Non Cooperative Game Theory

Author: Takako Fujiwara-Greve
Publisher: Springer
ISBN: 4431556451
Format: PDF, Docs
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This is a textbook for university juniors, seniors, and graduate students majoring in economics, applied mathematics, and related fields. Each chapter is structured so that a core concept of that chapter is presented with motivations, useful applications are given, and related advanced topics are discussed for future study. Many helpful exercises at various levels are provided at the end of each chapter. Therefore, this book is most suitable for readers who intend to study non-cooperative game theory rigorously for both theoretical studies and applications. Game theory consists of non-cooperative games and cooperative games. This book covers only non-cooperative games, which are major tools used in current economics and related areas. Non-cooperative game theory aims to provide a mathematical prediction of strategic choices by decision makers (players) in situations of conflicting interest. Through the logical analyses of strategic choices, we obtain a better understanding of social (economic, business) problems and possible remedies. The book contains many well-known games such as the prisoner’s dilemma, chicken (hawk–dove) game, coordination game, centipede game, and Cournot, Bertrand, and Stackelberg models in oligopoly. It also covers some advanced frameworks such as repeated games with non-simultaneous moves, repeated games with overlapping generations, global games, and voluntarily separable repeated prisoner’s dilemma, so that readers familiar with basic game theory can expand their knowledge. The author’s own research is reflected in topics such as formulations of information and evolutionary stability, which makes this book unique.

Foundations of Game Theory

Author: Nicolai N. Vorob'ev
Publisher: Birkhäuser
ISBN: 3034885148
Format: PDF, Mobi
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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.

Dynamic Noncooperative Game Theory

Author: Tamer Basar
Publisher: SIAM
ISBN: 089871429X
Format: PDF, ePub, Docs
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An overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and the role of different information patterns.

Noncooperative Approaches to the Theory of Perfect Competition

Author: Andreu Mas-Colell
Publisher: Academic Press
ISBN: 1483271609
Format: PDF, ePub, Mobi
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Economic Theory, Econometrics, and Mathematical Economics: A Series of Monographs and Textbooks: Noncooperative Approaches to the Theory of Perfect Competition focuses on the application of noncooperative approaches to the theory of perfect competition, including Cournot game, no-surplus condition, and Nash equilibria. The selection first elaborates on collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives and noncooperative price taking in large dynamic markets. Discussions focus on noncooperative equilibria which support the monopoly allocation, alternative definition of perfect epsilon-equilibrium, one-period Cournot game, fixed-demand case, and replication case. The book takes a look at noncooperative price taking in large dynamic markets, no-surplus condition as a characterization of perfectly competitive equilibrium, perfect competition, profit criterion, and the organization of economic activity. Topics include profits to individually improving welfare, structure of firms, competitive allocations as no surplus allocations, profits as rents, Walrasian and perfectly competitive equilibrium, and no-surplus and core equivalence as alternative characterizations of perfectly competitive equilibrium. The manuscript ponders on Nash equilibria of market games and efficiency properties of strategic market games, as well as commodities, agents, assignments, strategic markets games, proper and full Cournot-Nash equilibria, and finiteness and inefficiency. The selection is a valuable source of data for researchers interested in noncooperative approaches to the theory of perfect competition.

Cooperative and Noncooperative Multi Level Programming

Author: Masatoshi Sakawa
Publisher: Springer Science & Business Media
ISBN: 1441906762
Format: PDF, ePub, Docs
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To derive rational and convincible solutions to practical decision making problems in complex and hierarchical human organizations, the decision making problems are formulated as relevant mathematical programming problems which are solved by developing optimization techniques so as to exploit characteristics or structural features of the formulated problems. In particular, for resolving con?ict in decision making in hierarchical managerial or public organizations, the multi level formula tion of the mathematical programming problems has been often employed together with the solution concept of Stackelberg equilibrium. However,weconceivethatapairoftheconventionalformulationandthesolution concept is not always suf?cient to cope with a large variety of decision making situations in actual hierarchical organizations. The following issues should be taken into consideration in expression and formulation of decision making problems. Informulationofmathematicalprogrammingproblems,itistacitlysupposedthat decisions are made by a single person while game theory deals with economic be havior of multiple decision makers with fully rational judgment. Because two level mathematical programming problems are interpreted as static Stackelberg games, multi level mathematical programming is relevant to noncooperative game theory; in conventional multi level mathematical programming models employing the so lution concept of Stackelberg equilibrium, it is assumed that there is no communi cation among decision makers, or they do not make any binding agreement even if there exists such communication. However, for decision making problems in such as decentralized large ?rms with divisional independence, it is quite natural to sup pose that there exists communication and some cooperative relationship among the decision makers.

Game Theory and Economic Modelling

Author: David M. Kreps
Publisher: Oxford University Press
ISBN: 0198283814
Format: PDF, ePub, Docs
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This book examines why game theory has become such a popular tool of analysis. It investigates the deficiencies in this methodology and goes on to consider whether its popularity will fade or remain an important tool for economists. The book provides the reader with some basic concepts from noncooperative theory, and then goes on to explore the strengths, weaknesses, and future of the theory as a tool of economic modelling and analysis. All those interested in the applications of game theory to economics, from undergraduates to academics will find this study of particular value.

A Course on Cooperative Game Theory

Author: Satya R. Chakravarty
Publisher: Cambridge University Press
ISBN: 1107058791
Format: PDF, Kindle
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"Deals with real life situations where objectives of the participants are partially cooperative and partially conflicting"--

Mathematical Financial Economics

Author: Igor Evstigneev
Publisher: Springer
ISBN: 3319165712
Format: PDF, Mobi
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This textbook is an elementary introduction to the key topics in mathematical finance and financial economics - two realms of ideas that substantially overlap but are often treated separately from each other. Our goal is to present the highlights in the field, with the emphasis on the financial and economic content of the models, concepts and results. The book provides a novel, unified treatment of the subject by deriving each topic from common fundamental principles and showing the interrelations between the key themes. Although the presentation is fully rigorous, with some rare and clearly marked exceptions, the book restricts itself to the use of only elementary mathematical concepts and techniques. No advanced mathematics (such as stochastic calculus) is used.

Cooperative Extensions of the Bayesian Game

Author: Tatsuro Ichiishi
Publisher: World Scientific
ISBN: 9812563598
Format: PDF, Kindle
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This is the very first comprehensive monograph in a burgeoning, new research area ? the theory of cooperative game with incomplete information with emphasis on the solution concept of Bayesian incentive compatible strong equilibrium that encompasses the concept of the Bayesian incentive compatible core. Built upon the concepts and techniques in the classical static cooperative game theory and in the non-cooperative Bayesian game theory, the theory constructs and analyzes in part the powerful n-person game-theoretical model characterized by coordinated strategy-choice with individualistic incentives, the influence of outsiders' strategy choice upon the feasibility and implications of coalitional attainability, and incomplete information. The book presents the basic results of this theory. It also presents the research results to date on the simple, but central economic model of Bayesian pure exchange economy, and also on an alternative approach, anonymous coalition formation.The theory presented here points to an important future research direction in economics. In particular, it has the potential to provide game-theoretical foundations of organizational analysis in which organizations (coalitions) as corporations institute a non-market resource allocation mechanism while using the market resource allocation mechanism at the same time.The book provides appraisals of the various concepts, setups and results established to date as well as many discussions on philosophical issues on different approaches in the area, thereby clarifying the applicability and limitations of the current theory. It also contains numerous examples illustrating various concepts and points of discussions.Cooperative Extensions of the Bayesian Game is an essential reference in strategic cooperative game theory, and serves as an informative textbook for PhD courses in advanced economic theory, mathematical economics, game theory, and industrial organization.

Fixed Points and Economic Equilibria

Author: Ken Urai
Publisher: World Scientific
ISBN: 9812837191
Format: PDF, Mobi
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This book presents a systematic approach to problems in economic equilibrium based on fixed-point arguments and rigorous set-theoretical (axiomatic) methods. It describes the highest-level research on the classical theme, fixed points and economic equilibria, in the theory of mathematical economics, and also presents basic results in this area, especially in the general equilibrium theory and non-co-operative game theory. The arguments also contain distinguishable developments of the main theme in the homology theory for general topological spaces, in the model theory and mathematical logic, and in the methodology and philosophy of social sciences. It can thus serve as a graduate-level textbook on mathematical economics as well as an advanced monograph for students and researchers who are concerned about rigorous mathematical treatment in the social sciences.