Computational complexity of kk-stable matchings

We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more beneficial to at least $k$ out of the $n$ agents. The concept generalizes the recently studied majority stability. We prove that whereas the verification of $k$-stability for a given matching is polynomial-time solvable in all three models, the complexity of deciding whether a $k$-stable matching exists depends on $\frac{k}{n}$ and is characteristic to each model.Comment: SAGT 202

Dynamic refugee matching

Asylum seekers are often assigned to localities upon arrival using uninformed matching systems, which lead to inefficient and unfair allocations. This paper proposes an informed dynamic mechanism as an intuitive and easy-to-implement alternative. Our mechanism can be adopted in any dynamic refugee matching problem given locality-specific quotas and that asylum seekers map into specific categories. Any matching selected by the proposed mechanism is Pareto efficient, and envy between localities is bounded by a single asylum seeker. Our simulations show that the proposed mechanism outperforms uninformed mechanisms even in presence of severe misclassification error in the estimation of asylum seeker categories

Centralized refugee matching mechanisms with hierarchical priority classes

This study examines the refugee reallocation problem by modeling it as a two-sided matching problem between countries and refugees. Based on forced hierarchical priority classes, I study two interesting refugee matching algorithms to match refugees with countries. Axioms for fairness measures in resource allocation are presented by considering the stability and fairness properties of the matching algorithms. Two profiles are explicitly modeled -- country preferences and forced prioritization of refugee families by host countries. This approach shows that the difference between the profiles creates blocking pairs of countries and refugee families owing to the forced hierarchical priority classes. Since the forced priorities for countries can cause certain refugees to linger in a lower priority class in every country, this study highlights the importance of considering refugees' preferences. It also suggests that a hierarchical priority class-based approach without category-specific quotas can increase countries' willingness to solve the refugee reallocation problem

Refugee Settlement and Other Matching Problems with Priority Classes and Reserves: A Market Design Perspective

Recognizing the need to find a solution to the European refugee crisis, given the political deadlock preventing countries from participating in responsibility-sharing, this thesis addresses questions on international refugee placement from a market design perspective. Beyond refugee settlement, our theoretical findings also apply to immigration, centralized university admissions, public school choice systems, and other settings. Following the Introduction in Chapter 1, in Chapter 2 we advocate a centralized global refugee matching system and design new matching algorithms with explicitly modelled UNHCR-mandated hierarchical priority classes of refugee families. Combined with the preferences of both sides, this set-up allows us to capture and analyse the impact of the mandated priority classes on the stability and fairness of the resulting refugee matching. We conduct an axiomatic analysis to further support the new matching designs. Chapter 3 is motivated by the objective of designing a priority policy that effectively helps the prioritized agents. To benefit refugees in emergency zones, for example, a policy designed to create representation is not appealing, since strong candidates who would qualify without relying on their priority status may take up some or most of the reserved positions. Hence, we propose an alternative policy with targeted priority reserves, the DA-TPR mechanism, which targets those agents in the priority group who are in need of a reserved position. We also study a general class of matching mechanisms with priority reserve policies, which includes both the DA-TPR and the primary representation rule, Hafalir et al.'s (2013) DA-MiR mechanism. The DA-TPR is the most targeted policy in this class of mechanism, which we characterize by a priority reserve stability axiom and a strong incentive property. Chapter 4 introduces two new classes of matching mechanisms with explicitly specified partially targeted priority reserves. Both of these classes include the DA-TPR and DA-MiR mechanisms as extreme members. We identify one of these as a subclass of the characterized class of mechanisms from the previous chapter. Both studied classes of mechanisms are transparent and offer a range of policies between the DA-TPR and the DA-MiR policies, providing the designer with flexibility and clarity when choosing a priority reserve policy

Theoretical Studies On The Design of School Choice Mechanism

This thesis consists of three papers on market design which address broadly applicable questions on the design of school choice mechanisms, refugee placement, assignment in entry-level labour markets and similar matching rules.In the first paper a new family of rules is introduced for many-to-one matching problems, the Preference Rank Partitioned (PRP) rules. PRP rules are Student-Proposing Deferred Acceptance rules where the schools use a choice function based on the students' preference orderings in addition to the schools' strict priority orderings. Each PRP rule uses a choice function which is a function of a fixed partition of both student preference ranks and school priority ranks: the choice function first seeks to select students based on the priority classes and then based on the preference classes. The strict priorities are only used for tie-breaking. PRP rules include many well-known matching rules and some interesting new rules, and we analyze them in this unified framework. In the second paper we study a new class of matching rules, called Deferred Acceptance with Improvement Trading Cycles (DA-ITC), which start with the DA, and if the DA outcome is not Pareto-efficient then there is an iterated improvement trading cycle phase which allows for Pareto-improvements until a Pareto-efficient outcome is reached. We first revisit EADAM (Kesten, 2010) and show that a simple algorithm which retraces cycles in the DA procedure in a backward order of the rejections is equivalent to the EADAM rule. The new class of DA-ITC rules contains the EADAM and DA-TTC as its two extreme members and exhibits some of their desirable properties. In the third paper we focus on matching problems where stability need not be satisfied if the violation of priorities is "small," such as when a small priority difference is considered insignificant or when one is willing to consent but only if the priority reversal is small. Based on the degree of stability which specifies what is considered a small priority gap, we define two families of matching rules, the k-Consent rules and the k-DA rules, and explore their attributes

Essays on matchings and contests

This thesis is composed of two parts. Part I contributes to the matching literature and Part II contributes to the contest literature. Part I: A set of indivisible objects must be allocated among a group of agents, or agents from one side of the market must be matched to agents on the other. Each agent has their own preference over these objects, or over the agents on the other side. These preferences exhibit an underlying structure, motivated by real-world examples such as the refugee settlement problem, the job rotation problem and others. We study design of procedures to match agents to objects/agents, without resorting to randomization devices or monetary transfers. Three concerns play a central role in this design: incentive compatibility, efficiency and fairness. For each setting we consider, we appropriately formalise what we mean by these terms. Part II: A competitive league coach (team manager) must manage the energy pool of players in the team over the course of the entire season. High energy usage increases the chance of winning the current game, but also increases the risk of developing accumulated fatigue or injuries in later games. We explore this “winning in the short term” vs “saving energy for the future” dilemma that the coach faces over a long season

A location optimization approach to refugee resettlement decision-making

Whether due to customary causes or new emerging ones, the ever-growing refugee population precipitates a variety of issues all around the world. Resettlement of individuals and families is an issue that should be regarded carefully by considering different aspects and periods. Perceiving the refugee resettlement as a layered problem, the purpose of the present study is to help decision-makers with arduous resettlement planning by developing a preliminary optimization model. To that end, we transform the capacitated version of the traditional facility location problem into a multicriteria optimization problem that accounts for the physical capacities to meet the refugee needs, the cultural differences along with the physical distances and travel difficulties between origin and host societies, prioritization of the matchings, and the overall success of the resettlement process