How Proper is Sequential Equilibrium?
Author: George Joseph Mailath
Publisher:
Published: 1994
Total Pages: 42
ISBN-13:
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Refinements of the Nash Equilibrium Concept
Author: E. van Damme
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 161
ISBN-13: 3642499708
DOWNLOAD EBOOKIn this monograph, noncooperative games are studied. Since in a noncooperative game binding agreements are not possible, the solution of such a game has to be self enforcing, i. e. a Nash equilibrium (NASH [1950,1951J). In general, however, a game may possess many equilibria and so the problem arises which one of these should be chosen as the solution. It was first pointed out explicitly in SELTEN [1965J that I not all Nash equilibria of an extensive form game are qualified to be selected as the solution, since an equilibrium may prescribe irrational behavior at unreached parts of the game tree. Moreover, also for normal form games not all Nash equilibria are eligible, since an equilibrium need not be robust with respect to slight perturba tions in the data of the game. These observations lead to the conclusion that the Nash equilibrium concept has to be refined in order to obtain sensible solutions for every game. In the monograph, various refinements of the Nash equilibrium concept are studied. Some of these have been proposed in the literature, but others are presented here for the first time. The objective is to study the relations between these refine ments;to derive characterizations and to discuss the underlying assumptions. The greater part of the monograph (the chapters 2-5) is devoted to the study of normal form games. Extensive form games are considered in chapter 6.
Rationality in Extensive Form Games
Author: Andrés Perea
Publisher: Springer Science & Business Media
Published: 2001-10-31
Total Pages: 256
ISBN-13: 9780792375401
DOWNLOAD EBOOKThis book is concerned with situations in which several persons reach decisions independently and the final consequence depends, potentially, upon each of the decisions taken. Such situations may be described formally by an extensive form game: a mathematical object which specifies the order in which decisions are to be taken, the information available to the decision makers at each point in time, and the consequence that results for each possible combination of decisions. A necessary requirement for rational behavior in such games is that each decision maker should reach a decision that is optimal, given his preferences over his own decisions. This requirement is far from sufficient, however, since every decision maker should in addition base his preferences upon the conjecture that his opponents will act optimally as well. It is this principle that distinguishes noncooperative game theory from one-person decision theory. The main purpose of Rationality in Extensive Form Games is to discuss different formalizations of this principle in extensive form games, such as backward induction, Nash equilibrium, forward induction and rationalizability, under the assumption that the decision makers' preferences are given by subjective expected utility functions. The various formalizations, or rationality criteria, are illustrated by examples, and the relationships among the different criteria are explored.
Epistemic Game Theory
Author: Andrés Perea
Publisher: Cambridge University Press
Published: 2012-06-07
Total Pages: 581
ISBN-13: 1107008913
DOWNLOAD EBOOKThe first textbook to explain the principles of epistemic game theory.
Stability and Perfection of Nash Equilibria
Author: Eric van Damme
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 331
ISBN-13: 364296978X
DOWNLOAD EBOOKThe 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.
The Consistent Preferences Approach to Deductive Reasoning in Games
Author: Geir B. Asheim
Publisher: Springer Science & Business Media
Published: 2010-07-07
Total Pages: 203
ISBN-13: 0387262377
DOWNLOAD EBOOKDuring the last decade I have explored the consequences of what I have chosen to call the 'consistent preferences' approach to deductive reasoning in games. To a great extent this work has been done in coop eration with my co-authors Martin Dufwenberg, Andres Perea, and Ylva Sovik, and it has lead to a series of journal articles. This book presents the results of this research program. Since the present format permits a more extensive motivation for and presentation of the analysis, it is my hope that the content will be of interest to a wider audience than the corresponding journal articles can reach. In addition to active researcher in the field, it is intended for graduate students and others that wish to study epistemic conditions for equilibrium and rationalizability concepts in game theory. Structure of the book This book consists of twelve chapters. The main interactions between the chapters are illustrated in Table 0.1. As Table 0.1 indicates, the chapters can be organized into four dif ferent parts. Chapters 1 and 2 motivate the subsequent analysis by introducing the 'consistent preferences' approach, and by presenting ex amples and concepts that are revisited throughout the book. Chapters 3 and 4 present the decision-theoretic framework and the belief operators that are used in later chapters. Chapters 5, 6, 10, and 11 analyze games in the strategic form, while the remaining chapters-Chapters 7, 8, 9, and 12-are concerned with games in the extensive form.
Understanding Strategic Interaction
Author: Wulf Albers
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 526
ISBN-13: 3642604951
DOWNLOAD EBOOKStrategic interaction occurs whenever it depends on others what one finally obtains: on markets, in firms, in politics etc. Game theorists analyse such interaction normatively, using numerous different methods. The rationalistic approach assumes perfect rationality whereas behavioral theories take into account cognitive limitations of human decision makers. In the animal kingdom one usually refers to evolutionary forces when explaining social interaction. The volume contains innovative contributions, surveys of previous work and two interviews which shed new light on these important topics of the research agenda. The contributions come from highly regarded researchers from all over the world who like to express in this way their intellectual inspiration by the Nobel-laureate Reinhard Selten.
Non-Cooperative Game Theory
Author: Takako Fujiwara-Greve
Publisher: Springer
Published: 2015-06-17
Total Pages: 263
ISBN-13: 4431556451
DOWNLOAD EBOOKThis 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.
Social Goals and Social Organization
Author: Leonid Hurwicz
Publisher: Cambridge University Press
Published: 1985-12-27
Total Pages: 398
ISBN-13: 9780521262040
DOWNLOAD EBOOKThis book contains a collection of essays providing a comprehensive view of the design and evaluation of economic mechanisms.
An Introductory Course on Mathematical Game Theory
Author: Julio González-Díaz
Publisher: American Mathematical Society
Published: 2021-10-22
Total Pages: 324
ISBN-13: 1470465736
DOWNLOAD EBOOKGame 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.
