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

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

Complexity results for some classes of strategic games

Game theory is a branch of applied mathematics studying the interaction of self-interested entities, so-called agents. Its central objects of study are games, mathematical models of real-world interaction, and solution concepts that single out certain outcomes of a game that are meaningful in some way. The solutions thus produced can then be viewed both from a descriptive and from a normative perspective. The rise of the Internet as a computational platform where a substantial part of today's strategic interaction takes place has spurred additional interest in game theory as an analytical tool, and has brought it to the attention of a wider audience in computer science. An important aspect of real-world decision-making, and one that has received only little attention in the early days of game theory, is that agents may be subject to resource constraints. The young field of algorithmic game theory has set out to address this shortcoming using techniques from computer science, and in particular from computational complexity theory. One of the defining problems of algorithmic game theory concerns the computation of solution concepts. Finding a Nash equilibrium, for example, i.e., an outcome where no single agent can gain by changing his strategy, was considered one of the most important problems on the boundary of P, the complexity class commonly associated with efficient computation, until it was recently shown complete for the class PPAD. This rather negative result for general games has not settled the question, however, but immediately raises several new ones: First, can Nash equilibria be approximated, i.e., is it possible to efficiently find a solution such that the potential gain from a unilateral deviation is small? Second, are there interesting classes of games that do allow for an exact solution to be computed efficiently? Third, are there alternative solution concepts that are computationally tractable, and how does the value of solutions selected by these concepts compare to those selected by established solution concepts? The work reported in this thesis is part of the effort to answer the latter two questions. We study the complexity of well-known solution concepts, like Nash equilibrium and iterated dominance, in various classes of games that are both natural and practically relevant: ranking games, where outcomes are rankings of the players; anonymous games, where players do not distinguish between the other players in the game; and graphical games, where the well-being of any particular player depends only on the actions of a small group other players. In ranking games, we further compare the payoffs obtainable in Nash equilibrium outcomes with those of alternative solution concepts that are easy to compute. We finally study, in general games, solution concepts that try to remedy some of the shortcomings associated with Nash equilibrium, like the need for randomization to achieve a stable outcome

A game theoretic approach to coordinating unmanned aerial vehicles with communications payloads

This thesis considers the placement of two or more Unmanned Aerial Vehicles (UAVs) to provide communications to a community of ground mobiles. The locations for the UAVs are decided by the outcome of a non-cooperative game in which the UAVs compete to maximize their coverage of the mobiles. The game allows navigation decisions to be made onboard the UAVs with the effect of increasing coverage, reducing the need for a central planning function, and increasing the autonomy of the UAVs. A non-cooperative game that includes the key system elements is defined and simulated. The thesis compares methods for solving the game to evaluate their performance. A conflict between the quality of the solution and the time required to obtain that solution is identified and explored. It considers how the payload calculations could be used to modify the behaviour of the UAVs, and the sensitivity of the game to resource limitations such as RF power and radio spectrum. It finishes by addressing how the game could be scaled from two UAVs to many UAVs, and the constraints imposed by current methods for solving games

Radio Resource Allocation in Wireless OFDM Systems

Ph.DDOCTOR OF PHILOSOPH

A Method For Sustainable Development In A River Basin: Game Theory

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2005Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2005Bu çalışmada, oyun teorisi, havza planlamada stratejik karar verme sürecinin analizinde kullanılmaktadır. Bir nehir havzasında yer alan Büyükşehir Belediyesi ve küçük ölçekli bir sanayi yatırımcısı arasındaki stratejik karar verme süreci modellenmiştir. Mevcut durumu (Oyun I) ve ideal durumu (Oyun II) gösteren iki ödeme matriksi oluşturulmuştur. Birinci oyunda oyuncular çevre maliyetlerini dikkate almadan karar verirlerken, ikinci oyunda oyuncular çevre mevzuatını ve çevre maliyetlerini dikkate alarak hareket ederler. Oyunlar; iki kişili, oyuncular arasında işbirliğinin olmadığı, sıfır toplamlı olmayan, sonlu oyunlardır. Her iki oyunda da oyuncular için en iyi strateji çiftini gösteren Nash dengesi araştırılmıştır. Büyükşehir Belediyesi sanayinin aşağı havzada organize sanayi bölgelerinde geliştirilmesini istemektedir, ancak birinci oyunda sanayici yukarı havzada sanayi alanlarının dışında yer seçer. Çevre maliyetlerinin dikkate alındığı ikinci oyunda ise, Nash dengelerine göre, sanayici Büyükşehir Belediyesi içerisinde altyapısı tamamlanmış bir organize sanayi bölgesini seçmektedir. Sonuç olarak, ikinci oyunda her iki oyuncunun da gelirleri artmakta ve aynı zamanda çevre korunabilmektedir.In this study, Game Theory is used to analyze strategic decision making process for river basin planning. The strategic decision making process is modeled between the Metropolitan Municipality and a small industrial enterprise in a watershed. Two situations are represented by two payoff matrices; the present situation (Game I) and the ideal situation (Game II). In Game I, players make decisions without considering environmental costs whereas players act with consideration of environmental legislation and costs in Game II. These games are two-person, non-cooperative, non zero-sum and finite games. Nash equilibrium, which demonstrates the best strategy pairs for players, is explored for both games. The Metropolitan Municipality would like to develop industries in organized industrial districts in down-stream areas. However, in the first game, industrial enterprise prefers to locate outside industrial areas in up-stream. In the second game, according to Nash equilibriums, industrial enterprise prefers to locate in the organized industrial districts of the Metropolitan Municipality where the infrastructures are completed. In conclusion, players increase their payoffs and protection of environment is possible in the second game.DoktoraPh