Acyclicity and singleton cores in matching markets

This paper analyzes the role of acyclicity in singleton cores. We show that the absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Furthermore, acyclicity in the preferences of either side of the market is a minimal condition that guarantees the existence of singleton cores. If firms or workers preferences are acyclical, unique stable matching is obtained through a procedure that resembles a serial dictatorship. Thus, acyclicity generalizes the notion of common preferences. It follows that if the firms or workers preferences are acyclical, unique stable matching is strongly efficient for the other side of the marketStable matching, Acyclicity, Singleton cores

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

Construir el diálogo científico en la Matemática: la búsqueda del equilibrio entre símbolos y palabras en artículos de investigación sobre Teoría de Juegos

Maestría en Inglés con Orientación en Lingüística AplicadaMost scientific communication is conducted in English, which may be a difficult task and a source of obstacles for researchers whose primary language is not English (Bitchenera & Basturkmen, 2006; Borlogan, 2009; Duff, 2010; Matsuda & Matsuda, 2010). As a matter of concern for language scholars, this situation requires at least two actions: (1) the development of research focused on the problems faced by researchers when writing in a foreign language, and (2) the design and implementation of pedagogical and didactic programmes or services aimed at providing researchers with the tools to enhance their linguistic and rhetorical skills. In both cases, the ultimate objective of these lines of action is to help researchers integrate into and interact with their knowledge communities in an independent, active and successful way. Considering those needs and the emerging interest in English as a lingua franca or as an international language, many scholars have devoted to studying the features of writing and language use across the world and across disciplines (Hyland, 2004; Matsuda & Matsuda, 2010; Mercado, 2010). However, few have explored the case of Mathematics (Lemke, 2002; Morgan, 2008; O’Halloran, 2005; Schleppegrell, 2007), and even fewer have investigated the discourse of scientific research articles (SRA) in this discipline (Graves & Moghadassi, 2013, 2014). In view of this situation, investigation of the discourse of science in the field of Mathematics (Game Theory - GT) as used in the Institute of Applied Mathematics (IMASL), at the National University of San Luis (UNSL), becomes both an answer to local researchers’ needs and an attempt to contribute to current research in writing, evaluative discourse and use of English as an international language for the communication of science. Thus, the main objective of this work is to conduct a comparative description between unpublished GT SRAs written in English by IMASL researchers and published GT SRAs written in English by international authors, in terms of linguistic features used to build authorship and authorial stance. The exploration of the genre is made from the perspective of the system of Appraisal (Hood, 2010; Martin & White, 2005; White, 2000), with the aid of Corpus Linguistics (CL) tools (Cheng, 2012; Meyer, 2002; Tognini-Bonelli, 2001). The results of this research are expected to be useful for the enhancement of knowledge of language professionals devoted to the teaching of writing as well as translation, proofreading, editing and reviewing services. A further goal is to lay the foundations for the production of didactic material which can potentially be incorporated into writing courses or professional writing, translation, reviewing and proofreading training programmes.Fil: Lucero Arrua, Graciela Beatriz. Universidad Nacional de Córdoba. Facultad de Lenguas; Argentina

Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

We propose novel approaches and tests for estimating student preferences with data from centralized matching mechanisms, like the Gale-Shapley Deferred Acceptance, when students are strictly ranked by, e.g., test scores. Without requiring truth-telling to be the unique equilibrium, we show that the matching is (asymptotically) stable, or justified-envy-free, implying that every student is matched with her favorite school/college among those she is qualified for ex post. Having illustrated the approaches in simulations, we apply them to school choice data from Paris and demonstrate evidence supporting stability but not truth-telling. We discuss when each approach is more appropriate in real-life settings

Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

We propose novel approaches and tests for estimating student preferences with data from centralized matching mechanisms, like the Gale-Shapley Deferred Acceptance, when students are strictly ranked by, e.g., test scores. Without requiring truth-telling to be the unique equilibrium, we show that the matching is (asymptotically) stable, or justified-envy-free, implying that every student is matched with her favorite school/college among those she is qualified for ex post. Having illustrated the approaches in simulations, we apply them to school choice data from Paris and demonstrate evidence supporting stability but not truth-telling. We discuss when each approach is more appropriate in real-life settings

Affirmative actions under the Boston mechanism

We consider three popular a rmative action policies in school choice: quota-based, priority-based, and reserve-based a rmative actions. The Boston mechanism (BM) is responsive to the latter two policies in that a stronger priority-based or reserve-based a rmative action makes some minority student better o . However, a stronger quotabased a rmative action may yield a Pareto inferior outcome for the minority under the BM. These positive results disappear once we look for a stronger welfare consequence on the minority or focus on BM equilibrium outcomes

Philosophical and ethical aspects of economic design

This thesis studies some philosophical and ethical issues that economic design raises. Chapter 1 gives an overview of economic design and argues that a crossfertilisation between philosophy and economic design is possible and insightful for both sides. Chapter 2 examines the implications of mechanism design for theories of rationality. I show that non-classical theories, such as constrained maximization and team reasoning, are at odds with the constraint of incentive compatibility. This poses a problem for non-classical theories, which proponents of these theories have not addressed to date. Chapter 3 proposes a general epistemology of economic engineering, which is motivated by a novel case study, viz. the reform of a matching market for medical practitioners. My account makes use of causal graphs to explain how models allow encoding counterfactual information about how market outcomes change if the design of the market changes. The second part of the thesis examines ethical issues. In Chapter 4, I apply tools from matching theory to gain insights into the distribution of refugees, such as among countries of the European Union. There is an ethical trade-off between the fairness of matchings and their efficiency, and I argue that in this context, fairness is the morally weightier criterion. Chapter 5 deals with the ethics of kidney exchange. Against critics, I give two arguments for the implementation of kidney exchange programmes. The first argument is that they are instrumental in meeting a moral obligation, namely to donate effectively. The second is that kidney exchange may increase the motivation for altruistic donations, because the donation of one kidney may trigger > 1 life savings. The final chapter identifies questions for future research and it closes with some thoughts about the future trajectory of economic design

Efficiency and Stability in Large Matching Markets

We study efficient and stable mechanisms in matching markets when the number of agents is large and individuals’ preferences and priorities are drawn randomly. When agents’ preferences are uncorrelated, then both efficiency and stability can be achieved in an asymptotic sense via standard mechanisms such as deferred acceptance and top trading cycles. When agents’ preferences are correlated over objects, however, these mechanisms are either inefficient or unstable even in an asymptotic sense. We propose a variant of deferred acceptance that is asymptotically efficient, asymptotically stable and asymptotically incentive compatible. This new mechanism performs well in a counter- factual calibration based on New York City school choice data

Essays on Matching Markets

The thesis consists of three chapters in the theory of matching markets. In Chapter 2, I study a central authority's ability to commit to a publicly announced mechanism in a one-to-one agent-object matching model. The authority announces a strategy-proof mechanism and then privately selects a mechanism to initiate a matching. An agent's observation in form of the final matching has an innocent explanation (Akbarpour and Li, 2020), if given the agent's reported preferences, there is a combination with other agents' preferences leading to an identical observation under the announced mechanism. The authority can only commit up to safe deviations (Akbarpour and Li, 2020)---mechanisms that produce only observations with innocent explanations. For efficient or stable announcements, I show that no safe deviation exists if and only if the announced mechanism is dictatorial. I establish that the Deferred Acceptance (DA) Mechanism (Gale and Shapley, 1962) implies commitment to stability. Moreover, group strategy-proof and efficient announcements allow commitment to efficiency only if they are dictatorial. In Chapter 3, we study The Efficiency Adjusted Deferred Acceptance Matching Rule (EDA) which is a promising candidate mechanism for public school assignment. A potential drawback of EDA is that it could encourage students to game the system since it is not strategy-proof. However, to successfully strategize, students typically need information that is unlikely to be available to them in practice. We model school choice under incomplete information and show that EDA is regret-free truth-telling, which is a weaker incentive property than strategy-proofness and was introduced by (Fernandez, 2020). We also show that there is no efficient matching rule that weakly Pareto dominates a stable matching rule and is regret-free truth-telling. Note that without modifications the EDA as introduced by (Kesten, 2010) weakly Pareto dominates a stable matching rule, but it is not efficient. In Chapter 4, I study agents’ incentives in a one-to-one object allocation model where agents are envious. Among all agents whose assignment is tracked by some agent, the agent envies those who are matched to an object she prefers to her own assignment. Given a mechanism and agents’ actions, agent i’s envy towards agent j at object x under the induced matching is inevitable if i has no action where she does not envy j at x, given one keeps the actions of other agents unchanged. A matching mechanism is envyproof, if for each market and agent, any envy under truthful revelation of preferences is inevitable. Envy-proofness is a concept that is stronger than strategy-proofness. I show that the Top Trading Cycle (TTC) Mechanism is envy-proof. Moreover, the unique strategy-proof and stable mechanism, the Deferred Acceptance Mechanism, is not envy-proof