Foundations of Non-cooperative Game Theory

Foundations of Non-cooperative Game Theory
Author: Klaus Ritzberger
Publisher: Oxford University Press on Demand
Total Pages: 353
Release: 2002
Genre: Business & Economics
ISBN: 9780199247851

This textbook offers a comprehensive overview of the main developments in game theory since the 1950s. It provides a wide variety of examples and exercises, mostly drawn from applications in economics, to illustrate key concepts and ideas in the field. The book should prove an invaluable reference tool for teachers, students, and researchers of microeconomics and game theory.

A Course on Cooperative Game Theory

A Course on Cooperative Game Theory
Author: Satya R. Chakravarty
Publisher: Cambridge University Press
Total Pages: 277
Release: 2015-02-09
Genre: Business & Economics
ISBN: 1107058791

"Deals with real life situations where objectives of the participants are partially cooperative and partially conflicting"--

Noncooperative Game Theory

Noncooperative Game Theory
Author: João P. Hespanha
Publisher: Princeton University Press
Total Pages: 242
Release: 2017-06-13
Genre: Mathematics
ISBN: 0691175217

Noncooperative Game Theory is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. João Hespanha shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to "the game" solve the original design problem? Using the fundamentals of game theory, Hespanha explores these issues and more. The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria—such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, Hespanha examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty—the unforgiving variable that can wreck engineering designs. Hespanha looks at such standard topics as zero-sum, non-zero-sum, and dynamics games and includes a MATLAB guide to coding. Noncooperative Game Theory offers students a fresh way of approaching engineering and computer science applications. An introduction to game theory applications for students of engineering and computer science Materials presented sequentially and in an easy-to-understand fashion Topics explore zero-sum, non-zero-sum, and dynamics games MATLAB commands are included

Foundations of Game Theory

Foundations of Game Theory
Author: Nicolai N. Vorob'ev
Publisher: Birkhäuser
Total Pages: 501
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034885148

The English edition differs only slightly from the Russian original. The main struc tural difference is that all the material on the theory of finite noncooperative games has been collected in Chapter 2, with renumbering of the material of the remain ing chapters. New sections have been added in this chapter: devoted to general questions of equilibrium theory in nondegenerate games, subsections 3.9-3.17, by N.N. Vorob'ev, Jr.; and § 4, by A.G. Chernyakov; and § 5, by N.N. Vorob'ev, Jr., on the computational complexity of the process of finding equilibrium points in finite games. It should also be mentioned that subsections 3.12-3.14 in Chapter 1 were written by E.B. Yanovskaya especially for the Russian edition. The author regrets that the present edition does not reflect the important game-theoretical achievements presented in the splendid monographs by E. van Damme (on the refinement of equilibrium principles for finite games), as well as those by J.e. Harsanyi and R. Selten, and by W. Giith and B. Kalkofen (on equilibrium selection). When the Russian edition was being written, these direc tions in game theory had not yet attained their final form, which appeared only in quite recent monographs; the present author has had to resist the temptation of attempting to produce an elementary exposition of the new theories for the English edition; readers of this edition will find only brief mention of the new material.

Stability and Perfection of Nash Equilibria

Stability and Perfection of Nash Equilibria
Author: Eric van Damme
Publisher: Springer Science & Business Media
Total Pages: 331
Release: 2012-12-06
Genre: Business & Economics
ISBN: 364296978X

The last decade has seen a steady increase in the application of concepts from noncooperative game theory to such diverse fields as economics, political science, law, operations research, biology and social psychology. As a byproduct of this increased activity, there has been a growing awareness of the fact that the basic noncooperative solution concept, that of Nash equilibrium, suffers from severe drawbacks. The two main shortcomings of this concept are the following: (i) In extensive form games, a Nash strategy may prescribe off the equilibrium path behavior that is manifestly irrational. (Specifically, Nash equilibria may involve incredible threats), (ii) Nash equilibria need not be robust with respect to small perturbations in the data of the game. Confronted with the growing evidence to the detriment of the Nash concept, game theorists were prompted to search for more refined equilibrium notions with better properties and they have come up with a wide array of alternative solution concepts. This book surveys the most important refinements that have been introduced. Its objectives are fourfold (i) to illustrate desirable properties as well as drawbacks of the various equilibrium notions by means of simple specific examples, (ii) to study the relationships between the various refinements, (iii) to derive simplifying characterizations, and (iv) to discuss the plausibility of the assumptions underlying the concepts.

On Coordination in Non-Cooperative Game Theory

On Coordination in Non-Cooperative Game Theory
Author: Lauren Larrouy
Publisher: Springer Nature
Total Pages: 355
Release: 2023-08-17
Genre: Business & Economics
ISBN: 3031361717

By offering a critical assessment of the evolution of standard game theory, this book argues for a shift in the ontology and methodology of game theory for appraising games, one based on understanding the players’ strategic reasoning process. Analyzing the history of economic thought, the book highlights the methodological issues faced by standard game theory in its treatment of strategic reasoning and the consequence it has on the status of players’ beliefs. It also highlights how the two original contributions of T. C. Schelling and M. Bacharach can be applied to these issues. Furthermore, the book assesses the intersubjective dimension in games by applying the cognitive sciences and by integrating simulation theory into game theory. Consequently, this book offers an interdisciplinary approach for reassessing the nature of the intersubjectivity involved in strategic reasoning. It shows that the analysis of games should involve the study and identification of the reasoning process that leads the players to a specific outcome, i.e., to a specific solution. A game should not be understood (as is done in standard game theory) as a mathematical representation of an individual choice at equilibrium. This requires investigating the players’ capacity for coordination. Understanding the process of coordination allows us to understand strategic reasoning and ultimately to provide new answers to the indeterminacy problem, one of the central hurdles in game theory, and one that underscores its normative difficulties.

An Introductory Course on Mathematical Game Theory

An Introductory Course on Mathematical Game Theory
Author: Julio González-Díaz
Publisher: American Mathematical Society
Total Pages: 324
Release: 2021-10-22
Genre: Mathematics
ISBN: 1470465736

Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as political science, biology, and, more recently, computer science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. Cooperative games are explained in detail, with bargaining and TU-games being treated as part of a general framework. The authors stress the relation between game theory and operations research. The book is suitable for a graduate or an advanced undergraduate course on game theory.

Dynamic Noncooperative Game Theory

Dynamic Noncooperative Game Theory
Author: Tamer Basar
Publisher: SIAM
Total Pages: 534
Release: 1999-01-01
Genre: Mathematics
ISBN: 9781611971132

Recent interest in biological games and mathematical finance make this classic 1982 text a necessity once again. Unlike other books in the field, this text provides an overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and simultaneously stresses the role of different information patterns. The first edition was fully revised in 1995, adding new topics such as randomized strategies, finite games with integrated decisions, and refinements of Nash equilibrium. Readers can now look forward to even more recent results in this unabridged, revised SIAM Classics edition. Topics covered include static and dynamic noncooperative game theory, with an emphasis on the interplay between dynamic information patterns and structural properties of several different types of equilibria; Nash and Stackelberg solution concepts; multi-act games; Braess paradox; differential games; the relationship between the existence of solutions of Riccati equations and the existence of Nash equilibrium solutions; and infinite-horizon differential games.

Twenty Lectures on Algorithmic Game Theory

Twenty Lectures on Algorithmic Game Theory
Author: Tim Roughgarden
Publisher: Cambridge University Press
Total Pages: 356
Release: 2016-08-30
Genre: Computers
ISBN: 1316781178

Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.

The Evolution of Cooperation

The Evolution of Cooperation
Author: Robert Axelrod
Publisher: Basic Books
Total Pages: 258
Release: 2009-04-29
Genre: Business & Economics
ISBN: 0786734884

A famed political scientist's classic argument for a more cooperative world We assume that, in a world ruled by natural selection, selfishness pays. So why cooperate? In The Evolution of Cooperation, political scientist Robert Axelrod seeks to answer this question. In 1980, he organized the famed Computer Prisoners Dilemma Tournament, which sought to find the optimal strategy for survival in a particular game. Over and over, the simplest strategy, a cooperative program called Tit for Tat, shut out the competition. In other words, cooperation, not unfettered competition, turns out to be our best chance for survival. A vital book for leaders and decision makers, The Evolution of Cooperation reveals how cooperative principles help us think better about everything from military strategy, to political elections, to family dynamics.