Stability and Perfection of Nash Equilibria


Book Description

This book discusses the main shortcomings of the classical solution concept from noncooperative game theory (that of Nash equilibria) and provides a comprehensive study of the more refined concepts (such as sequential, perfect, proper and stable equilibria) that have been introduced to overcome these drawbacks. The plausibility of the assumptions underlying each such concept are discussed, desirable properties as well as deficiencies are illustrated, characterizations are derived and the relationships between the various concepts are studied. The first six chapters provide an informal discussion with many examples as well as a comprehensive overview for normal form games. The remaining chapters are devoted to specific applications, illustrating the strength (resp. weakness) of the various concepts.




Stability and Perfection of Nash Equilibria


Book Description

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.




Game Theory


Book Description

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.




Refinements of the Nash Equilibrium Concept


Book Description

In 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.




Evolutionary Games and Equilibrium Selection


Book Description

The author examines the interplay between evolutionary game theory and the equilibrium selection problem in noncooperative games. Evolutionary game theory is one of the most active and rapidly growing areas of research in economics. Unlike traditional game theory models, which assume that all players are fully rational and have complete knowledge of details of the game, evolutionary models assume that people choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. In games that are repeated many times, low-payoff strategies tend to be weeded out, and an equilibrium may emerge. Larry Samuelson has been one of the main contributors to the evolutionary game theory literature. In Evolutionary Games and Equilibrium Selection, he examines the interplay between evolutionary game theory and the equilibrium selection problem in noncooperative games. After providing an overview of the basic issues of game theory and a presentation of the basic models, the book addresses evolutionary stability, the dynamics of sample paths, the ultimatum game, drift, noise, backward and forward induction, and strict Nash equilibria.




A General Theory of Equilibrium Selection in Games


Book Description

The authors, two of the most prominent game theorists of this generation, have devoted a number of years to the development of the theory presented here, and to its economic applications. They propose rational criteria for selecting one particular uniformly perfect equilibrium point as the solution of any noncooperative game. And, because any cooperative game can be remodelled as a noncooperative bargaining game, their theory defines a one-point solution for any cooperative game as well.By providing solutions - based on the same principles of rational behavior - for all classes of games, both cooperative and noncooperative, both those with complete and with incomplete information, Harsanyi and Selten's approach achieves a remarkable degree of theoretical unification for game theory as a whole and provides a deeper insight into the nature of game-theoretic rationality.The book applies this theory to a number of specific game classes, such as unanimity games; bargaining with transaction costs; trade involving one seller and several buyers; two-person bargaining with incomplete information on one side, and on both sides. The last chapter discusses the relationship of the authors' theory to other recently proposed solution concepts, particularly the Kohberg-Mertens stability theory.John C. Harsanyi is Flood Research Professor in Business Administration and Professor of Economics, University of California, Berkeley. Reinhard Selten is Professor of Economics Institute of Social and Economic Sciences: University of Bonn, Federal Republic of Germany.




Advances in Economic Theory: Volume 1


Book Description

This book gives the reader a unique survey of advances in economic theory.




Problems of Coordination in Economic Activity


Book Description

Coordination is extremely important in economic, political, and social life. The concept of economic equilibrium is based on the coordination of producers and consumers in buying and selling. This book reviews the topic of coordination from an economic, theoretical standpoint. The aim of this volume is twofold: first, the book contributes to the ongoing research on the economics of coordination; and second, it disseminates results and encourages interest in the topic. The volume contains original research on coordination including general game-theoretic questions, particular coordination issues within specific fields of economics (i.e. industrial organization, international trade, and macroeconomics), and experimental research.




Game Theory and Applications


Book Description

Game Theory and Applications outlines game theory and proves its validity by examining it alongside the neoclassical paradigm. This book contends that the neoclassical theory is the exceptional case, and that game theory may indeed be the rule. The papers and abstracts collected here explore its recent development and suggest new research directions. - Explains many of the recent central developments in game theory - Highlights new research directions in economic theory which surpass the neoclassical paradigm - Includes game-theoretical analyses in economics, political science, and biology - Written by leading game theorists, economists, political scientists, and biologists




An Introductory Course on Mathematical Game Theory


Book Description

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.