Essays on Matching Markets and Their Equilibria

Matching theory and matching markets are a core component of modern economic theory and market design. This dissertation presents three original contributions to this area. The first essay constructs a matching mechanism in an incomplete information matching market in which the positive assortative match is the unique efficient and unique stable match. The mechanism asks each agent in the matching market to reveal her privately known type. Through its novel payment rule, truthful revelation forms an ex post Nash equilibrium in this setting. This mechanism works in one-, two- and many-sided matching markets, thus offering the first mechanism to unify these matching markets under a single mechanism design framework. The second essay confronts a problem of matching in an environment in which no efficient and incentive compatible matching mechanism exists due to matching externalities. I develop a two-stage matching game in which a contracting stage facilitates subsequent conditionally efficient and incentive compatible Vickrey auction stage. Infinite repetition of this two-stage matching game enforces the contract in every period. This mechanism produces inequitably distributed social improvement: parties to the contract receive all of the gains and then some. The final essay demonstrates the existence of prices which stably and efficiently partition a single set of agents into firms and workers, and match those two sets to each other. This pricing system extends Kelso and Crawford's general equilibrium results in a labor market matching model and links one- and two-sided matching markets as well.

Efficient Competition through Cheap Talk: Competing Auctions and Competitive Search without Ex Ante Price

We consider a frictional two-sided matching market in which one side uses public cheap talk announcements so as to attract the other side. We show that if the first-price auction is adopted as the trading protocol, then cheap talk can be perfectly informative, and the resulting market outcome is efficient, constrained only by search frictions. We also show that the performance of an alternative trading protocol in the cheap-talk environment depends on the level of price dispersion generated by the protocol: If a trading protocol compresses (spreads) the distribution of prices relative to the first-price auction, then an efficient fully revealing equilibrium always (never) exists. Our results identify the settings in which cheap talk can serve as an efficient competitive instrument, in the sense that the central insights from the literature on competing auctions and competitive search continue to hold unaltered even without ex ante price commitment.

Manipulation via Capacities Revisited

This paper revisits manipulation via capacities in centralized two-sided matching markets. Sönmez (1997) showed that no stable mechanism is nonmanipulable via capacities. We show that non-manipulability via capacities can be equivalently described by two types of non-manipulation via capacities: non-Type-I-manipulability meaning that no college with vacant positions can manipulate by dropping some of its empty positions; and non-Type-II-manipulability meaning that no college with no vacant positions can manipulate by dropping some of its filled positions. Our main result shows that the student-optimal stable mechanism is the unique stable mechanism which is non-Type-I-manipulable via capacities and independent of truncations. Our characterization supports the use of the student-optimal stable mechanism in these matching markets because of its limited manipulability via capacities by colleges.

The effects of a centralized college admission mechanism on migration and college enrollment: evidence from Brazil

No Brasil, a recente reformulação do Exame Nacional de Ensino Médio (ENEM) e a criação do Sistema de Seleção Unificada (SISU), um mecanismo de admissão centralizado que aloca os alunos às instituições, promoveram mudanças relevantes no Ensino Superior. Neste artigo, investigamos os efeitos da introdução do SISU na migração e evasão dos alunos ingressantes a partir dos dados do Censo de Educação Superior. Para tal, exploramos a variação temporal na adesão das instituições ao SISU e encontramos que a adoção do SISU está associada a um aumento da mobilidade entre municípios e entre estados dos alunos ingressantes em 3.8 pontos percentuais (p.p) e 1.6 p.p., respectivamente. Além disso, encontramos um aumento da evasão em 4.5 p.p. Nossos resultados indicam que custos associados à migração e comportamento estratégico são importantes determinantes da evasão dos alunos.

Sequential Pre-Marital Investment Games: Implications for Unemployment

Agents on the same side of a two-sided matching market (such as the marriage or labor market) compete with each other by making self-enhancing investments to improve their worth in the eyes of potential partners. Because these expenditures generally occur prior to matching, this activity has come to be known in recent literature (Peters, 2007) as pre-marital investment. This paper builds on that literature by considering the case of sequential pre-marital investment, analyzing a matching game in which one side of the market invests first, followed by the other. Interpreting the first group of agents as workers and the other group as firms, the paper provides a new perspective on the incentive structure that is inherent in labor markets. It also demonstrates that a positive rate of unemployment can exist even in the absence of matching frictions. Policy implications follow, as the prevailing set of equilibria can be altered by restricting entry into the workforce, providing unemployment insurance, or subsidizing pre-marital investment.

Manipulability in matching markets: conflict and coincidence of interests

We study comparative statics of manipulations by women in the men-proposing deferred acceptance mechanism in the two-sided one-to-one marriage market. We prove that if a group of women employs truncation strategies or weakly successfully manipulates, then all other women weakly benefit and all men are weakly harmed. We show that our results do not appropriately generalize to the many-to-one college admissions model.

One-sided tolerance interval in a two-way balanced nested model with mixed effects

In many research areas (such as public health, environmental contamination, and others) one deals with the necessity of using data to infer whether some proportion (%) of a population of interest is (or one wants it to be) below and/or over some threshold, through the computation of tolerance interval. The idea is, once a threshold is given, one computes the tolerance interval or limit (which might be one or two - sided bounded) and then to check if it satisfies the given threshold. Since in this work we deal with the computation of one - sided tolerance interval, for the two-sided case we recomend, for instance, Krishnamoorthy and Mathew [5]. Krishnamoorthy and Mathew [4] performed the computation of upper tolerance limit in balanced and unbalanced one-way random effects models, whereas Fonseca et al [3] performed it based in a similar ideas but in a tow-way nested mixed or random effects model. In case of random effects model, Fonseca et al [3] performed the computation of such interval only for the balanced data, whereas in the mixed effects case they dit it only for the unbalanced data. For the computation of twosided tolerance interval in models with mixed and/or random effects we recomend, for instance, Sharma and Mathew [7]. The purpose of this paper is the computation of upper and lower tolerance interval in a two-way nested mixed effects models in balanced data. For the case of unbalanced data, as mentioned above, Fonseca et al [3] have already computed upper tolerance interval. Hence, using the notions persented in Fonseca et al [3] and Krishnamoorthy and Mathew [4], we present some results on the construction of one-sided tolerance interval for the balanced case. Thus, in order to do so at first instance we perform the construction for the upper case, and then the construction for the lower case.

Symmetrically multilateral-bargained allocations in multi-sided assignment markets

[cat] Aquest treball tracta d’extendre la noció d’equilibri simètric de negociació bilateral introduït per Rochford (1983) a jocs d’assignació multilateral. Un pagament corresponent a un equilibri simètric de negociación multilateral (SMB) és una imputación del core que garanteix que qualsevol agent es troba en equilibri respecte a un procés de negociación entre tots els agents basat en allò que cadascun d’ells podria rebre -i fer servir com a amenaça- en un ’matching’ òptim diferent al que s’ha format. Es prova que, en el cas de jocs d’assignació multilaterals, el conjunt de SMB és sempre no buit i que, a diferència del cas bilateral, no sempre coincideix amb el kernel (Davis and Maschler, 1965). Finalment, responem una pregunta oberta per Rochford (1982) tot introduïnt un conjunt basat en la idea de kernel, que, conjuntament amb el core, ens permet caracteritzar el conjunt de SMB.

Symmetrically multilateral-bargained allocations in multi-sided assignment markets

[cat] Aquest treball tracta d’extendre la noció d’equilibri simètric de negociació bilateral introduït per Rochford (1983) a jocs d’assignació multilateral. Un pagament corresponent a un equilibri simètric de negociación multilateral (SMB) és una imputación del core que garanteix que qualsevol agent es troba en equilibri respecte a un procés de negociación entre tots els agents basat en allò que cadascun d’ells podria rebre -i fer servir com a amenaça- en un ’matching’ òptim diferent al que s’ha format. Es prova que, en el cas de jocs d’assignació multilaterals, el conjunt de SMB és sempre no buit i que, a diferència del cas bilateral, no sempre coincideix amb el kernel (Davis and Maschler, 1965). Finalment, responem una pregunta oberta per Rochford (1982) tot introduïnt un conjunt basat en la idea de kernel, que, conjuntament amb el core, ens permet caracteritzar el conjunt de SMB.

Essays on the Axiomatic Theory of Matching

This dissertation mimics the Turkish college admission procedure. It started with the purpose to reduce the inefficiencies in Turkish market. For this purpose, we propose a mechanism under a new market structure; as we prefer to call, semi-centralization. In chapter 1, we give a brief summary of Matching Theory. We present the first examples in Matching history with the most general papers and mechanisms. In chapter 2, we propose our mechanism. In real life application, that is in Turkish university placements, the mechanism reduces the inefficiencies of the current system. The success of the mechanism depends on the preference profile. It is easy to show that under complete information the mechanism implements the full set of stable matchings for a given profile. In chapter 3, we refine our basic mechanism. The modification on the mechanism has a crucial effect on the results. The new mechanism is, as we call, a middle mechanism. In one of the subdomain, this mechanism coincides with the original basic mechanism. But, in the other partition, it gives the same results with Gale and Shapley's algorithm. In chapter 4, we apply our basic mechanism to well known Roommate Problem. Since the roommate problem is in one-sided game patern, firstly we propose an auxiliary function to convert the game semi centralized two-sided game, because our basic mechanism is designed for this framework. We show that this process is succesful in finding a stable matching in the existence of stability. We also show that our mechanism easily and simply tells us if a profile lacks of stability by using purified orderings. Finally, we show a method to find all the stable matching in the existence of multi stability. The method is simply to run the mechanism for all of the top agents in the social preference.

Assortative matching of exporters and importers

This paper uses the opening of the US textile/apparel market for China at the end of the Multifibre Arrangement in 2005 as a natural experiment to provide evidence for positive assortative matching of Mexican exporting firms and US importing firms by their capability. We identify three findings for liberalized products by comparing them to other textile/apparel products: (1) US importers switched their Mexican partners to those making greater preshock exports, whereas Mexican exporters switched their US partners to those making fewer preshock imports; (2) for firms who switched partners, trade volume of the old partners and the new partners are positively correlated; (3) small Mexican exporters stop exporting. We develop a model combining Becker-type matching of final producers and suppliers with the standard Melitz-type model to show that these findings are consistent with positive assortative matching but not with negative assortative matching or purely random matching. The model indicates that the findings are evidence for a new mechanism of gain from trade.

Matching theory based travel plan aware charging algorithms in V2G smart grid networks

The frequency, time and places of charging have large impact on the Quality of Experience (QoE) of EV drivers. It is critical to design effective EV charging scheduling system to improve the QoE of EV drivers. In order to improve EV charging QoE and utilization of CSs, we develop an innovative travel plan aware charging scheduling scheme for moving EVs to be charged at Charging Stations (CS). In the design of the proposed charging scheduling scheme for moving EVs, the travel routes of EVs and the utility of CSs are taken into consideration. The assignment of EVs to CSs is modeled as a two-sided many-to-one matching game with the objective of maximizing the system utility which reflects the satisfactory degrees of EVs and the profits of CSs. A Stable Matching Algorithm (SMA) is proposed to seek stable matching between charging EVs and CSs. Furthermore, an improved Learning based On-LiNe scheduling Algorithm (LONA) is proposed to be executed by each CS in a distributed manner. The performance gain of the average system utility by the SMA is up to 38.2% comparing to the Random Charging Scheduling (RCS) algorithm, and 4.67% comparing to Only utility of Electric Vehicle Concerned (OEVC) scheme. The effectiveness of the proposed SMA and LONA is also demonstrated by simulations in terms of the satisfactory ratio of charging EVs and the the convergence speed of iteration.

Exclusive Nightclubs and Lonely Hearts Columns: Nonmonotone Participation in Optional Intermediation

In many decentralised markets, the traders who benefit most from an exchange do not employ intermediaries even though they could easily afford them. At the same time, employing intermediaries is not worthwhile for traders who benefit little from trade. Together, these decisions amount to non-monotone participation choices in intermediation: only traders of middle “type” employ intermediaries, while the rest, the high and the low types, prefer to search for a trading partner directly. We provide a theoretical foundation for this, hitherto unexplained, phenomenon. We build a dynamic matching model, where a trader’s equilibrium bargaining share is a convex increasing function of her type. We also show that this is indeed a necessary condition for the existence of non-monotone equilibria.

Unemployment vs. mismatch of talents: Reconsidering unemployment benefits

We develop an equilibrium search-matching model with risk-neutral agentsand two-sided ex-ante heterogeneity. Unemployment insurance has thestandard effect of reducing employment, but also helps workers to get a suitable job. The predictions of our simple modelare consistent with the contrasting performance of the labor market in Europeand US in terms of unemployment, productivity growth and wage inequality.To show this, we construct two fictitious economies with calibratedparameters which only differ by the degree of unemployment insurance andassume that they are hit by a common technological shock which enhancesthe importance of mismatch. This shock reduces the proportion of jobs whichworkers regards as acceptable in the economy with unemployment insurance(Europe). As a result, unemployment doubles in this economy.In the laissez-faire economy (US), unemployment remains constant,but wage inequality increases more and productivity grows less due to largermismatch. The model can be used to address a number of normative issues.

Multi-sided Böhm-Bawerk assignment markets: the core

[cat] En aquest treball introduïm la classe de "multi-sided Böhm-Bawerk assignment games", que generalitza la coneguda classe de jocs d’assignació de Böhm-Bawerk bilaterals a situacions amb un nombre arbitrari de sectors. Trobem els extrems del core de qualsevol multi-sided Böhm-Bawerk assignment game a partir d’un joc convex definit en el conjunt de sectors enlloc del conjunt de venedors i compradors. Addicionalment estudiem quan el core d’aquests jocs d’assignació és estable en el sentit de von Neumann-Morgenstern.