Generic Finiteness of Outcome Distributions for Two Person Game Forms with Three Outcomes

Generic finiteness; game forms; Nash equilibrium

Generic Determinacy of Nash Equilibrium in Network Formation Games

This paper shows that the set of probability distributions over networks induced by Nash equilibria of the network formation game proposed by Myerson (1991) is finite for a generic assignment of payoffs to networks. The same result can be extended to several variations of the game found in the literature.Networks; generic finiteness; Nash Equilibrium

Bayesian and Consistent Assessments

In a Bayesian assessment beliefs are computed from the strategy profile following Bayes’ rule at positive probability information sets and for every subgame. We characterize the set of extensive-forms (extensive-form games without a payoff assignment) for which the sets of Bayesian assessments and consistent assessments coincide. In doing so we disentangle the different restrictions imposed by consistency across information sets.Backwards induction; Bayesian assessments; Consistent assessments; Sequential equilibrium; Extensive-forms

Undominated (and) perfect equilibria in Poisson games

In games with population uncertainty some perfect equilibria are in dominated strategies. We prove that every Poisson game has at least one perfect equilibrium in undominated strategies

Costly Network Formation and Regular Equilibria

We prove that for generic network-formation games where players incur some strictly positive cost to propose links the number of Nash equilibria is finite. Furthermore all Nash equilibria are regular and, therefore, stable sets.Network-formation games; Regular equilibrium; Stable sets

On the equivalence between subgame perfection and sequentiality

We identify the maximal set of finite extensive forms for which the sets of subgame perfect and sequential equilibrium strategies coincide for any possible assignment of the payoff function. We also identify the maximal set of finite extensive forms for which the outcomes induced by the two solution concepts coincide

On the equivalence between subgame perfection and sequentiality.

We identify the maximal set of finite extensive forms for which the sets of subgame perfect and sequential equilibrium strategies coincide for any possible assignment of the payoff function. We also identify the maximal set of finite extensive forms for which the outcomes induced by the two solution concepts coincide.

Three essays on game theory

The main text of this thesis is divided into three chapters. The three papers are contributions to the literature on equilibrium refinements in noncooperative game theory. Each chapter can be read independently of the rest. Chapter 2 characterizes the class of finite extensive forms for which the sets of Subgame Perfect and Sequential equilibrium strategy profiles coincide for any possible payoff function. In addition, it identifies the class of finite extensive forms for which the outcomes induced by these two solution concepts coincide, and study the implications of our results for perfect Bayesian equilibrium. Chapter 3 shows that in games with population uncertainty some perfect equilibria are in dominated strategies. It is proved that every Poisson game has at least one perfect equilibrium in undominated strategies. Chapter 4 shows that the set of probability distributions over networks induced by Nash equilibria of the network formation game proposed by Myerson (1991) is finite for a generic assignment of payoffs to networks. The same result can be extended to several variations of the game found in the literature. ____________________________________________________________________________________________________El texto de esta tesis está dividido en tres capítulos. Cada uno de ellos es una contribución a la literatura de los refinamientos de equilibrio en juegos no cooperativos. Cada capítulo se puede leer de manera independiente. El capítulo 2 caracteriza la clase de formas extensivas finitas para las que los conjuntos de estrategias de equilibrio para el equilibrio perfecto en subjuegos y el equilibrio secuencial coinciden para cualquier función de pagos. Además, identifica la clase de formas extensivas finitas para las que los conjuntos de resultados derivados de ambos conceptos de equilibrio coinciden, y estudia las implicaciones que estos resultados tienen en cuanto al equilibrio perfecto en subjuegos. El capítulo 3 muestra que en juegos con incertidumbre acerca del número de jugadores algunos equilibrios perfectos pueden estar dominados y demostramos que todo juego de Poisson tiene al menos un equilibrio perfecto en estrategias no dominadas. El capítulo 4 se demuestra que el conjunto de distribuciones de probabilidad sobre redes inducidas por equilibrios de Nash del juego de formación de redes propuesto por Myerson (1991) es finito para toda asignación genérica de pagos a redes. Este mismo resultado se puede extender a varias versiones del juego que se pueden encontrar en la literatura

Design and Analysis of a Wave Energy Converter of Point Absorber Type for the Energy Extraction from the Waves

The generation of electric power from ocean waves has been in constant technological growth during the last decades, for being a clean source of abundant and renewable energy. However, the existing systems are extensive in size and cost. Thus, in this thesis, a design methodology for the construction of a wave energy prototype is developed. The proposed device is a slider-crank mechanism connected to a spherical buoy. The buoy, situated on the surface of the water, takes advantage of the vertical movement of the waves converting their oscillation movement into a rotational motion that actuates over the shaft of the armature coils within the generator to obtain electric power. The design of the mechanical components was conducted by the application of the principle of Virtual Work and D'Alembert, which allowed the determination of the dynamical model of the system; then, using these results, the mass and inertia of each element were obtained by an optimization procedure using the Optimization Toolbox of Matlab. Lastly, the results of the mathematical model were validated by experimentation in a scaled prototype of the dispositive.MaestríaMagister en Ingeniería Eléctric

Poisson.Cournot Games

We construct a Cournot model with uncertainty in the number of firms in the industry. We model such an uncertainty as a Poisson game and characterize the set of equilibria after deriving novel properties of the Poisson distribution. When marginal costs are zero, the number of equilibria increases with the expected number of firms (n) and for n ≥ 3 every equilibrium exhibits overproduction relative to the model with deterministic population size. For a fixed n, overproduction is robust to sufficiently small marginal costs. The set of equilibria can be Pareto ranked. If n ≥ 3, even the expected consumer surplus induced by the lowest quantity equilibrium is larger than the consumer surplus in the model without population uncertainty