking cycles allowed in a solution. The effectiveness of the proposed models is assessed through extensive computational experiments on a wide set of instances.

cs.GT↗

arXiv2019

IP Solutions for International Kidney Exchange Programmes

In kidney exchange programmes patients with end-stage renal failure may exchange their willing, but incompatible living donors among each other. National kidney exchange programmes are in operation in ten European countries, and some of them have already conducted international exchanges through regulated collaborations. The exchanges are selected by conducting regular matching runs (typically every three months) according to well-defined constraints and optimisation criteria, which may differ across countries. In this work we give integer programming formulations for solving international kidney exchange problems, where the optimisation goals and constraints may be different in the participating countries and various feasibility criteria may apply for the international cycles and chains. We also conduct simulations showing the long-run effects of international collaborations for different pools and under various national restrictions and objectives.

math.OC↗

arXiv2017

Stable project allocation under distributional constraints

In a two-sided matching market when agents on both sides have preferences the stability of the solution is typically the most important requirement. However, we may also face some distributional constraints with regard to the minimum number of assignees or the distribution of the assignees according to their types. These two requirements can be challenging to reconcile in practice. In this paper we describe two real applications, a project allocation problem and a workshop assignment problem, both involving some distributional constraints. We used integer programming techniques to find reasonably good solutions with regard to the stability and the distributional constraints. Our approach can be useful in a variety of different applications, such as resident allocation with lower quotas, controlled school choice or college admissions with affirmative action.

cs.GT↗