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

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

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

Labor Differentiation and Agglomeration in General Equilibrium

The aim of this paper is to explore the structure of cities as a function of labor differentiation, gains to trade, a fixed cost for constructing the transportation network, a variable cost of commodity transport, and the commuting costs of consumers. Firms use different types of labor to produce different outputs. Locations of all agents are endogenous as are prices and quantities. To our knowledege, this is the first paper that applies smooth economy techniques to urban economics. Existence of equilibrium and its determinacy properties depend crucially on the relative numbers of outputs, types of labor and firms. More differentiated labor implies more equilibria. We provide tight lower bounds on labor differentiation for existence of equilibrium. If these sufficient conditions are satisfied, then generically there is a continuum of equilibria for given parameter values. Finally, an equilibrium allocation is not necessarily Pareto optimal in this model.city structure, heterogeneous labor, transportation network, general equilibrium

Labor differentiation and agglomeration in general equilibrium

The aim of this paper is to explore the structure of cities as a function of labor differentiation, gains to trade, a fixed cost for constructing the transportation network, a variable cost of commodity transport, and the commuting costs of consumers. Firms use different types of labor to produce different outputs. Locations of all agents are endogenous as are prices and quantities. This is among the first papers to apply smooth economy techniques to urban economics. Existence of equilibrium and its determinacy properties depend crucially on the relative numbers of outputs, types of labor and firms. More differentiated labor implies more equilibria. We provide tight lower bounds on labor differentiation for existence of equilibrium. If these sufficient conditions are satisfied, then generically there is a continuum of equilibria for given parameter values. Finally, an equilibrium allocation is not necessarily Pareto optimal in this model.city structure; heterogeneous labor; transportation network; general equilibrium

Global Analysis of an Expectations Augmented Evolutionary Dynamics

We consider a deterministic evolutionary model where players form expectations about future play. Players are not fully rational and have expectations that change over time in response to current payoffs and feedback from the past. We provide a complete characterization of the qualitative dynamics so induced for a two strategies population game,and relate our findings to standard evolutionary dynamics and equilibrium selection when agents have rational forward looking expectationsevolutionary games; dynamic systems; bounded rationality

Global Analysis of an Expectations Augmented Evolutionary Dynamics

We consider a deterministic evolutionary model where players form expectations about future play. Players are not fully rational and have expectations that change over time in response to current payoffs and feedback from the past. We provide a complete characterization of the qualitative dynamics so induced for a two strategies population game, and relate our findings to standard evolutionary dynamics and equilibrium selection when agents have rational forward looking expectations.evolutionary games, dynamic systems, bounded rationality

The Power of Sunspots: An Experimental Analysis

We present an experiment in which extrinsic information (signals) may generate sunspot equilibria. The underlying coordination game has a unique symmetric non-sunspot equilibrium, which is also risk-dominant. Other equilibria can be ordered according to risk dominance. We compare treatments with different salient, but extrinsic signals. By increasing the precision of private signals, we manipulate the available public information, which allows us to measure the force of extrinsic signals. We also vary the number of signals and combine public and private signals, allowing us to see how subjects aggregate available (and possibly irrelevant) information. Results indicate that sunspot equilibria emerge naturally if there are salient (but extrinsic) public signals. However, salient private signals of high precision may also cause sunspot-driven behavior, even though this is no equilibrium. The higher the precision of signals and the easier they can be aggregated, the more powerful they are in dragging behavior away from the risk-dominant to risk-dominated strategies. Sunspot-driven behavior may lead to welfare losses and exert negative externalities on agents, who do not receive extrinsic signals.coordination games, strategic uncertainty, sunspot equilibria, irrelevant information

Stability, Specialization and Social Recognition

Yang s theory of economic specialization under increasing returns to scale (Yang 2001) is a formal development of the fundamental Smith-Young theorem on the extent of the market and the social division of labor.In this theory specialization and, thus, the social division of labor is firmly embedded within a system of perfectly competitive markets.This leaves unresolved whether and how such development processes are possible in economies based on more primitive, nonmarket organizations.In this paper we introduce a general relational model of economic interaction.Within this non-market environment we discuss the emergence of economic specialization and ultimately of economic trade and a social division of labor.We base our approach on three stages in organizational development: the presence of a stable relational structure; the presence of relational trust and subjective specialization; and, finally, the emergence of objective specialization through the social recognition of subjectively defined economic rolesnetworks;stability;social division of labor;specialization

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure