The principal-agent matching market

We propose a model based on competitive markets in order to analyze an economy with several principals and agents. We model the principal-agent economy as a two-sided matching game and characterize the set of stable outcomes of this principal-agent matching market. A simple mechanism to implement the set of stable outcomes is proposed. Finally, we put forward examples of principal-agent economies where the results fit into.

Matching Markets under (In)complete Information

We are the first to introduce incomplete information to centralized many-to-one matching markets such as those to entry-level labor markets or college admissions. This is important because in real life markets (i) any agent is uncertain about the other agents' true preferences and (ii) most entry-level matching is many-to-one (and not one-to-one). We show that for stable (matching) mechanisms there is a strong and surprising link between Nash equilibria under complete information and Bayesian Nash equilibria under incomplete information. That is,given a common belief, a strategy profile is a Bayesian Nash equilibrium under incomplete information in a stable mechanism if and only if, for any true profile in the support of the common belief, the submitted profile is a Nash equilibrium under complete information at the true profile in the direct preference revelation game induced by the stable mechanism. This result may help to explain the success of stable mechanisms in these markets.

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Preference Structure and Random Paths to Stability in Matching Markets

This paper examines how preference correlation and intercorrelation combine to influence the length of a decentralized matching market's path to stability. In simulated experiments, marriage markets with various preference specifications begin at an arbitrary matching of couples and proceed toward stability via the random mechanism proposed by Roth and Vande Vate (1990). The results of these experiments reveal that fundamental preference characteristics are critical in predicting how long the market will take to reach a stable matching. In particular, intercorrelation and correlation are shown to have an exponential impact on the number of blocking pairs that must be randomly satisfied before stability is attained. The magnitude of the impact is dramatically different, however, depending on whether preferences are positively or negatively intercorrelated.

The Pennsylvania Adoption Exchange Improves Its Matching Process

The Pennsylvania Adoption Exchange (PAE) helps case workers who represent children in state custody by recommending prospective families for adoption. We describe PAE's operational challenges using case worker surveys and analyze child outcomes through a regression analysis of data collected over multiple years. A match recommendation spreadsheet tool implemented by PAE incorporates insights from this analysis and allows PAE managers to better utilize available information. Using a discrete-event simulation of PAE, we justify the value of a statewide adoption network and demonstrate the importance of better information about family preferences for increasing the percentage of children who are successfully adopted. Finally, we detail a series of simple improvements that PAE achieved through collecting more valuable information and aligning incentives for families to provide useful preference information.

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.

In Search of Advice for Physicians in Entry-Level Medical Markets

We consider entry-level medical markets for physicians in the United Kingdom. These markets experienced failures which led to the adoption of centralized market mechanisms in the 1960's. However, different regions introduced different centralized mechanisms. We advise physicians who do not have detailed information about the rank-order lists submitted by the other participants. We demonstrate that in each of these markets in a low information environment it is not beneficial to reverse the true ranking of any two acceptable hospital positions. We further show that (i) in the Edinburgh 1967 market, ranking unacceptable matches as acceptable is not profitable for any participant and (ii) in any other British entry-level medical market, it is possible that only strategies which rank unacceptable positions as acceptable are optimal for a physician.

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.

Essays in Macroeconomics

My dissertation consists of three self-contained essays on macroeconomics. Chapter 2 "Churning, firm inter-connectivity, and labor market fluctuations'' studies the implications of firm inter-connectivity and irreversibility of inter-firm cooperation relationships on the business cycle. Chapter 3 "Inter-sector matching efficiency and sectoral comovement'' examines the comovement of sectoral labor markets when there is search friction in the inter-firm matching market. Chapter 4 "Lumpy investment and endogenous investment price'' (Joint work with Linxi Chen) studies the endogenous fluctuation of investment price induced by search friction in the investment goods market and partial irreversibility of capital adjustment. Each of the essays investigates the implication of market frictions, such as search friction and partial irreversibility, to the business cycle from a different perspective.

Labor market heterogeneity and the aggregate matching function

The matching function -a key building block in models of labor market frictions- impliesthat the job finding rate depends only on labor market tightness. We estimate such amatching function and find that the relation, although remarkably stable over 1967-2007,broke down spectacularly after 2007. We argue that labor market heterogeneities are notfully captured by the standard matching function, but that a generalized matching functionthat explicitly takes into account worker heterogeneity and market segmentation is fullyconsistent with the behavior of the job finding rate. The standard matching function canbreak down when, as in the Great Recession, the average characteristics of the unemployedchange too much, or when dispersion in labor market conditions -the extent to which somelabor markets fare worse than others- increases too much.

A bidimensional model of matching in the marriage market with women labor decision

We construct a frictionless matching model of the marriage market where women have bidimensional attributes, one continuous (income) and the other dichotomous (home ability). Equilibrium in the marriage market determines intrahousehold allocation of resources and female labor participation. Our model is able to predict partial non-assortative matching, with rich men marrying women with low income but high home ability. We then perform numerical exercises to evaluate the impacts of income taxes in individual welfare and find that there is considerable divergence in the female labor participation response to taxes between the short run and the long run.

Stability property of matchings is a natural solution concept in coalitional market games

Stability of matchings was proved to be a new cooperative equilibrium concept in Sotomayor (Dynamics and equilibrium: essays in honor to D. Gale, 1992). That paper introduces the innovation of treating as multi-dimensional the payoff of a player with a quota greater than one. This is done for the many-to-many matching model with additively separable utilities, for which the stability concept is defined. It is then proved, via linear programming, that the set of stable outcomes is nonempty and it may be strictly bigger than the set of dual solutions and strictly smaller than the core. The present paper defines a general concept of stability and shows that this concept is a natural solution concept, stronger than the core concept, for a much more general coalitional game than a matching game. Instead of mutual agreements inside partnerships, the players are allowed to make collective agreements inside coalitions of any size and to distribute his labor among them. A collective agreement determines the level of labor at which the coalition operates and the division, among its members, of the income generated by the coalition. An allocation specifies a set of collective agreements for each player.

Youth unemployment outflow rates and labor market programs: Australian evidence

A matching function methodology is used to investigate the macroeconomic effects of labor market program (LMP) commencements on youth unemployment outflows in Australia using unpublished data that classify commencements and outflows by duration of unemployment. The results indicate that LMPs have had significant effects on outflows from short-term unemployment. There is a net positive effect from LMP commencements on short-term unemployed female outflow rates. However; females experienced negative spillover effects from male LMP commencements. These spillover effects appear to be associated with wage subsidy programs and suggest the net impact Of such programs may have been overstated in previous studies.

Enhancing Agent Mediated Electronic Markets with Ontology Matching Services and Social Network Support

Os Mercados Eletrónicos atingiram uma complexidade e nível de sofisticação tão elevados, que tornaram inadequados os modelos de software convencionais. Estes mercados são caracterizados por serem abertos, dinâmicos e competitivos, e constituídos por várias entidades independentes e heterogéneas. Tais entidades desempenham os seus papéis de forma autónoma, seguindo os seus objetivos, reagindo às ocorrências do ambiente em que se inserem e interagindo umas com as outras. Esta realidade levou a que existisse por parte da comunidade científica um especial interesse no estudo da negociação automática executada por agentes de software [Zhang et al., 2011]. No entanto, a diversidade dos atores envolvidos pode levar à existência de diferentes conceptualizações das suas necessidades e capacidades dando origem a incompatibilidades semânticas, que podem prejudicar a negociação e impedir a ocorrência de transações que satisfaçam as partes envolvidas. Os novos mercados devem, assim, possuir mecanismos que lhes permitam exibir novas capacidades, nomeadamente a capacidade de auxiliar na comunicação entre os diferentes agentes. Pelo que, é defendido neste trabalho que os mercados devem oferecer serviços de ontologias que permitam facilitar a interoperabilidade entre os agentes. No entanto, os humanos tendem a ser relutantes em aceitar a conceptualização de outros, a não ser que sejam convencidos de que poderão conseguir um bom negócio. Neste contexto, a aplicação e exploração de relações capturadas em redes sociais pode resultar no estabelecimento de relações de confiança entre vendedores e consumidores, e ao mesmo tempo, conduzir a um aumento da eficiência da negociação e consequentemente na satisfação das partes envolvidas. O sistema AEMOS é uma plataforma de comércio eletrónico baseada em agentes que inclui serviços de ontologias, mais especificamente, serviços de alinhamento de ontologias, incluindo a recomendação de possíveis alinhamentos entre as ontologias dos parceiros de negociação. Este sistema inclui também uma componente baseada numa rede social, que é construída aplicando técnicas de análise de redes socias sobre informação recolhida pelo mercado, e que permite melhorar a recomendação de alinhamentos e auxiliar os agentes na sua escolha. Neste trabalho são apresentados o desenvolvimento e implementação do sistema AEMOS, mais concretamente: • É proposto um novo modelo para comércio eletrónico baseado em agentes que disponibiliza serviços de ontologias; • Adicionalmente propõem-se o uso de redes sociais emergentes para captar e explorar informação sobre relações entre os diferentes parceiros de negócio; • É definida e implementada uma componente de serviços de ontologias que é capaz de: • o Sugerir alinhamentos entre ontologias para pares de agentes; • o Traduzir mensagens escritas de acordo com uma ontologia em mensagens escritas de acordo com outra, utilizando alinhamentos previamente aprovados; • o Melhorar os seus próprios serviços recorrendo às funcionalidades disponibilizadas pela componente de redes sociais; • É definida e implementada uma componente de redes sociais que: • o É capaz de construir e gerir um grafo de relações de proximidade entre agentes, e de relações de adequação de alinhamentos a agentes, tendo em conta os perfis, comportamento e interação dos agentes, bem como a cobertura e utilização dos alinhamentos; • o Explora e adapta técnicas e algoritmos de análise de redes sociais às várias fases dos processos do mercado eletrónico. A implementação e experimentação do modelo proposto demonstra como a colaboração entre os diferentes agentes pode ser vantajosa na melhoria do desempenho do sistema e como a inclusão e combinação de serviços de ontologias e redes sociais se reflete na eficiência da negociação de transações e na dinâmica do mercado como um todo.