A Newton Collocation Method for Solving Dynamic Bargaining Games

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numerical experiments, we successfully implement a globally convergent variant of Broyden's method on a preconditioned version of the collocation equations, and the method economizes on computation cost by more than 50% compared to the value iteration method. We rely on a continuity property of the equilibrium set to obtain increasingly precise approximations of solutions to the continuum model. We showcase these techniques with an illustration of the dynamic core convergence theorem of Duggan and Kalandrakis (2008) in a nine-player, two-dimensional model with negative quadratic preferences.

Discipline Through Disagreement ∗

Abstract. This paper studies politicians who have a present-bias for spending: they want to increase current spending and procrastinate spending cuts. We argue that legislators ’ bias is more severe in economies with low institutional quality. We show that disagreement in legislatures leads to policy persistence and that this attenuates the temptation to overspend. Depending on the environment, legislators ’ decisions to be fiscally responsible may either complement or substitute other legislator’s decisions. In economies with weak institutions, politicians ’ actions are strategic complements. Thus, institutional changes that induce fiscal responsibility are desirable, they generate a positive responsibility multiplier and reduce inefficient spending. However, in economies with better institutions, the same institutional change would induce some legislators to free ride on others ’ responsibility and may lead to more inefficient spending. JEL Classification: D72, H00

Bargaining in standing committees with an endogenous default

Committee voting has mostly been investigated from the perspective of the standard Baron–Ferejohn model of bargaining over the division of a pie, in which bargaining ends as soon as the committee reaches an agreement. In standing committees, however, existing agreements can be amended. This article studies an extension of the Baron–Ferejohn framework to a model with an evolving default that reflects this important feature of policymaking in standing committees: In each of an infinite number of periods, the ongoing default can be amended to a new policy (which is, in turn, the default for the next period). The model provides a number of quite different predictions. (i) From a positive perspective, the key distinction turns on whether the quota is less than unanimity. In that case, patient enough players waste substantial shares of the pie each period and the size principle fails in some pure strategy Markov perfect equilibria. In contrast, the unique Markov perfect equilibrium payoffs in a unanimity committee coincide with those in the corresponding Baron–Ferejohn framework. (ii) If players have heterogeneous discount factors then a large class of subgame perfect equilibria (including all Markov perfect equilibria) are inefficient

Game theory based distributed model predictive control: an approach to large-scale systems control

Los sistemas de gran escala son sistemas conformados por diferentes elementos interactuando entre sí. Cada uno de estos elementos tiene asignado un controlador local encargado de de-cidir las acciones de control locales que deben ser aplicadas con el fin de alcanzar un objetivo. Por lo general, estas acciones son tomadas sin tener en cuenta su efecto en el comportamiento de los demás elementos ni en el desempeño global del sistema. Este comportamiento puede llevar al sistema a puntos de operación indeseables. Con el ´animo de resolver este problema, el control de sistemas de gran escala se ha venido formulando como un problema de optimización con restricciones, siendo el control predictivo basado en modelos la estrategia de control más promisoria para el control de este tipo de sistemas. Sin embargo, debido a que el control predictivo basado en modelos es una estrategia de control basada en optimización, no es posible su aplicación directa a sistemas de gran escala, ya que típicamente el control predictivo se implementa de forma centralizada y esto requiere la transmisión de grandes volúmenes de información y el uso de un alto poder computacional. Por tales motivos, los métodos de control distribuido basados en controladores predictivos surgen como una alternativa para su implementación en sistemas de gran escala. A pesar de los esfuerzos dedicados al diseño de estrategias de control distribuido basadas en control predictivo, la cooperación entre subsistemas sigue siendo un problema de investigación abierto. Con el fin de superar este problema, la teoría de juegos surge como un marco teórico alternativo para formular y caracterizar el problema de control predictivo distribuido. La teoría de juegos es una rama de las matemáticas aplicadas dedicada a identificar patrones de comportamiento en situaciones estratégicas, donde el beneficio percibido por cada uno de los individuos involucrados está determinado tanto por sus decisiones como por las decisiones que toman los demás individuos. En esta tesis, se propone una estrategia de control predictivo distribuida basada en juegos de negociación. Sin entrar en detalles, un juego de negociación es una situación en la que varios individuos deciden, conjuntamente, que estrategia es la mejor para alcanzar un beneficio mutuo. El uso de este tipo de juegos como marco de referencia permite tratar el problema de cooperación entre subsistemas usando control predictivo distribuido. Adicionalmente, este marco de referencia permite formular soluciones para el problema de control distribuido en las que los subsistemas no tienen que resolver más de un problema de optimización, facilitando la reducción de la carga computacional asociada a cada problema de optimización local. En el caso particular de esta tesis, tal solución fue propuesta a partir de una caracterización axiomática. Para esta solución, las condiciones para la estabilidad en lazo cerrado también se discuten./Abstarct. Large-scale systems are systems composed of several interacting components. Each component has a local controller with a local control objective, designed to take local decisions without considering the effect of their local control actions into the whole system performance. This issue may drive the system to undesirable closed-loop performance due to the "competition"\ among controllers. In order to overcome this issue, the control of large-scale systems has been formulated as a constrained optimization problem. In this way, model predictive control schemes have been arising as a promising alternative for controlling large-scale systems. Since model predictive control is an optimization based control scheme its centralized application in large-scale systems may become impractical because it may require the exchange of large amounts of information and the usage of high computational power. Therefore, distributed model predictive control schemes arise as an alternative for the implementation of model predictive control schemes in large-scale systems. Despite of the efforts dedicated to design methods for distributed model predictive control, the cooperation among subsystems still remains as an open research problem. In order to overcome this issue, game theory arises as an alternative to formulate and characterize the distributed model predictive problem. Game theory is a branch of applied mathematics used to capture behaviors in strategic situations where the outcome of a player is function not only of his choices but also depends on the choices of others. In this thesis, a bargaining game based distributed model predictive control scheme is proposed. Roughly speaking, a bargaining game is a situation where several players jointly decide which strategy is best with respect to their mutual benefit. This allows to deal with the cooperation issues of the distributed model predictive control problem. Additionally, the bargaining game framework allows to formulate solutions for the distributed model predictive control problem where the subsystems do not have to solve more than one optimization problem at each time step. This, also allows to reduce the computational burden of the local optimization problems. In the particular case of this thesis, such solution is proposed based on an axiomatic characterization. For the proposed solution, the conditions for the closed-loop stability are also discussed.Doctorad

Three Essays on Exchange Rate Pass-Through.

No abstract availableForeign exchange rates;

Flexibility vs. protection from an unrepresentative legislative majority

We derive the equilibrium institutional design of representative democracy by citizens who first vote on the supermajority required for a new policy to be adopted, and then delegate decision making to a legislature that selects policy given that institutional constraint. A legislature that can freely tailor policy to reflect society’s current preferences is good. However, the views of the median legislator or agenda setter may differ from the median citizen’s, and an unchecked legislature can implement bad policy. We characterize how the primitives describing the preferences of actors and the status quo policy affect the equilibrium degree of legislative flexibility

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal