Equilibria of nonatomic anonymous games

We define a new notion of equilibrium for nonatomic anonymous games, termed epsilon-estimated equilibrium, and prove its existence for any positive s. This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk-Nash. This augmented scope is our main motivation. Our approach also resolves some conceptual problems present in Schmeidler (1973) pointed out by Shapley

Market inconsistencies of the market-consistent European life insurance economic valuations: pitfalls and practical solutions

International audienceThe Solvency II directive has introduced a specific so-called risk-neutral framework to valuate economic accounting quantities throughout European life insurance companies. The adaptation of this theoretical notion for regulatory purposes requires the addition of a specific criterion, namely the market-consistency, in order to objectify the choice of the valuation probability measure. This paper aims at pointing out and fixing some of the major risk sources embedded in the current regulatory life insurance valuation scheme. We compare actuarial and financial valuation schemes. We then address first operational issues and potential market manipulation sources in life insurance, induced by both theoretical and regulatory pitfalls. For example, we show that calibrating the interest rate model in October 2014 instead of December 31 st 2014 generates a 140%-increase in the economic own funds of a representative French life insurance company. We propose various adaptations of the current implementations, including product-specific valuation scheme, to limit the impact of these market-inconsistencies

Essays on two-sided matching and mechanism design

En esta Disertación Doctoral se analizan problemas económicos en la intersección de las áreas de la Teoría de los Juegos, los Problemas de Emparejamiento y el Diseño de Mecanismos. En particular, he trabajado en el análisis de problemas de emparejamiento en esquemas descentralizados tales como Mercados de Trabajo, Problemas de Admisiones a la Universidad y Problemas Generales de emparejamiento. Recientemente, la investigación sobre estos problemas ha ganado un importante impulso, tanto teórica como empíricamente, debido al estudio de problemas cruciales que no ‘pueden ser analizados bajo los paradigmas clásicos de oferta y demanda. En mi disertación analizo dos problemas principales. Por un lado, hago un análisis de equilibrio de mecanismos descentralizados de emparejamiento con agentes que tomas sus decisiones estratégicamente. Por otro lado, también analizo el problema clásico de emparejamiento en presencia de externalidades, es decir, problemas de emparejamiento donde las preferencias de los agentes dependen de todos los emparejamientos factibles entre agentes y no solo del conjunto de potenciales parejas en un lado opuesto del mercado. Esta disertación se compone de los siguientes tres capítulos, que en sí mismos constituyen contribuciones independientes en esta área de la economía. En el primer capítulo, titulado Incomplete Information and Costly Signaling in College Admissions, analizo el problema de admisión a las universidades con información incompleta acerca de las habilidades de los estudiantes. En este modelo considero, que universidades con calidades observables y estudiantes con información privada se emparejan de acuerdo con un mecanismo descentralizado donde los estudiantes pueden señalizar sus habilidades con señales que son costosas. Bajo estas condiciones, caracterizo un equilibrio simétrico separador del juego inducido por este mecanismo en el cual se maximiza el número de emparejamientos y los mejores estudiantes se matriculan en las mejores universidades. Esta caracterización del equilibrio permite realizar diversos ejercicios de estática comparativa, en ellos se muestra que el cambio de diversos parámetros del modelo afecta asimétricamente a los estudiantes. Por ejemplo, un incremento en el número de estudiantes lleva a que aquellos de baja cualificación reduzcan su inversión en señalización, mientras los de alta cualificación podrían aumentarla. Se observan patrones similares cuando los estudiantes enfrentan un incremento en el número de plazas escolares o un incremento en las calidades de las universidades. Finalmente, se analizan las ganancias del proceso de señalización comparando los pagos de equilibrio de este juego con uno en el que no hay señalización. Entre otros resultados, encuentro que bajo ciertas distribuciones de las habilidades de los estudiantes, una demanda suficientemente alta por las plazas de las universidades llevaría a todos los colegios a tener ganancias positivas. En el segundo capítulo, titulado Many-to-one Matching: externalities and Stability, se analiza la existencia de asignaciones estables en problemas de emparejamiento con externalidades. En este problema, los agentes no solo toman en cuenta sus parejas sino también las parejas de los demás agentes para determinar sus preferencias. Es decir, el emparejamiento de los demás afecta la valoración que yo tengo de mi propio emparejamiento. Una vez que estas externalidades se toman en cuenta, los agentes forman expectativas sobre el conjunto de emparejamientos que ellos consideran admisibles, dichas predicciones son llamadas estimation functions. Dado un conjunto de estimation functions j, un emparejamiento es j-stable si este es admisible para todos los agentes y no es bloqueado por ninguna coalición. Un primer resultado muestra que los emparejamientos j-stables podrían no existir. Aun más, se muestra que ningún conjunto de estimation functions puede asegurar la existencia de emparejamientosj-stable. Además se muestra que un emparejamiento j-stable puede existir, en el caso en el que todos los emparejamientos sean considerados admisibles por todos los agentes, bajo una restrición de las preferencias de los agentes llamada bottom q-substitutability. Finalmente, se analiza también una noción del core en esta clase de problemas de emparejamiento con externalidades llamado el j-core. Se demuestra que el j-core y el conjunto de emparejamientos j-stables siempre coinciden independientemente del conjunto de estimation functions j. Finalmente, en el tercer capítulo, titulado A Simple Decentralized Matching Mechanism in Markets with Couples, se analiza un mecanismo descentralizado de emparejamiento muy simple llamado One Application Mechanism. Bajo este mecanismo, se puede sostener en Equilibrio perfecto en Subjuego (SPE) cualquier emparejamiento estable del mercado. Sin embargo, se encuentra que también es posible sostener emparejamiento inestables en este tipo de equilibrio. Se muestra que solo un tipo muy especial de inestabillidad es admisible en SPE, se argumenta que esta inestabilidad tiene su origen en fallas de coordinación entre los miembros de una pareja. En mi principal resultado, se muestra que el One Application Mechanism implementa en SPE el conjunto de emparejamientos (pairwise) estables de mercados de emparejamiento con parejas. . .This dissertation involves the analysis of economic problems in the intersection of the fields of Game theory, Two-sided Matching and Mechanism Design. In particular, I work on decentralized two-sided matching problems such as job markets, college admissions, marriage problems, etc. In recent years, these economic problems have become crucial, both theoretically and empirically, since there are many important real-world markets where the traditional supply-demand paradigm cannot be applied. My disertation includes the analysis of two main problems. On the one hand, I consider the equilibrium analysis of decentralized matching mechanisms with strategic decision makers. On the other hand, I also analyze two-sided matching problems with externalities where agents’ preferences depend on the complete assignment between workers and firms, students and colleges, etc. and not only on the set of agents on the opposite side of the market. The dissertation consists of the following three chapters that constitute independent contributions in this area. In the first chapter, entitled Incomplete Information and Costly Signaling in College Admissions, I analyze a problem of college admissions with incomplete information about student skills. Colleges with observable qualities and students with private information are matched according to a decentralized mechanism where students can signal their abilities with costly observable signals. I characterize a separating symmetric equilibrium of this game where the number of potential matches is maximized and the best students enroll at the best colleges. My closed form characterization allows to conduct meaningful comparative statics analyses. I show that the effect of a change in the underlying parameters of the model is not symmetric across students. For instance, an increase in the number of students leads the low skilled students to decrease the investment in signaling while the high skilled applicants may increase it. Similar patterns arise when students face a change in the number of school places or college qualities. Finally, I analyze the gains of the signaling process by comparing equilibrium payoffs between this separating equilibrium and a pooling equilibrium with no signaling. Among other results, I show that under certain distributions of the student skills, a large enough demand for school places leads all colleges to get positive gains. In the second chapter, entitled Many-to-one Matching: externalities and Stability, I analyze the existence of stable assignments in matching problems with externalities. In this setting, agents not only care about whom they are matched with but also the partners of the others. Once externalities are considered, agents form expectations on the set of matchings that they consider admissible, such predictions are called estimation functions. Given a set estimation functions j, a matching is j-stable if it is admissible for every agent and not blocked by any coalition. I show that a j-stable matching may not exist. Further, no set of estimation functions assures the existence of j-stable matchings. In the case where all matchings are considered admissible for every agent, a j-stable matching exists under a restriction on agents’ preferences called bottom q-substitutability. Finally, I analyze a notion of the core in matching problems with externalities called the j-core. I find that the j-core and the set of j-stable matchings always coincides for any given set of estimation functions j. Finally, in the third chapter, entitled A Simple Decentralized Matching Mechanism in Markets with Couples, I analyze a simple decentralized matching mechanism called One Application Mechanism. Under this mechanism any stable matching of the market can be achieved in Subgame Perfect Equilibrium (SPE). However, I find that the mechanism may achieve also unstable matchings in SPE. I show that only one special kind of instability is admissible in equilibrium. Further, I argue that this instability only comes from coordination failures between members of couples. My main result shows that the One Application Mechanism implements in SPE the set of pairwise stable matchings of markets with couples. .

Notice and the New Deal

The New Deal Supreme Court revised a well-known set of constitutional doctrines. Legal scholarship has principally focused on the changes that occurred in three areas—federalism, delegation, and economic liberty. This Article identifies a new and important fourth element of New Deal constitutionalism: a change in the constitutional doctrine of due process notice, the doctrine that specifies the minimum standards for constitutionally adequate notice of the law. The law of due process notice—which includes the doctrines of vagueness, retroactivity, and the rule of lenity—evolved dramatically over the course of the New Deal to permit lesser clarity and to tolerate more retroactivity. The upshot has been the near-total elimination of successful notice-based challenges other than in the limited context of First Amendment vagueness attacks. Unlike the more famous doctrinal changes of this period, changes to due process notice doctrine were not obviously necessary to accommodate the New Deal legislative agenda, either as a matter of jurisprudence or as a matter of politics. Due process notice doctrine nonetheless underwent a radical transformation in this era, as the Court came to regard its broader shift toward deferring to legislative and executive policy decisions as requiring the relaxation of due process notice doctrine. The link forged between deference and notice had significant functional effects on the most important audience for the Court\u27s notice jurisprudence—Congress. By loosening the strictures of due process notice doctrine, the Court lowered sharply the enactment costs of federal legislation and thereby facilitated its proliferation. This is a distinct, and hitherto unacknowledged, mechanism by which the Court in this period enhanced national power and encouraged the flourishing of the emerging administrative state. Like much of the New Deal settlement, the New Deal reformulation of due process notice doctrine is today the subject of ferment in the courts. Recognizing the New Deal roots of due process notice doctrine is critical for understanding these ongoing judicial debates—and for beginning the conceptual work of mapping the future shape of this vital cluster of doctrines

Neuronal Tissue Deposition of Gadolinium following Single in Vivo Intravenous Exposure of Low Doses Of Gadodiamide In the Brains of Healthy Dogs and Comparison of Single- And Multi-Voxel Spectroscopy in the Normal Canine Brain at 3 Tesla

Proton MR spectroscopy is a tool that provides quantified brain bioprofiles. Two methods exist: single- and multi-voxel spectroscopy. No studies compare their clinical validity in vivo. Gadolinium based MR contrast agents are used to improve lesional conspicuity. Adverse events are reported. Brain deposition occurs following administration in people and murine models. In dogs, doses are anecdotal and deposition is not described. Eight normal dogs underwent MRI at 3 Tesla with two methods of spectroscopy and were administered varying doses of gadodiamide. No differences were seen between single- and multi-voxel spectroscopy when interrogating identical regions of interest. Brains were harvested and evaluated for gadolinium depots using inductively coupled plasma mass spectrometry. Gadolinium was found in the brains of all dogs with dose dependency. Further, adequate normal brain conspicuity was seen at a dose of 0.5 mmol/kg. Thus, clinical trials of gadolinium chelated contrast agents at this dose are recommended