Two Sided Matching Markets

Two-sided matching problems arise in various domains, such as school admissions, organ donation, and online dating, where elements from two distinct sets are matched based on the set of preferences. Efficient matching algorithms play a crucial role in corresponding market design, aiming to optimize match success. This paper emphasizes the importance of extracting genuine preferences for agents in two-sided matching problems. Traditional methods for identifying criteria face challenges related to sample representativeness, response bias, and inflexibility, highlighting the need for an unbiased approach that minimizes mismatches and turnover rates. This research demonstrates the effective derivation of criteria from the natural language description of the matching problem in an unbiased manner. We propose an unbiased criteria identification methodology for twosided matching problems based on Environment-Based Design (EBD), Recursive Object Model (ROM), and Environment-based Life Cycle Analysis (eLCA) to uncover relevant, consistent, and transparent criteria for matching. The proposed methodology fosters efficiency, satisfaction, and optimal resource allocation. By bridging the existing gap in the literature, the proposed methodology offers a comprehensive and impartial approach to improving the quality of matches in two-sided matching problems. Furthermore, this work not only addresses the critical need for unbiased criteria identification in two-sided matching markets but also introduces a novel approach to modeling multi-criteria decision-making problems in operations research, where criteria are traditionally determined through expert opinion or surveys. The applicability of the proposed methodology is demonstrated in the context of job matching, aiming to discover inclusive evaluation criteria that lead to stable, and mutually satisfactory job-candidate matches. Successful matches foster a harmonious and productive work environment, benefiting individuals and organizations.

In the first 20 years of the market economy in Estonia, the public school market was decentralised in Tallinn. Recently, a hybrid market was established by centralising the school allocations to comprehensive schools and also allowing some selective schools to autonomously select students for some groups. We contribute to mechanism design literature by studying the centralised clearing-house used in Tallinn – the Tallinn mechanism. By using genetic algorithms, we show that, the Tallinn mechanism incentivises families to manipulate their preference revelation by reporting only a few schools and not always from the top of their preference list. Also we see that the expected utility in the Tallinn mechanism is higher compared to the widely used Deferred-Acceptance mechanism, although the number of unassigned students is also higher.

This paper provides three simple mechanisms to implement allocations in the core of matching markets. \Ve analyze sorne sequential rnechanisms which mimic matching procedures for many-to-one reallife matching markets. \Ve show that only cor,e allocations should be attained when agents act strategically faced váth these mechanisms. Two mechanisms implement the core correspondence in SPE, whereas the third implements the students• optimal stable solution.

This paper proposes a way to allocate students to schools such that conciliates Pareto efficiency and stability. Taking as a starting point the recent reform proposed by the Boston School Committee, we propose a marginal modification to reach our objective redefine how students are prioritize. Our proposal is to allow schools to prioritize only a small set of students an then use a common priority order for the rest. Under this condition we propose a score based priority ranking that makes the output of the new Boston Mechanism Pareto ...

This paper introduces τ-fairness as a compromise solution reconciling Pareto efficiency and equity in School Choice Problems. We show that, by considering a weak notion of equity that we refer to as λ-equity, it is possible to contribute positively to solve an open debate, originated by the efficiency-equity trade-off of the schooling problem. We also suggest a slight modification to some allocative procedures recently introduced in the United States to compute τ-fair allocations and provide support for this (possible) reformulation.

This paper proposes the notion of E-stability to conciliate Pareto efficiency and fairness. We propose the use of a centralized procedure, the Exchanging Places Mechanism. It endows students a position according with the Gale and Shapley students optimal stable matching as tentative allocation and allows the student to trade their positions. We show that the final allocation is E-stable, i.e. efficient, fair and immune to any justifiable objection that students can formulate.

Roth and Sotomayor (1990). Also see Gus…eld and Irving (1989) on the complementary work in operations research and computer science on algorithms regarding two-sided matching theory. 3 For surveys on market design of the US Federal Communications Commission (FCC) auctions (see http://wireless.fcc.gov/auctions/default.htm?job=auctions_home , retrieved on 10/16/2008), electricity markets (e.g., for California market see http://www.caiso.com, retrieved on 10/16/2008), and other aspects of matching markets and their links to game theory and more speci…cally to auction and matching theory

WHEN A COLLEGE GRADUATE decides to pursue a higher degree at a particular institution, one of the first challenges she faces is finding an apartment. Most institutions have on-campus housing available that is often subsidized and hence more appealing than its alternatives. Usually there are several types of on-campus housing and the attractiveness of each type changes from person to person. Therefore housing offices need to find 44mechanisms" to allocate available housing among the applicants who might have various preferences. In this paper we deal with this class of problems to which we refer as house allocation problems.2 Formally, there are n agents who collectively own n indivisible objects, say houses, and each agent has preferences over objects.3 An allocation is a matching of houses to agents and a matching mechanism is a systematic procedure to select a matching for each problem. A widely studied class of matching mechanisms is the class of simple serial dictatorships:...

Within the first 20 years of the market economy in Estonia, the public school market has been decentralized in Tallinn. Firstly, we describe how students are allocated to primary schools in a narrative, and secondly, in a formal mechanism design language. We indicate the closest equivalent algorithms from the matching markets design theory and conclude that the current system in Tallinn is a hybrid. The decentralized part of the market namely inter-district exam schools apply autonomous school proposing deferred acceptance; and the centralized part of the market intra-district regular schools apply school random serial dictatorship. Finally using data from Tallinn primary school matching, we show by an empirical evaluation of matching mechanisms. Since the currently the collected data does not reveal the students preference ordering we simulate some potential orderings for comparison.

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The purpose of this paper is to use what learned from the literature for presenting a proposal of redesign of the entry-level of the Academic Job Market in Italy. The matching researchers/Universities is currently obtained through local contests and it suffers inefficiencies caused by its decentralized structure. The first step of the study was to create a unique centralized procedure of matching based on a researchers-proposing deferred-acceptance algorithm that cleverly solve the first three issues. On the other hand, the question of merit – established as the possibility that non-deserving candidates will be hired instead of more qualified ones - represents a new challenge in the practice of market design. It has been treated as a misrepresentation of the Universities' preferences due to an agency problem between the institutions – that express propensities in regulations – and committees – who practically have to realize the list of candidates using their judgments in line with the institutions' guidelines – into the decision process. A misalignment of interests between the two agents causes the false declaration of Universities' preferences and the outcomes of the matching procedure result to be not stable (Roth and Sotomayor 1992; Roth 2008). I formalize the agency problem in the study of the Universities' decision process in order to analyze the players' behaviors and relations for working out a set of rules to control it. I propose a solution at this problem by splitting into two steps the process of building up the Universities’ list of preferences and controlling it.

In this thesis, we mainly focus on lung exchange. There are signicant dierences between lung and kidney exchanges. While in kidney exchange patients come with a single donor, lung exchange often requires two donors. Incompatible patient-donor-donor triples can exchange donor lungs with other triples.We consider a model in which some patients bring three donors; one is compatible and two are incompatible with themselves. We design a two stage mechanism to show that bringing additional donor to the exchange pool will improve eciency of the matching system through increasing number of patients that can be matched. Additionally, we provide a necessary condition that shows when allowing additional donors can also reduce the number of necessary transplant teams to run the exchange sequence, and therefore increase,what we call, implementational eciency. Eylül 2015 Bu tez çal³mamzda, temelde akci §er takasna odaklanlmaktadr. Akci §er ve böbrek takaslar arasnda önemli farkllklar bulunmaktadr. Böbrek takasna hastalar tek bir verici ile katlrken, akci §er takasnda iki verici gerekmektedir. Birbiriyle uyu³maz hasta-verici-verici üçlülerindeki hastalar sahip olduklar verici akci §erlerini di §er üçlülerin verici akci §erleri ile takas edebilirler. Burada baz hastalarn bir tanesi kendileriyle uyumlu ve di §er iki tanesi kendileriyle uyumsuz olan üç tane verici getirebildi §i bir model dü³ünülmektedir.E³le³tirilebilen hasta saysnn artmas yoluyla takas havuzuna ek verici getirmenin e³le³tirme sisteminin refah verimlili §inin geli³tirebilece §ini göstermek için iki a³amal bir mekanizma tasarlanm³tr. Ayrca, ek vericilere izin verildi §i taktirde hem takas sralamasn çal³trmak için gerekli nakil ekibi saysnn azalabilece §ini hemde bu yüzden uygulama verimlili §i olarak adllandrlan kavramn artaca §n gösteren gerekli bir ko³ul verilmi³tir. Anahtar Kelimeler: : Pazar tasarm, E³le³tirme, Akci §er takas,Uygulama verimlili §i. iv ACKNOWLEDGMENTS I would like to express my gratefulness to my supervisor Assistant.Prof.Dr Kemal Yldz for his patience when giving feedback over and over, for his excellent guidance, for his condence in me , his invaluable encouragement making this thesis possible and for everything I have learnt from him. I feel privileged

This paper provides an 'escape route' from the efficiency-equity trade-off in the School Choice problem. We achieve our objective by presenting a weak notion of fairness, called τ-fairness, which is always non-empty.
Then, we propose the adoption of the Student Optimal Compensating Exchange Place rule, a procedure that assigns a τ-fair allocation to each problem. When students' preferences are restricted to satisfy the β-condition, the mechanism is strategy-proof.

This paper proposes a way to allocate students to schools such that conciliates Pareto efficiency and stability. Taking as a starting point the recent reform proposed by the Boston School Committee, we propose a marginal modification to reach our objective redefine how students are prioritize. Our proposal is to allow schools to prioritize only a small set of students an then use a common priority order for the rest.

This paper introduces τ-fairness as a compromise solution reconciling Pareto efficiency and equity in School Choice Problems. We show that, by considering a weak notion of equity that we refer to as λ-equity, it is possible to contribute positively to solve an open debate, originated by the efficiency-equity trade-off of the schooling problem. We also suggest a slight modification to some allocative procedures recently introduced in the United States to compute τ-fair allocations and provide support for this (possible) reformulation.

This paper introduces τ-fairness as a compromise solution reconciling Pareto efficiency and equity in School Choice Problems. We show that, by considering a weak notion of equity that we refer to as λ-equity, it is possible to contribute positively to solve an open debate, originated by the efficiency-equity trade-off of the schooling problem. We also suggest a slight modification to some allocative procedures recently introduced in the United States to compute τ-fair allocations and provide support for this (possible) reformulation.

This paper proposes a reform for school allocation procedures in order to help integration policies reach their objective. For this purpose, we suggest the use of a natural two-step mechanism. The (stable) first step is introduced as an adaptation of the deferred-acceptance algorithm designed by Gale and Shapley (1962), when students are divided into two groups. The (efficient) second step captures the idea of exchanging places inherent to Gale's Top Trading Cycle. This latter step could be useful for Municipal School Boards when implementing some integration policies.