Matching markets

Introduction: the Asylum Crisis in North America and Europe As I write this on April 23, 2024, five more people have died when too many packed into an inflatable rubber boat to cross the English Channel, despite efforts by French police to stop such boat launches; and the British Parliament has passed its revised bill to send migrants who attempt such crossings to supposed refuge in Rwanda instead. Across the northern hemisphere, there is widespread sense that the system for claiming asylum once within a receiving nationas opposed to applying for refugee status while still abroadis broken. While many politicians and media figures want to take advantage of this crisis, there is more involved than emotive politicking. The dire situation generates what I call "authentic asylum skeptics" who are not mainly motivated by racism or xenophobic fears of (say) Muslim migrants, but rather by sense that serious kinds of injustice are involved in the arrival of large waves of migrants who come under no regular visa program. In this section, I try to briefly quantify the issues before introducing a framework for policy solutions that combines normative considerations with ideas from game theory and matching markets "Migration panic" is a fertile ground for strategic manipulation of public fears in part because most people in wealthy northern nations grasp neither the numbers nor the relevant legal concepts. Here better education could help: teachers and leaders could explain the distinction in US law between asyleespeople seeking asylum once within or at the border of a receiving nationversus "refugees" (in a narrow sense) who are granted temporary protection while still outside the granting nation (Krikorian), and "regular" immigrants with visas for study, work, marriage, family reunification, etc. Much of the public only sees that increasing numbers of "migrants" (the generic term) are arriving, but does not understand even the basic fact that it is legal in virtually all developed nations to ask for asylum at ports of entry, although often not after clandestine entry. In the US, the Department of Homeland Securitywhose Secretary was impeached by the House of Representatives in April 2024 for not enforcing the laws (a case dismissed as baseless by the Senate), had promulgated the "Circumvention of Lawful Pathways" rule in May 2023 (which remains in forced while on appeal in federal court). Waivers are possible: while at least 860,000 people were witnessed illegally entering the US but not caught [2] by the Border Control during 2023 (Bedard), and House Republicans have asserted that the US experienced "1.7 million known gotaways" from February 2021 through October 2023, many of them may end up applying for asylum later. But from January 2023 on, the rule has encouraged hundreds of thousands to wait in Mexico while asking for an appointment with Border Control via a new app, rather than crossing illegally (Montoya-Galvez). These are sobering figures. As of October 2023, roughly 2 million asylum cases were pending in the United States, either before immigration judges or the US Citizenship and Immigration Services (US-CIS), up from 1.6 million in March (USCIS; Arthur). For years, the backlog has been increasing, as new applications exceed cases resolved per annum (Sullivan). These are large numbers as compared to the period between 1990 and mid-2023 when roughly 768,000 people were granted asylum status (USAFacts.org), along with roughly 1 million admitted as refugees. 1 The asylee backlog is still small relative to the roughly 33 million granted lawful permanent residence in the US during that time, 2 or the 46 million foreign-born residents currently living in the USwhich includes foreign students and legal guest workers, along with maybe 10 million undocumented migrants who have no pending asylum case yet. 3 But it is the number of arrivals that has captured attention through shipment of tens of thousands of asylees to unprepared cites in the north, such as New York City, where over 180,000 have arrived since spring 2022 (Donaldson). Public reaction the US parallels outrage in northern Europe at the arrival of millions of asylum seekers entering from Türkiye or Africa through Greece, eastern Europe, Italy, and Spain during the last 15 years, generating a cumulative total of approximately 8.8 million new asylum claims in EU nations from 2008 through the end of 2022 (Eurostat). Despite "asylum deterrence" efforts by EU nations, e.g. by paying Türkiye to give migrants refugee status and deter them from crossing into the Eurozone, Europe received over 1 million new asylum applications during 2023including many from Syria, Afghanistan, and Venezuela. Large waves of asylees coming 1 One cannot simply add the number of cases pending, plus the number of people granted asylum or refugee status to approximate the total number of applications for any type of temporary protection, because the latter includes all those whose application was ultimately denied despite any appeals. 2 See 2022 Yearbook of Immigration Statistics, Table 2, pp.8-10. 3 Either because they never applied for asylum, or because they abandoned pursuit of their case and stayed on illegally. [3] from Muslim nations or from sub-Saharan Africa are generating strong anti-immigrant political movements. Yet globally, the picture is very different than most suspicious westerners imagine. Among the 110 million forcibly displaced persons (FDPs) who the UNHCR counted by December 2023 as fleeing from identity-based persecution, ethnic conflict, widespread violence, or serious ongoing human rights violations, consider just the 36.4 million of these granted refugee status outside their country of birth or origin: 75% of them are hosted in such middle-or low-income nations as Türkiye,

Many salient rules to allocate private goods are not only strategyproof, but also group strategy-proof, in appropriate domains of de…nition, hence diminishing the traditional con ‡ict between incentives and e¢ ciency. That is so for solutions to matching, division, cost sharing, house allocation and auctions, in spite of the substantive disparity between these cases. In a general framework encompassing all of them, we prove that the equivalence between the two forms of strategy-proofness is due to an underlying common structure, that transcends the many di¤erences between the contexts and the mechanisms for which it holds.

We generalize exactness to games with non-transferable utility (NTU). In an exact game for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We study five generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be unified under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex

This paper studies two-sided matching markets with non-transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

This paper studies two-sided matching markets with non-transferable utility when the number of market participants grows large. We consider a model in which each agent has a random preference ordering over individual potential matching partners, and agents' types are only partially observed by the econometrician. We show that in a large market, the inclusive value is a sufficient statistic for an agent's endogenous choice set with respect to the probability of being matched to a spouse of a given observable type. Furthermore, while the number of pairwise stable matchings for a typical realization of random utilities grows at a fast rate as the number of market participants increases, the inclusive values resulting from any stable matching converge to a unique deterministic limit. We can therefore characterize the limiting distribution of the matching market as the unique solution to a fixed point condition on the inclusive values. Finally we analyze identification and estimation of payoff parameters from the asymptotic distribution of observable characteristics at the level of pairs resulting from a stable matching.

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

In this paper, we characterize the strongly stable fractional matchings for the marriage model as the union of the convex hull of connected sets of stable matchings. Moreover, we present an algorithm that computes the set of matchings necessary to generate the above-mentioned connected sets. Finally, we show that the set of strongly stable fractional matchings has a lattice structure.

Being argumentative in nature and referring to Oaxaca Decomposition for the purpose of de ining the main drivers of rental lats and houses, be new, old, repaired, or unrepaired, together with applying difference in difference method to evaluate the effectiveness of policy, this paper calls into the question of how to inaugurate a country-speci ic two-sided matching algorithm for rental house allocation based on the empirical results. Model 3 is built on time series data to evaluate the policy implementation by Azerbaijani government to provide households with inancial aid. Based on Blinder-Oaxaca Decomposition, the main indings of the study manifest that for the repaired and unrepaired houses, the price discrimination is mainly explained by the room number while this is area of the houses per meter square that explains the price gap between old and new lats. The Difference in Difference model signi ies that the increase in the amount of mortgage loans from 50.000AZN to 150.000AZN declined demand more than increase in supply. Additionally, study offers 2 Matching Algorithm and Mechanism Design for the allocation of rental houses with existing tenants and newcomers in addition to tenants and owners without initial endowments through YRMH-IGYT in two-sided matching markets.

Decentralized markets are modeled by means of a sequential game where, starting from any matching situation, …rms are randomly given the opportunity to make job o¤ers. In this random context, we prove the existence of ordinal subgame perfect equilibria where …rms act according to a list of preferences. Moreover, every such equilibrium preserves stability for a particular pro…le of preferences. In particular, when …rms act truthfully, every outcome is stable for the true preferences. Conversely, when the initial matching is the empty matching, every stable matching can be reached as the outcome of an ordinal equilibrium play of the game.

We consider centralized matching markets in which, starting from an arbitrary match¬ ing, firms are successively chosen in a random fashion and offer their positions to the workers they prefer the most. We propose an algorithm that generalizes some well-known algorithms and explore some of its properties. In particular, different executions of the algorithm may lead to diferent output matchings. We then study incentives in the rev¬ elation game induced by the algorithm. We prove that ordinal equilibria always exist. Furthermore, every ...

In their recent paper, Roth et al. [Pairwise kidney exchange, J. Econ. Theory 125 (2005) 151-188] consider pairwise kidney exchanges, and show within this subset of feasible exchanges that a priority mechanism is strategy-proof. We show that this result can be broadened to allow much more general mechanisms and restrictions on the feasible set of allocations, including allowing three-way exchanges, regional specifications, and others. The key requirement is that the choice mechanism be consistent, i.e., if an allocation is chosen from some set of feasible allocations, it is also chosen from any subset of that set.

A pozíciós játékok többnyire véges, kétszemélyes, zérusösszegű, teljes információs játékok, amelyekben még kevert stratégiák alkalmazására sincs szükség. A pozíciós játékok megadási módjuk miatt viszont mátrixjátékként nem kezelhetők jól, így a vizsgálatukra változatos matematikai eszköztár alakult ki. Jelen áttekintés célja ezek vázlatos ismertetése, néhol kiterjesztése

The main purpose is to prove the supermodularity (convexity) property of a cooperative game arising from an economical situation. The underlying oligopoly situation is based on a linear inverse demand function as well as linear cost functions for the participating firms. The characteristic function of the so-called oligopoly game is determined by maximizing, for any cartel of firms, the net profit function over the feasible production levels of the firms in the cartel, taking into account their individual capac- ities of production and production technologies. The (rather effective) proof of the supermodularity of the characteristic function of the oligopoly game relies on the use of maximizers for the relevant max- imization problems. A similar proof technique will be reviewed for a related cooperative oligopoly game arising from a slightly modified oligopoly situation where the production technology of the car- tel is determined by the most efficient member firm.

In this paper, we characterize the strongly stable fractional matchings for the marriage model as the union of the convex hull of connected sets of stable matchings. Moreover, we present an algorithm that computes the set of matchings necessary to generate the above-mentioned connected sets. Finally, we show that the set of strongly stable fractional matchings has a lattice structure.

We present a two-sided matching framework to investigate the entry-level marketing assistant professor job market. Under this framework, candidates' and departments' decisions to mutually choose one another are driven by the matching value produced by the pair, which is in turn determined by observable department brand cues and candidates' human brand cues such as field of research, research productivity, and ranking status. Our results suggest that matches between candidates and faculty trained in the same field do not always generate the highest matching value. Candidates' publications in top marketing journals enhance their likelihood of matching with research-oriented hiring departments, and this effect is moderated by their field of research. In general, the ranking status of candidates boosts their chance of being matched with research-oriented hiring departments. However, this effect differs across fields, and it also interacts with candidates' own research productivity. In particular, publications by candidates from top-ranked degree-granting departments are taken as three to four times more valuable by research-oriented hiring departments. Our work extends the current research on the marketing job market and, most importantly, quantifies and compares the significance of various human brand cues in influencing mutual choices in the job market.

We consider both Nash and strong Nash implementation of various matching rules for college admissions problems. We show that all such rules are supersolutions of the stable rule. Among these rules the "lower bound" stable rule is implementable in both senses. The "upper bound" Pareto and individually rational rule is strong Nash implementable yet it is not Nash implementable. Two corollaries of interest are the stable rule is the minimal (Nash or strong Nash) implementable solution that is Pareto optimal and individually rational, and the stable rule is the minimal (Nash or strong Nash) implementable extension of any of its subsolutions. JEL Classification Numbers: C78, D78. * We wish to thank Professor William Thomson for his efforts in supervision as well as his useful suggestions. We are grateful to the participants in his reading class, workshops at Bilkent University, University of Rochester, and in particular Jeffrey Banks, Stephen Ching, Bhaskar Dutta, Rangarajan Sundaram and an anonymous referee for their helpful comments. Correspondence to: T. Kara 1 Gale and Shapley [4] introduces the college admissions problems. Gale and Sotomayor [53, Roth [15, 16, 17, 18], Roth and Sotomayor [19] study various aspects of the college admissions problems.

We consider school choice problems (Abdulkadiroglu and Sönmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the corresponding order of pairs, at each step a rank-priority mechanism considers a rank-priority pair and matches an available student to an unfilled school if the student and the school rank and prioritize each other in accordance with the rank-priority pair. The Boston or immediate acceptance mechanism is a particular rank-priority mechanism. Our first main result is a characterization of the subfamily of rank-priority mechanisms that Nash implement the set of stable (i.e., fair) matchings (Theorem 1). We show that our characterization also holds for "sub-implementation" and "sup-implementation" (Corollaries 3 and 4). Our second main result is a strong impossibility result: under incomplete information, no rank-priority mechanism implements the set of stable matchings (Theorem 2).

When men and women are objectively ranked in a marriage problem, say by beauty, then pairing individuals of equal rank is the only stable matching. We generalize this observation by providing bounds on the size of the rank gap between mates in a stable matching in terms of the size of the ranking sets. Using a metric on the set of matchings, we provide bounds on the diameter of the core-the set of stable matchings-in terms of the size of the ranking sets and in terms of the size of the rank gap. We conclude that when the set of rankings is small, so are the core and the rank gap in stable matchings. We construct examples showing that our bounds are essentially tight, and that certain natural variants of the bounds fail to hold.

We consider the hospital-residents problem where both hospitals and residents can have lower quotas. The input is a bipartite graph G = (R ∪ H, E), each vertex in R ∪ H has a strict preference ordering over its neighbors. The sets R and H denote the sets of residents and hospitals respectively. Each hospital has an upper and a lower quota denoting the maximum and minimum number of residents that can be assigned to it. Residents have upper quota equal to one, however, there may be a requirement that some residents must not be left unassigned in the output matching. We call this as the residents’ lower quota. We show that whenever the set of matchings satisfying all the lower and upper quotas is nonempty, there always exists a matching that is popular among the matchings in this set. We give a polynomial-time algorithm to compute such a matching. 2012 ACM Subject Classification Mathematics of computing → Combinatorial algorithms

We prove with the help of a counterexample that Lemma 6 and Corollary 7 from Eeckhout [1] are incorrect. Theorem 1 in Eeckhout [1] provides the following sufficient condition for the existence of unique stable matchings. Condition 1 There exists an ordering of the set of females F = (X i) and an ordering of the set of males M = (x i) such that the preference profile satisfies ∀X i ∈ F : x i Xi x j , ∀j > i, and ∀x i ∈ M : X i xi X j , ∀j > i It is claimed in Eeckhout [1] that Condition 1 is also necessary for uniqueness of stable matchings when N ≤ 6. We observe here that although the claim holds for N = 4 (Lemma 5), it is incorrect for the case N = 6 (Lemma 6). Claim 2 There exists a matching problem (F, M,) with |N | = 6 where the set of stable marriages S is a singleton and the preference profile does not satisfy Condition 1. Proof. Consider the matching problem (F, M,) with the following preference lists:

The process of match formation in matching markets can be divided into three parts: information sharing, investments in information acquisition, and the formation of matches based on available information. The last stage where agents are assumed to know their preferences has been studied in seminal work of Gale and Shapley (1962), and a model of second stage costly information acquisition is introduced and studied in Lee and Schwarz (2007). This paper focuses on the first stage – information sharing – and examines mechanisms which allow workers to signal their preferences over matching partners prior to the assignment of interviews. The incentives of firms and workers vis-a-vis information revelation are partially aligned – all other things being equal, a worker prefers to have an interview with a firm that is high in his preference ranking and a firm prefers to invest in interviewing a worker who ranks a firm highly because such worker is more likely to accept a job if offered. How...

Mean-Field Control (MFC) is a powerful tool to solve Multi-Agent Reinforcement Learning (MARL) problems. Recent studies have shown that MFC can well-approximate MARL when the population size is large and the agents are exchangeable. Unfortunately, the presumption of exchangeability implies that all agents uniformly interact with one another which is not true in many practical scenarios. In this article, we relax the assumption of exchangeability and model the interaction between agents via an arbitrary doubly stochastic matrix. As a result, in our framework, the mean-field ‘seen’ by different agents are different. We prove that, if the reward of each agent is an affine function of the mean-field seen by that agent, then one can approximate such a non-uniform MARL problem via its associated MFC problem within an error of e = O( 1 √ N [ √

Next generation networks aim at improving connectivity and capacity, adding to the current range of available services and expanding their reachability. For these systems to work, they need to be compatible with legacy technologies in addition to making use of (limited) available spectrum resources. This is one of the reasons why spectrum sharing has been at the forefront of the list of enablers for such systems. From federal-commercial sharing to finding opportunities in millimeter-wave spectrum, we have witnessed the formulation of multiple approaches to making spectrum sharing happen. Existing work on spectrum sharing is wide ranging and includes technological as well as market based approaches. Spectrum markets settings have called for different definitions of spectrum-related resources as a means to increase market thickness and thus improve the opportunities for finding market liquidity. In a similar way, we find proposals of network models which aim at adapting technical defi...

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 (equitable) first step is introduced as an adaptation of the deferred-acceptance algorithm designed by , 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.

This note analyzes the possibility of implementing stable outcomes for marriage markets. Our first result shows a contradiction between the use of stable mechanisms and the hypothesis of agents' behavior considered in the Nash equilibrium concept. We analyze the possibility of implementing two sets of stable allocations, by employing two types of mechanisms. The first mechanism is a ``now-or-never'' choice process that permits us to implement in undominated Nash equilibria the set of all the stable allocations. The second choice process is the classic algorithm in matching theory, the Gale Shapley mechanism. A reversal property is observed in such a mechanism when agents act strategically. The use of a mechanism which selects the best solution for one side of the market in the absence of strategic behavior yields the best stable solution for the agents on the other side under dominance solvability. Journal of Economic Literature Classification Numbers: C72, D78, J41.

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 ...

Forgo Ferenc a Budapesti Corvinus Egyetem tudostanara, az egyetem Operaciokutatas es Aktuariustudomanyok tanszekenek volt vezetője, a magyar operaciokutatas jelentős alakja 70 eves. Kollegai, tanitvanyai ebből az alkalombol koszontik őt ezzel a tanulmanykotettel, amelynek cime nem csak a Forgo Ferenc altal művelt tudomanyteruleteket idezi, hanem egyenisegenek fontos vonasait is hordozza. A 28 szerző altal jegyzett tanulmanyok a jatekelmelet, a makrookonomiai modellezes, a matematikai programozas alkalmazasai es a donteselmelet teruleteit erintik, ezek mindegyikeben valamilyen modon kapcsolatot talalva Forgo Ferenc munkassagaval.

We examine the indivisible resource allocation problem with multi-unit demand. In the literature on matching, stability and strategy-proofness have been important concepts. We pay our attention to the role of these concepts and show the following results in matching markets with multi-unit demand. First, the stable and strategy-proof rule, if exists, is unique, which coincides with the agent-optimal stable rule. Next, the stable and strategy-proof rule is robustly stable. Moreover, from the point of view of decentralized procedure, the stable and strategy-proof rule is Nash implementable.

In this paper, we consider the Hospital Residents problem (HR) and the Hospital Residents problem with Lower Quotas (HRLQ). In this model with two sided preferences, stability is a well accepted notion of optimality. However, in the presence of lower quotas, a stable and feasible matching need not exist. For the HRLQ problem, our goal therefore is to output a good feasible matching assuming that a feasible matching exists. Computing matchings with minimum number of blocking pairs (MinBP) and minimum number of blocking residents (MinBR) are known to be NP-Complete. The only approximation algorithms for these problems work under severe restrictions on the preference lists. We present an algorithm which circumvents this restriction and computes a popular matching in the HRLQ instance. We show that on data-sets generated using various generators, our algorithm performs very well in terms of blocking pairs and blocking residents. Yokoi (ISAAC 2017) recently studied envy-free matchings fo...

We analyze the role of formal and informal information gathering in students' preference formation. We analyzed this role in the college admission process using Spanish individual data. We introduce students' risk aversion and information costs on the standard college admission problem. Then, we model the students' list formation as a two-stage procedure. In first stage, students must decide whether they gather information or not about a college. In the second stage, they give their preferred list to the matching office. The observed changes in preferences suggest that information gathering is important in the last two months of the process and that students with less ex-ante information are more affected by these changes.

CONTEXT All Australian engineering degree programs require students to have exposure to professional practice prior to graduation. At CSU Engineering, this takes the form of a compulsory sequence of four yearlong paid cadet placements. The process of ensuring that all cadets are successfully matched with a host organisation (host) has significant complexity due to the diversity of types and locations of hosts, the discipline mix of placements and cadets’ preferences and constraints. The management of ongoing partnerships with the hosts must be balanced with the ability of cadets to proactively and independently seek their own placements. An equitable and fair method of matching cadets to the hosts is required for ethical operation of the placement program.

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

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 (equitable) 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.

Abstract-------------------------------------------------------------This paper studies sequential mechanisms which mimic a matching procedures for many-to-one real life matching markets. We provide a family of mechanisms implementing the students' optimal allocation in Subgame Perfect Equilibrium.

This paper introduces a property over agents' preferences, called Tops Responsiveness Condition. Such a property guarantees that the core in Hedonic Coalition Formation games is not empty. It is also shown that a mechanism exists that selects a stable allocation. It turns out that this mechanism, to be called tops covering, is strategy-proof even if the core is not a singleton. Furthermore, we also find out that the tops covering mechanism is the only strategy-proof mechanism that always selects stable allocations.

We present a survey of the emerging literature on the design of matching markets. We survey the articles on discrete resource allocation problems, their solutions, and their applications in three related domains. The first domain gives the theoretical background regarding the basic models, namely “house allocation and exchange” problems. First, we investigate the allocation and exchange problems separately, and then we combine them to present a real-life application: on-campus housing at universities. As the second application domain, we extend the basic allocation and exchange models to the “kidney exchange” problem and present new theory and applications regarding this problem. We present proposed and adopted mechanisms that take very specific institutional details into account. Then, we present the school admissions problem in three subcategories: the “college admissions” model where both schools and students are strategic agents, the “school placement” model where only students ...

In a wide variety of real-life resource allocation problems such as school choice or assignment of public positions, implementation of affirmative action policies rely on choice rules that balance meritocracy with equity. We study choice rules where meritocracy is attained through reliance on a priority list, and equity is attained through reserved positions for target groups of disadvantaged individuals. Focusing on overlapping reserves, the case where an individual can belong to multiple types of reserved positions, we characterize choice rules that satisfy maximal compliance with reservations, elimination of justified envy, and non-wastefulness. When an individual accommodates only one of the reserved positions, the horizontal envelope choice rule is the only rule to satisfy these three axioms. When an individual accommodates each of the reserved positions she qualifies for, there are complementarities between individuals. Under this alternative convention, and assuming there are...

We study manipulation of solutions by hospitals via underreporting their capacities in the context of centralized two-sided matching markets. We show that the solution that is used to match medical interns and hospitals in United States is manipulable in this way. Our main result is that there is no solution that is stable and non-manipulable via capacities.

Although a national live-donor kidney exchange program is being launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange ...

We analyze the ''equilibrium'' outcomes of the preference re¨elation games induced by Pareto efficient and indi¨idually rational solutions in the context of marriage problems. We employ a Nash equilibrium refinement which allows deviations by a set of permissible coalitions, and show that the set of equilibrium outcomes coincides with a variant of the core that allows blocking by only permissible coalitions, Journal of Economic Literature Classification Numbers: C71, C78, D71, D78.

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.

A MIDAS dinamikus mikroszimulacios nyugdijmodell magyar valtozata tartalmaz egy haztartas-formalodasi modult, amely a szimulacio soran eletpalyajukon vegigkisert egyeneket osszekapcsolja. Ez lehetőve teszi a feloszto-kirovo nyugdijrendszer azon elemeinek modellezeset, amelyekben a jarulek vagy a jaradek fugg az egyen csaladi kapcsolataitol. Ilyen elemek az ozvegyi es egyeb hozzatartozoi nyugdijak, a csaladi allapottol fuggő jarulek- es jaradekmegallapitas, a valtozatos gyermekkedvezmenyek vagy a gyermekneveles-fuggő nyugdijmegallapitas. A magyar adatkornyezetben a haztartas-formalodasi modul programozasa specialis nehezsegekbe utkozik, mivel nem all rendelkezesre olyan adminisztrativ vagy kerdőives kikerdezesre epulő adatallomany, amely azon felul, hogy az egyenre nezve kapcsolattorteneti es haztartas-szerkezeti adatokat tartalmaz, kiterjed a parokra, vagy ha kiterjed is, ezt a tenyt nem rogziti. A szoba johető survey jellegű adatbazisok egyeni mintakat tartalmaznak, az adminisztrat...

Jelen dolgozat celja Neumann Janos jatekelmeleti munkassaganak bemutatasa, eredmenyeinek matematikatorteneti elhelyezese. Reszletesen foglalkozunk a hires minimax tetellel, illetve a Neumann-Morgenstern-fele megoldassal, ennek kritikaival es az utobbi tobb mint otven ev alatt javasolt alternativ megoldaskoncepcioival. Beszamolunk a jatekelmeleti kutatas jelenlegi helyzeteről, az aktualis problemakrol es alkalmazasokrol. Journal of Economic Literature (JEL) kod: C7, N01.

Certain aggregate externalities, like those due to knowledge and public goods, do not change very much in response to changes in two individuals' actions. Thus, individuals rationally regard the level of the externality as fixed in their negotiations with each other. We leverage this observation to develop a general framework for the existence of stable matchings in moderately sized one-to-one matching games, and we characterize intuitive restrictions on preferences that are sufficient for existence. JEL Classification: C78 and D62.