The Language of Game Theory

Author: Adam Brandenburger
Publisher: World Scientific
ISBN: 981451344X
Format: PDF, ePub
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This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make how players reason about a game a central feature of the theory. The program OCo now called epistemic game theory OCo extends the classical definition of a game model to include not only the game matrix or game tree, but also a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determine the implications of how players reason for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior. Sample Chapter(s). Foreword (39 KB). Introduction (132 KB). Chapter 1: An Impossibility Theorem on Beliefs in Games (299 KB). Contents: An Impossibility Theorem on Beliefs in Games (Adam Brandenburger and H Jerome Keisler); Hierarchies of Beliefs and Common Knowledge (Adam Brandenburger and Eddie Dekel); Rationalizability and Correlated Equilibria (Adam Brandenburger and Eddie Dekel); Intrinsic Correlation in Games (Adam Brandenburger and Amanda Friedenberg); Epistemic Conditions for Nash Equilibrium (Robert Aumann and Adam Brandenburger); Lexicographic Probabilities and Choice Under Uncertainty (Lawrence Blume, Adam Brandenburger, and Eddie Dekel); Admissibility in Games (Adam Brandenburger, Amanda Friedenberg and H Jerome Keisler); Self-Admissible Sets (Adam Brandenburger and Amanda Friedenberg). Readership: Graduate students and researchers in the fields of game theory, theoretical computer science, mathematical logic and social neuroscience."

The Language of Game Theory

Author: Adam Brandenburger
Publisher: World Scientific
ISBN: 9814513458
Format: PDF, Docs
Download Now
This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make how players reason about a game a central feature of the theory. The program — now called epistemic game theory — extends the classical definition of a game model to include not only the game matrix or game tree, but also a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determine the implications of how players reason for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior. Contents:An Impossibility Theorem on Beliefs in Games (Adam Brandenburger and H Jerome Keisler)Hierarchies of Beliefs and Common Knowledge (Adam Brandenburger and Eddie Dekel)Rationalizability and Correlated Equilibria (Adam Brandenburger and Eddie Dekel)Intrinsic Correlation in Games (Adam Brandenburger and Amanda Friedenberg)Epistemic Conditions for Nash Equilibrium (Robert Aumann and Adam Brandenburger)Lexicographic Probabilities and Choice Under Uncertainty (Lawrence Blume, Adam Brandenburger, and Eddie Dekel)Admissibility in Games (Adam Brandenburger, Amanda Friedenberg and H Jerome Keisler)Self-Admissible Sets (Adam Brandenburger and Amanda Friedenberg) Readership: Graduate students and researchers in the fields of game theory, theoretical computer science, mathematical logic and social neuroscience. Keywords:Game Theory;Epistemic Game Theory;Foundations;Applied Mathematics;Social Neuroscience;Rationalizability;Nash Equilibrium;Probability;UncertaintyKey Features:Focuses on epistemic game theory — an emerging approach to game theoryLikely strong interest in these tools from other disciplines, includingtheoretical computer science, mathematical logic, and social neuroscienceProminent co-author team: Robert Aumann (Hebrew University, Nobel Laureate 2005); Lawrence Blume (Cornell University); Eddie Dekel (Northwestern University and Tel Aviv University); Amanda Freedeneurg (Arizona State University); H Jerome Keisler (University of Wisconsin Madison)Reviews: "Adam Brandenburger's work on the knowledge requirements implicit in game theory has become classic. These are of profound importance in understanding the relevance of game theory and, indeed, economic theory in general to the real economy. It is very good to have them collected, with an introduction that brings out the underlying themes." Kenneth J Arrow Stanford University, USA "Over the past decade epistemic game theory has emerged as one of the principled alternatives to more traditional approaches to economic interactions and Adam Brandenburger has played a central role in that emergence. For anyone interested in epistemic game theory, or game theory in general, this book is a must have. But even more important is the opportunity this volume, and epistemic game theory in general, presents to empirical scientists. As Brandenburger notes in his Introduction, until now epistemic game theory has been a theoretical discipline. This volume should make it clear, however, that it could be — and likely soon will be — an empirical undertaking. Anyone interested in behavioral, psychological, or neurobiological studies of how we make decisions during strategic play will find in this volume a profoundly fascinating set of empirically testable hypotheses just waiting to be examined." Paul Glimcher New York University, USA "Three hundred years ago, Francis Waldegrave found the first minimax solution of a matrix game. But in his correspondence with mathematicians Pierre Rémond de Montmort and Nicolaus Bernoulli, Waldegrave counseled that epistemic considerations involving knowledge, beliefs, uncertainty, and incomplete information also mattered. The principal practitioners of game theory, with the notable exceptions of John Harsanyi and Robert Aumann, have ignored this advice. In recent years, these two theorists have been joined by Adam Brandenburger, whose work on epistemic game theory has been collected in this splendid volume. Eight classic papers by Brandenburger with a number of co-authors present an authoritative view of the field while an insightful introduction provides a roadmap to research both present and future." Harold W Kuhn Princeton University, USA "This book features a collection of foundational papers by Adam Brandenburger in epistemic game theory. Though still evolving, this approach marks a tectonic shift in game theory by offering a new, epistemic dimension which might be compared to the introduction of synchronized sound to motion pictures in the early 20th century: it might not immediately provide a complete picture, but it has the potential of changing the field forever." Sergei N Artemov The Graduate Center of the City University of New York, USA "Adam Brandenburger has played a leading role in developing the program of epistemic game theory, the goal of which is to provide a deeper and clearer foundation for game theory as a whole. This volume collects a remarkable body of work by Brandenburger and his collaborators, in which penetrating conceptual analysis and the development of a rich mathematical theory go hand in hand. The work offers much of great interest to computer scientists, who will see many connections with their study of recursive and corecursive structures, of processes and their logics, and of multi-agent systems; and to mathematicians and logicians interested in making precise models of the reflexive structures inherent in systems containing rational agents who can reason about the system of which they form a part. I hope that this timely collection will help to stimulate cross-disciplinary work on these fundamental topics." Samson Abramsky Oxford University, UK "Games are playgrounds where players meet and interact, guided by streams of information and opinion. Adam Brandenburger's work has been instrumental in creating a new rich epistemic framework doing justice to both games and their players. This timely book will help a broader audience learn and appreciate the resulting theory." Johan van Benthem University of Amsterdam, The Netherlands and Stanford University, USA "Economics, so grounded in the notion of equilibrium, has required substantial foundational work on reasoning about reasoning — epistemics — in interacting situations (games). Yet, if plain reasoning is difficult enough, just imagine epistemics. Adam Brandenburger, as is evident from the elegant and clear chapters of this book, is a master of the trade. His highly regarded research, always subtle and deep, is of the kind that establishes milestones while at the same time opening up vistas to new, and unexpected, frontiers. This book is specialized, certainly, but it is a must." Andreu Mas-Colell Universitat Pompeu Fabra, Spain “The papers in this book had a huge impact on the field, created an inter– and multi–discipliner research within the intersection of economics, philosophy, mathematics and computer science, and also inspired countless amount of PhD dissertations. Brandenburger's work contains very precise and beautiful mathematics, an earthly reading of epistemics and a puzzling innovation.” Zentralblatt MATH

Pareto Nash Stackelberg Game and Control Theory

Author: Valeriu Ungureanu
Publisher: Springer
ISBN: 3319751514
Format: PDF, ePub
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This book presents a comprehensive new, multi-objective and integrative view on traditional game and control theories. Consisting of 15 chapters, it is divided into three parts covering noncooperative games; mixtures of simultaneous and sequential multi-objective games; and multi-agent control of Pareto-Nash-Stackelberg-type games respectively. Can multicriteria optimization, game theory and optimal control be integrated into a unique theory? Are there mathematical models and solution concepts that could constitute the basis of a new paradigm? Is there a common approach and method to solve emerging problems? The book addresses these and other related questions and problems to create the foundation for the Pareto-Nash-Stackelberg Game and Control Theory. It considers a series of simultaneous/Nash and sequential/Stackelberg games, single-criterion and multicriteria/Pareto games, combining Nash and Stackelberg game concepts and Pareto optimization, as well as a range of notions related to system control. In addition, it considers the problems of finding and representing the entire set of solutions. Intended for researches, professors, specialists, and students in the areas of game theory, operational research, applied mathematics, economics, computer science and engineering, it also serves as a textbook for various courses in these fields.

Uncertainty Within Economic Models

Author: Hansen Lars Peter
Publisher: World Scientific
ISBN: 9814578134
Format: PDF, ePub, Mobi
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Written by Lars Peter Hansen (Nobel Laureate in Economics, 2013) and Thomas Sargent (Nobel Laureate in Economics, 2011), Uncertainty within Economic Models includes articles adapting and applying robust control theory to problems in economics and finance. This book extends rational expectations models by including agents who doubt their models and adopt precautionary decisions designed to protect themselves from adverse consequences of model misspecification. This behavior has consequences for what are ordinarily interpreted as market prices of risk, but big parts of which should actually be interpreted as market prices of model uncertainty. The chapters discuss ways of calibrating agents' fears of model misspecification in quantitative contexts.

Models of Bounded Rationality and Mechanism Design

Author: Jacob Glazer
Publisher: World Scientific Publishing Company
ISBN: 9813141336
Format: PDF, ePub, Mobi
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This book brings together the authors' joint papers from over a period of more than twenty years. The collection includes seven papers, each of which presents a novel and rigorous model in Economic Theory. All of the models are within the domain of implementation and mechanism design theories. These theories attempt to explain how incentive schemes and organizations can be designed with the goal of inducing agents to behave according to the designer's (principal's) objectives. Most of the literature assumes that agents are fully rational. In contrast, the authors inject into each model an element which conflicts with the standard notion of full rationality, demonstrating how such elements can dramatically change the mechanism design problem. Although all of the models presented in this volume touch on mechanism design issues, it is the formal modeling of bounded rationality that the authors are most interested in. A model of bounded rationality signifies a model that contains a procedural element of reasoning that is not consistent with full rationality. Rather than looking for a canonical model of bounded rationality, the articles introduce a variety of modeling devices that will capture procedural elements not previously considered, and which alter the analysis of the model. The book is a journey into the modeling of bounded rationality. It is a collection of modeling ideas rather than a general alternative theory of implementation.

Epistemic Game Theory

Author: Andrés Perea
Publisher: Cambridge University Press
ISBN: 1107008913
Format: PDF, ePub, Mobi
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The first textbook to explain the principles of epistemic game theory.

The Economy As an Evolving Complex System III

Author: Lawrence E. Blume
Publisher: Oxford University Press
ISBN: 9780195162592
Format: PDF, ePub
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Derived from the 2001 Santa Fe Institute Conference, "The Economy as an Evolving Complex System III" addresses a wide variety of issues in the fields of economics and complexity, accessing eclectic techniques from many disciplines, provided that they shed light on the economic problem. The subject, a perennial centerpiece of the SFI program of studies, has gained a wide range of followers for its methods of employing empirical evidence in the development of analytical economic theories.

Discourses on Social Software

Author: Jan van Eijck
Publisher: Amsterdam University Press
ISBN: 9089641238
Format: PDF, ePub
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The unusual format of a series of discussions among a logician, a computer scientist, a philosopher and some researchers from other disciplines encourages the reader to develop his own point of view. --Book Jacket.

The Structure of Scientific Revolutions

Author: Thomas S. Kuhn
Publisher: University of Chicago Press
ISBN: 0226458148
Format: PDF, ePub, Mobi
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A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were—and still are. The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach. With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context. Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.

New Perspectives on Games and Interaction

Author: Krzysztof R. Apt
Publisher: Amsterdam University Press
ISBN: 9089640576
Format: PDF
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This volume is a collection of papers presented at the 2007 colloquium on new perspectives on games and interaction at the Royal Dutch Academy of Sciences in Amsterdam.