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Strategic Equilibrium for Cooperative Games

Author: Giovanni Efraín Reyes Ortiz, PH D

Publisher: Independently Published

Published: 2021-07-26

Total Pages: 156

ISBN-13:

The main purpose of this book is to introduce a theory of solutions for the n-person cooperative game through the simple case with 3-persons. It is intended to give the necessary background for readers, students and researchers in the quantitative and social sciences to enhance their theories and approaches with basic mathematical tools applied and developed for game theory analysis within a systems perspective. Von Neumann and Morgenstern introduced the theory of games as the "proper instrument with which to develop a theory of economic behavior". The snowballing development of game theory and its applications, in the last seventy years, has proven to be not only the proper instrument to develop a theory of economic behavior but the appropriate one for developing the theories for different types of interactive behavior as studied in political, social, environmental, biological, economic and behavioral sciences. Modeling examples of such applications are presented throughout the book.

Collective Rationality

Author: Paul Weirich

Publisher: Oxford University Press

Published: 2009-12-01

Total Pages: 288

ISBN-13: 0190452781

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Groups of people perform acts that are subject to standards of rationality. A committee may sensibly award fellowships, or may irrationally award them in violation of its own policies. A theory of collective rationality defines collective acts that are evaluable for rationality and formulates principles for their evaluation. This book argues that a group's act is evaluable for rationality if it is the products of acts its members fully control. It also argues that such an act is collectively rational if the acts of the group's members are rational. Efficiency is a goal of collective rationality, but not a requirement, except in cases where conditions are ideal for joint action and agents have rationally prepared for joint action. The people engaged in a game of strategy form a group, and the combination of their acts yields a collective act. If their collective act is rational, it constitutes a solution to their game. A theory of collective rationality yields principles concerning solutions to games. One principle requires that a solution constitute an equilibrium among the incentives of the agents in the game. In a cooperative game some agents are coalitions of individuals, and it may be impossible for all agents to pursue all incentives. Because rationality is attainable, the appropriate equilibrium standard for cooperative games requires that agents pursue only incentives that provide sufficient reasons to act. The book's theory of collective rationality supports an attainable equilibrium-standard for solutions to cooperative games and shows that its realization follows from individuals' rational acts. By extending the theory of rationality to groups, this book reveals the characteristics that make an act evaluable for rationality and the way rationality's evaluation of an act responds to the type of control its agent exercises over the act. The book's theory of collective rationality contributes to philosophical projects such as contractarian ethics and to practical projects such as the design of social institutions.

Collective Rationality

Author: Paul Weirich

Publisher: OUP USA

Published: 2010

Total Pages: 283

ISBN-13: 0195388380

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Groups of people perform acts that are subject to standards of rationality. The book's theory of collective rationality explains how to evaluate collective acts. The people engaged in a game of strategy collectively produce an outcome, and the theory reveals what makes some outcomes solutions. It generates new equilibrium standards for solutions to cooperative games.

Game Theoretic Analysis

Author: Leon A Petrosyan

Publisher: World Scientific

Published: 2019-10-14

Total Pages: 621

ISBN-13: 9811202028

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This is a collection of recent novel contributions in game theory from a group of prominent authors in the field. It covers Non-cooperative Games, Equilibrium Analysis, Cooperative Games and Axiomatic Values in static and dynamic contexts.Part 1: Non-cooperative Games and Equilibrium AnalysisIn game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing (e.g. through credible threats) alliances (or competition between groups of players, called 'coalitions') are possible due to the absence of external means to enforce cooperative behavior (e.g. contract law), as opposed to cooperative games. In fact, non-cooperative games are the foundation for the development of cooperative games by acting as the status quo. Non-cooperative games are generally analysed through the framework of equilibrium, which tries to predict players' individual strategies and payoffs. Indeed, equilibrium analysis is the centre of non-cooperative games. This volume on non-cooperative games and equilibrium analysis contains a variety of non-cooperative games and non-cooperative game equilibria from prominent authors in the field.Part 2: Cooperative Games and Axiomatic ValuesIt is well known that non-cooperative behaviours, in general, would not lead to a Pareto optimal outcome. Highly undesirable outcomes (like the prisoner's dilemma) and even devastating results (like the tragedy of the commons) could appear when the involved parties only care about their individual interests in a non-cooperative situation. Cooperative games offer the possibility of obtaining socially optimal and group efficient solutions to decision problems involving strategic actions. In addition, axiomatic values serve as guidance for establishing cooperative solutions. This volume on cooperative games and axiomatic values presents a collection of cooperative games and axiomatic values from prominent authors in the field.

Game Theory

Author: John Eatwell

Publisher: Springer

Published: 1989-09-01

Total Pages: 275

ISBN-13: 1349201812

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This is an extract from the 4-volume dictionary of economics, a reference book which aims to define the subject of economics today. 1300 subject entries in the complete work cover the broad themes of economic theory. It concentrates on the topic of game theory.

Non-Cooperative Game Theory

Author: Takako Fujiwara-Greve

Publisher: Springer

Published: 2015-06-17

Total Pages: 260

ISBN-13: 4431556451

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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.

Dynamic Noncooperative Game Theory

Author: Tamer Basar

Publisher: SIAM

Published: 1999-01-01

Total Pages: 526

ISBN-13: 1611971136

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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.

Noncooperative Game Theory

Author: João P. Hespanha

Publisher: Princeton University Press

Published: 2017-06-13

Total Pages: 242

ISBN-13: 0691175217

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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

Game Theory

Author: Roger A. McCain

Publisher: World Scientific

Published: 2010

Total Pages: 632

ISBN-13: 9814289655

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Fundamentals; Two-Person Games; Larger Numbers and Uncertainty; Games in Extensive Form and Repeated Play; Cooperation; Behavioral Game Theory; Selected Applications.

Game Theoretic Analysis

Author: Leon Aganesovich Petrosi︠a︡n

Publisher:

Published: 2019

Total Pages: 620

ISBN-13: 9789811202018

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"This is a collection of recent novel contributions in game theory from a group of prominent authors in the field. It covers Non-cooperative Games, Equilibrium Analysis, Cooperative Games and Axiomatic Values in static and dynamic contexts. Part 1: Non-cooperative Games and Equilibrium Analysis: In game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing (e.g. through credible threats) alliances (or competition between groups of players, called "coalitions") are possible due to the absence of external means to enforce cooperative behavior (e.g. contract law), as opposed to cooperative games. In fact, non-cooperative games are the foundation for the development of cooperative games by acting as the status quo. Non-cooperative games are generally analysed through the framework of equilibrium, which tries to predict players' individual strategies and payoffs. Indeed, equilibrium analysis is the centre of non-cooperative games. This volume on non-cooperative games and equilibrium analysis contains a variety of non-cooperative games and non-cooperative game equilibria from prominent authors in the field. Part 2: Cooperative Games and Axiomatic Values: It is well known that non-cooperative behaviours, in general, would not lead to a Pareto optimal outcome. Highly undesirable outcomes (like the prisoner's dilemma) and even devastating results (like the tragedy of the commons) could appear when the involved parties only care about their individual interests in a non-cooperative situation. Cooperative games offer the possibility of obtaining socially optimal and group efficient solutions to decision problems involving strategic actions. In addition, axiomatic values serve as guidance for establishing cooperative solutions. This volume on cooperative games and axiomatic values presents a collection of cooperative games and axiomatic values from prominent authors in the field."--