Top Trading Cycles, Consistency, and Acyclic Priorities for House Allocation with Existing Tenants

We study the house allocation with existing tenants model (Abdulkadiroğlu and Sönmez, 1999) and consider rules that allocate houses based on priorities. We introduce a new acyclicity requirement and show that for house allocation with existing tenants a top trading cycles (TTC) rule is consistent if and only if its underlying priority structure satisfies our acyclicity condition. Next we give an alternative description of TTC rules based on ownership-adapted acyclic priorities in terms of two specific rules, YRMH-IGYT (you request my house - I get your turn) and efficient priority rules, that are applied in two steps. Moreover, even if no priority structure is a priori given, we show that a rule is a top trading cycles rule based on ownership-adapted acyclic priorities if and only if it satisfies Pareto-optimality, individual-rationality, strategy-proofness, consistency, and either reallocation-proofness or non-bossiness

Strategy-proof tie-breaking

We study a general class of priority-based allocation problems with weak priority orders and identify conditions under which there exists a strategy-proof mechanism which always chooses an agent-optimal stable, or constrained efficient, matching. A priority structure for which these two requirements are compatible is called solvable. For the general class of priority-based allocation problems with weak priority orders,we introduce three simple necessary conditions on the priority structure. We show that these conditions completely characterize solvable environments within the class of indifferences at the bottom (IB) environments, where ties occur only at the bottom of the priority structure. This generalizes and unifies previously known results on solvable and unsolvable environments established in school choice, housing markets and house allocation with existing tenants. We show how the previously known solvable cases can be viewed as extreme cases of solvable environments. For sufficiency of our conditions we introduce a version of the agent-proposing deferred acceptance algorithm with exogenous and preference-based tie-breaking

Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable Mechanism or the Top Trading Cycles Mechanism to assign children to public schools. There is clear evidence that for school districts that employ (variants of) the so-called Boston Mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures impede students to submit a preference list that contains all their acceptable schools. Therefore, any desirable property of the mechanisms is likely toget distorted. We study the non trivial preference revelation game where students can only declare up to a fixed number (quota) of schools to be acceptable. We focus on the stability of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guaranteestability. This stands in sharp contrast with the Boston Mechanism which yields stable Nash equilibrium outcomes, independently of the quota. Hence, the transition to any of the two mechanisms is likely to come with a higher risk that students seek legal actionas lower priority students may occupy more preferred schools

Essays on Matching Markets

The thesis "Essays on Matching Markets" contributes to the theory and applications of matching theory. The first chapter analyzes the German university admissions system and proposes an alternative admissions procedure that outperforms the currently used mechanism. In particular, the new mechanism provides strong (i.e. dominant strategy) incentives for applicants to reveal their true preferences and achieves a notion of stability that is adapted to the German system. In the second chapter we analyze the school choice problem with indifferences in priority orders. In this context, stability (with respect to student preferences and school priorities) can be understood as a fairness criterion which ensures that no student ever envies another student for a school at which she has higher priority. Since school seats are objects to be allocated among students, it is important to ensure that a constrained efficient allocation is selected, i.e. an allocation that is stable and not (Pareto-) dominated by any other stable matching. A counterexample of Erdil and Ergin (American Economic Review, 2008) shows that there may not exist a non-manipulable and constrained efficient mechanism. We consider the case where students either all have the same priority or all have distinct priorities for a given school. For this important special case we investigate whether the negative result of Erdil and Ergin is the rule or an exception and derive sufficient conditions for the existence of a constrained efficient and (dominant strategy) incentive compatible mechanism. The proof is constructive and shows how preferences of students can (sometimes) be used to prevent any welfare loss from tie-breaking decisions. The third chapter deals with a more general matching model recently introduced by Ostrovsky (American Economic Review, 2008). For this model we analyze the relation between Ostrovsky's chain stability concept, efficiency, and several competing stability concepts. We characterize the largest class of matching models for which chain stable outcomes are guaranteed to be stable and robust to all possible coalitional deviations. Furthermore, we provide two rationales, one based on efficiency and the other based on robustness considerations, for chain stability in the general supply chain model

Strategy-proof Allocation of Indivisible Goods when Preferences are Single-peaked

We consider assignment problems where heterogeneous indivisible goods are to be assigned to individuals so that each individual receives at most one good. Individuals have single-peaked preferences over the goods. In this setting, first we show that there is no strategy-proof, non-bossy, Pareto efficient, and strongly pairwise reallocation-proof assignment rule on a minimally rich single-peaked domain when there are at least three individuals and at least three objects in the market. Next, we characterize all strategy-proof, Pareto efficient, top-envy-proof, non-bossy, and pairwise reallocation-proof assignment rules on a minimally rich single-peaked domain as hierarchical exchange rules. We additionally show that strategy-proofness and non-bossiness together are equivalent to group strategy-proofness on a minimally rich single-peaked domain, and every hierarchical exchange rule satisfies group-wise reallocation-proofness on a minimally rich single-peaked domain

Designing and Optimizing Matching Markets

Matching market design studies the fundamental problem of how to allocate scarce resources to individuals with varied needs. In recent years, the theoretical study of matching markets such as medical residency, public housing and school choice has greatly informed and improved the design of such markets in practice. Impactful work in matching market design frequently makes use of techniques from computer science, economics and operations research to provide end–to-end solutions that address design questions holistically. In this dissertation, I develop tools for optimization in market design by studying matching mechanisms for school choice, an important societal problem that exemplifies many of the challenges in effective marketplace design. In the first part of this work I develop frameworks for optimization in school choice that allow us to address operational problems in the assignment process. In the school choice market, where scarce public school seats are assigned to students, a key operational issue is how to reassign seats that are vacated after an initial round of centralized assignment. We propose a class of reassignment mechanisms, the Permuted Lottery Deferred Acceptance (PLDA) mechanisms, which generalize the commonly used Deferred Acceptance school choice mechanism and retain its desirable incentive and efficiency properties. We find that under natural conditions on demand all PLDA mechanisms achieve equivalent allocative welfare, and the PLDA based on reversing the tie-breaking lottery during the reassignment round minimizes reassignment. Empirical investigations on data from NYC high school admissions support our theoretical findings. In this part, we also provide a framework for optimization when using the prominent Top Trading Cycles (TTC) mechanism. We show that the TTC assignment can be described by admission cutoffs, which explain the role of priorities in determining the TTC assignment and can be used to tractably analyze TTC. In a large-scale continuum model we show how to compute these cutoffs directly from the distribution of preferences and priorities, providing a framework for evaluating policy choices. As an application of the model we solve for optimal investment in school quality under choice and find that an egalitarian distribution can be more efficient as it allows students to choose schools based on idiosyncracies in their preferences. In the second part of this work, I consider the role of a marketplace as an information provider and explore how mechanisms affect information acquisition by agents in matching markets. I provide a tractable “Pandora's box” model where students hold a prior over their value for each school and can pay an inspection cost to learn their realized value. The model captures how students’ decisions to acquire information depend on priors and market information, and can rationalize a student’s choice to remain partially uninformed. In such a model students need market information in order to optimally acquire their personal preferences, and students benefit from waiting for the market to resolve before acquiring information. We extend the definition of stability to this partial information setting and define regret-free stable outcomes, where the matching is stable and each student has acquired the same information as if they had waited for the market to resolve. We show that regret-free stable outcomes have a cutoff characterization, and the set of regret-free stable outcomes is a non-empty lattice. However, there is no mechanism that always produces a regret-free stable matching, as there can be information deadlocks where every student finds it suboptimal to be the first to acquire information. In settings with sufficient information about the distribution of preferences, we provide mechanisms that exploit the cutoff structure to break the deadlock and approximately implement a regret-free stable matching

Essays on Two-Sided Matching Theory:

Thesis advisor: M. Utku ÜnverThesis advisor: Tayfun SönmezThis thesis is a collection of three essays in market design concerning designs of matching markets with aggregate constraints, affirmative action schemes, and investigating boundaries of simultaneous efficiency-stability relaxation for one-to-one matching mechanisms.In Chapter 1, I establish and propose a possible solution for a college housing crisis, a severe ongoing problem taking place in many countries. Every year many colleges provide housing for admitted students. However, there is no college admissions process that considers applicants’ housing needs, which often results in college housing shortages. In this chapter, I formally introduce housing quotas to the college admissions problem and solve it for centralized admissions with common dormitories. The proposed setting is inspired by college admissions where applicants apply directly to college departments, and colleges are endowed with common residence halls. Such setting has many real-life applications: hospital/residents matching in Japan (Kamada and Kojima, 2011, 2012, 2015), college admissions with scholarships in Hungary (Biró, 2012), etc. A simple example shows that there may not be a stable allocation for the proposed setting. Therefore, I construct two mechanisms that always produce some weakened versions of a stable matching: a Take-House-from-Applicant-stable and incentive compatible cumulative offer mechanism that respects improvements, and a Not-Compromised-Request-from-One-Agent-stable (stronger version of stability) cutoff minimising mechanism. Finally, I propose an integer programming solution for detecting a blocking-undominated Not-Compromised-Request-from-One-Agent-stable matching. Building on these results, I argue that presented procedures could serve as a helpful tool for solving the college housing crisis. In Chapter 2, I propose a number of solutions to resource allocation problems in an affirmative action agenda. Quotas are introduced as a way to promote members of minority groups. In addition, reserves may overlap: any candidate can belong to many minority groups, or, in other words, have more than one trait. Moreover, once selected, each candidate fills one reserve position for each of her traits, rather than just one position for one of her traits. This makes the entire decision process more transparent for applicants and allows them to potentially utilize all their traits. I extend the approach of Sönmez and Yenmez (2019) who proposed a paired-admissions choice correspondence that works under no more than two traits. In turn, I allow for any number of traits focusing on extracting the best possible agents, such that the chosen set is non-wasteful, the most diverse, and eliminates collective justified envy. Two new, lower- and upper-dominant choice rules and a class of sum-minimizing choice correspondences are introduced and characterized. In Chapter 3, I implement optimization techniques for detecting the efficient trade off between ex-post Pareto efficiency (for one side of a two-sided matching market) and ex-ante stability for small one-to-one matching markets. Neat example (Roth, 1982) proves that there is no matching mechanism that achieves both efficiency (for one side of the one-to-one matching market) and stability. As representative mechanisms I choose deferred-acceptance for stability, and top trading cycles for Pareto efficiency (both of them are strategy-proof for one side of the market). I compare performances of a randomized matching mechanism that simultaneously relaxes efficiency and stability, and a convex combination of two representative mechanisms. Results show that the constructed mechanism significantly improves efficiency and stability in comparison to mentioned convex combination of the benchmark mechanisms.Thesis (PhD) — Boston College, 2023.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Economics

Scalable and responsive real time event processing using cloud computing

PhD ThesisCloud computing provides the potential for scalability and adaptability in a cost e ective manner. However, when it comes to achieving scalability for real time applications response time cannot be high. Many applications require good performance and low response time, which need to be matched with the dynamic resource allocation. The real time processing requirements can also be characterized by unpredictable rates of incoming data streams and dynamic outbursts of data. This raises the issue of processing the data streams across multiple cloud computing nodes. This research analyzes possible methodologies to process the real time data in which applications can be structured as multiple event processing networks and be partitioned over the set of available cloud nodes. The approach is based on queuing theory principles to encompass the cloud computing. The transformation of the raw data into useful outputs occurs in various stages of processing networks which are distributed across the multiple computing nodes in a cloud. A set of valid options is created to understand the response time requirements for each application. Under a given valid set of conditions to meet the response time criteria, multiple instances of event processing networks are distributed in the cloud nodes. A generic methodology to scale-up and scale-down the event processing networks in accordance to the response time criteria is de ned. The real time applications that support sophisticated decision support mechanisms need to comply with response time criteria consisting of interdependent data ow paradigms making it harder to improve the performance. Consideration is given for ways to reduce the latency,improve response time and throughput of the real time applications by distributing the event processing networks in multiple computing nodes

Measuring knowledge sharing processes through social network analysis within construction organisations

The construction industry is a knowledge intensive and information dependent industry. Organisations risk losing valuable knowledge, when the employees leave them. Therefore, construction organisations need to nurture opportunities to disseminate knowledge through strengthening knowledge-sharing networks. This study aimed at evaluating the formal and informal knowledge sharing methods in social networks within Australian construction organisations and identifying how knowledge sharing could be improved. Data were collected from two estimating teams in two case studies. The collected data through semi-structured interviews were analysed using UCINET, a Social Network Analysis (SNA) tool, and SNA measures. The findings revealed that one case study consisted of influencers, while the other demonstrated an optimal knowledge sharing structure in both formal and informal knowledge sharing methods. Social networks could vary based on the organisation as well as the individuals’ behaviour. Identifying networks with specific issues and taking steps to strengthen networks will enable to achieve optimum knowledge sharing processes. This research offers knowledge sharing good practices for construction organisations to optimise their knowledge sharing processes

The 45th Australasian Universities Building Education Association Conference: Global Challenges in a Disrupted World: Smart, Sustainable and Resilient Approaches in the Built Environment, Conference Proceedings, 23 - 25 November 2022, Western Sydney University, Kingswood Campus, Sydney, Australia

This is the proceedings of the 45th Australasian Universities Building Education Association (AUBEA) conference which will be hosted by Western Sydney University in November 2022. The conference is organised by the School of Engineering, Design, and Built Environment in collaboration with the Centre for Smart Modern Construction, Western Sydney University. This year’s conference theme is “Global Challenges in a Disrupted World: Smart, Sustainable and Resilient Approaches in the Built Environment”, and expects to publish over a hundred double-blind peer review papers under the proceedings