Refinements of the Nash Equilibrium Concept

Refinements of the Nash Equilibrium Concept

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.

Author: E. van Damme

Publisher: Springer Science & Business Media

ISBN: 9783642499708

Category: Business & Economics

Page: 155

View: 130

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.
Categories: Business & Economics

Stability and Perfection of Nash Equilibria

Stability and Perfection of Nash Equilibria

I have been pleased with the favourable reception of the first edition of this book and I am grateful to have the opportunity to prepare this second edition.

Author: Eric van Damme

Publisher: Springer Science & Business Media

ISBN: 9783642582424

Category: Mathematics

Page: 339

View: 331

I have been pleased with the favourable reception of the first edition of this book and I am grateful to have the opportunity to prepare this second edition. In this revised and enlarged edition I corrected some misprints and errors that occurred in the first edition (fortunately I didn't find too many) and I added a large number of notes that give the reader an impression of what kind of results have been obtained since the first edition was printed and that give an indication of the direction the subject is taking. Many of the notes discuss (or refer to papers discussing) applications of the refinements that are considered. Of course, it is the quantity and the quality of the insights and the applications that lend the refinements their validity. Although the guide to the applications is far from complete, the notes certainly allow the reader to form a good judgement of which refinements have really yielded new insights. Hence, as in the first edition, I will refrain from speculating on which refinements of Nash equilibria will survive in the long run. To defend this position let me also cite Binmore [1990] who compares writing about refinements to the Herculean task of defeating the nine-headed Hydra which grew too heads for each that was struck off. It is a pleasure to have the opportunity to thank my secretary, Marjoleine de Wit, who skilfully and, as always, cheerfully typed the manuscript and did the proofreading.
Categories: Mathematics

Stability and Perfection of Nash Equilibria

Stability and Perfection of Nash Equilibria

1–6 of this book are virtually identical to the monograph “Refinements of the Nash equilibrium concept” that I published with SpringerVerlag in 1983. Werner Müller, the economics editor of Springer kindly asked me to extend that ...

Author: Eric van Damme

Publisher: Springer Science & Business Media

ISBN: 9783642969782

Category: Business & Economics

Page: 318

View: 303

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.
Categories: Business & Economics

Evolutionary Game Theory

Evolutionary Game Theory

1.4 Refinements of Nash Equilibrium Since the late 1970s there has been a flurry of refinements of the Nash equilibrium concept , each refinement being motivated by the desire to get rid of certain implausible or fragile Nash equilibria ...

Author: Jörgen W. Weibull

Publisher: MIT Press

ISBN: 0262731215

Category: Mathematics

Page: 265

View: 994

Introduces current evolutionary game theory--where ideas from evolutionary biology and rationalistic economics meet--emphasizing the links between static and dynamic approaches and noncooperative game theory. This text introduces current evolutionary game theory--where ideas from evolutionary biology and rationalistic economics meet--emphasizing the links between static and dynamic approaches and noncooperative game theory. Much of the text is devoted to the key concepts of evolutionary stability and replicator dynamics. The former highlights the role of mutations and the latter the mechanisms of selection. Moreover, set-valued static and dynamic stability concepts, as well as processes of social evolution, are discussed. Separate background chapters are devoted to noncooperative game theory and the theory of ordinary differential equations. There are examples throughout as well as individual chapter summaries. Because evolutionary game theory is a fast-moving field that is itself branching out and rapidly evolving, Jörgen Weibull has judiciously focused on clarifying and explaining core elements of the theory in an up-to-date, comprehensive, and self-contained treatment. The result is a text for second-year graduate students in economic theory, other social sciences, and evolutionary biology. The book goes beyond filling the gap between texts by Maynard-Smith and Hofbauer and Sigmund that are currently being used in the field. Evolutionary Game Theory will also serve as an introduction for those embarking on research in this area as well as a reference for those already familiar with the field. Weibull provides an overview of the developments that have taken place in this branch of game theory, discusses the mathematical tools needed to understand the area, describes both the motivation and intuition for the concepts involved, and explains why and how it is relevant to economics.
Categories: Mathematics

Essays on Equilibrium Refinements

Essays on Equilibrium Refinements

The second essay proposes a refinement of Nash equilibria by selecting those consistent with the decision theoretic axiom of forward induction.

Author: Tien Yuek Man

Publisher:

ISBN: 1124048987

Category:

Page: 109

View: 371

The second essay proposes a refinement of Nash equilibria by selecting those consistent with the decision theoretic axiom of forward induction. Forward induction is the notion that individuals rationalize their opponents' behaviors even when confronted with an unexpected event. An admissible, invariant forward induction equilibrium concept is constructed. Forward induction equilibrium exists for all finite generic extensive form games with perfect recall. It does not satisfy backward induction. Yet for generic extensive form games the set of forward induction outcomes contains an invariant backward induction equilibrium outcome. Forward induction is not equivalent to iterative elimination of dominated strategies. It encompasses most commonly used refinements for signaling games.
Categories:

The Philosophy of Science

The Philosophy of Science

Refinements of Nash Equilibrium Although it is generally agreed that a solution to a game must be a strategy profile in a Nash ... a number of refinements and extensions to the concept of a Nash equilibrium have been introduced, ...

Author: Sahotra Sarkar

Publisher: Psychology Press

ISBN: 9780415939270

Category: Philosophy

Page: 965

View: 383

The first in-depth reference in the field that combines scientific knowledge with philosophical inquiry, The Philosophy of Science: An Encyclopedia is a two-volume set that brings together an international team of leading scholars to provide over 130 entries on the essential concepts in the philosophy of science. The areas covered include: biology chemistry epistemology and metaphysics physics psychology and mind the social sciences key figures in the combined studies of science and philosophy. The essays represent the most up-to-date philosophical thinking on timeless scientific topics such as: determinism, explanation, laws of nature, perception, individuality, time, and economics as well as timely topics like adaptation, conservation biology, quantum logic, consciousness, evolutionary psychology, and game theory.
Categories: Philosophy

Evolutionary Games and Equilibrium Selection

Evolutionary Games and Equilibrium Selection

This approach has precedents in the refinements literature , where set - valued equilibrium concepts have been proposed as refinements of Nash equilibrium . The technique in both the refinements and evolutionary literature ...

Author: Larry Samuelson

Publisher: MIT Press

ISBN: 0262692198

Category: Business & Economics

Page: 309

View: 530

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.
Categories: Business & Economics

Game Theory in the Social Sciences

Game Theory in the Social Sciences

It is worth noting that neither the definition of the equilibrium concept nor the existence theorem mention whether the game at hand is a variablesum one or not. Indeed, this aspect is irrelevant, as the Nash equilibrium can be thought ...

Author: Luca Lambertini

Publisher: Routledge

ISBN: 9781136737596

Category: Business & Economics

Page: 208

View: 551

Individuals, firms, governments and nations behave strategically, for good and bad. Over the last few decades, game theory has been constructed and progressively refined to become the major tool used by social scientists to understand, predict and regulate strategic interaction among agents who often have conflicting interests. In the surprisingly anodyne jargon of the theory, they ‘play games’. This book offers an introduction to the basic tools of game theory and an overview of a number of applications to real-world cases, covering the areas of economics, politics and international relations. Each chapter is accompanied by some suggestions about further reading.
Categories: Business & Economics

Methods and Finance

Methods and Finance

A student of von Neumann's—the film A Beautiful Mind recounts his life—Nash developed an equilibrium concept ... that started the quest for 'refinements' of the Nash equilibrium, that is, for alternative solution concepts that would ...

Author: Emiliano Ippoliti

Publisher: Springer

ISBN: 9783319498720

Category: Science

Page: 194

View: 478

The book offers an interdisciplinary perspective on finance, with a special focus on stock markets. It presents new methodologies for analyzing stock markets’ behavior and discusses theories and methods of finance from different angles, such as the mathematical, physical and philosophical ones. The book, which aims at philosophers and economists alike, represents a rare yet important attempt to unify the externalist with the internalist conceptions of finance.
Categories: Science

Network Economics and the Allocation of Savings

Network Economics and the Allocation of Savings

Because the (undominated) Nash equilibrium is a concept that supports only strategies from which individual deviations are not worthwhile, we will also investigate the refinements of the Nash equilibrium concept known as CoalitionProof ...

Author: Philipp Servatius

Publisher: Springer Science & Business Media

ISBN: 3642210961

Category: Business & Economics

Page: 297

View: 913

This book provides a game theoretic model of interaction among VoIP telecommunications providers regarding their willingness to enter peering agreements with one another. The author shows that the incentive to peer is generally based on savings from otherwise payable long distance fees. At the same time, termination fees can have a countering and dominant effect, resulting in an environment in which VoIP firms decide against peering. Various scenarios of peering and rules for allocation of the savings are considered. The first part covers the relevant aspects of game theory and network theory, trying to give an overview of the concepts required in the subsequent application. The second part of the book introduces first a model of how the savings from peering can be calculated and then turns to the actual formation of peering relationships between VoIP firms. The conditions under which firms are willing to peer are then described, considering the possible influence of a regulatory body.
Categories: Business & Economics

Networks and Groups

Networks and Groups

Since no player wants to break a link, and it needs the consent of two players to form an additional link, any cooperation structure can be sustained as a Nash equilibrium. We, therefore, use refinements of the Nash equilibrium concept.

Author: Bhaskar Dutta

Publisher: Springer Science & Business Media

ISBN: 9783540247906

Category: Business & Economics

Page: 496

View: 226

When Murat Sertel asked us whether we would be interested in organizing a special issue of the Review of Economic Design on the formation of networks and groups, we were happy to accept because of the growing research on this important topic. We were also pleasantly surprised at the response to our request for submissions to the special issue, receiving a much larger number of sub missions than we had anticipated. In the end we were able to put together two special issues of insightful papers on this topic. Given the growing interest in this topic, we also decided (with encouragement from Murat) to combine the special issues in the form of a book for wider dissemination. However, once we had decided to edit the book, it was natural to move beyond the special issue to include at least some of the papers that have been influential in the literature on the formation of networks. These papers were published in other journals, and we are very grateful to the authors as well as the journals for permission to include these papers in the book.
Categories: Business & Economics

Methodological Foundations of Macroeconomics

Methodological Foundations of Macroeconomics

The syntactic nature of the concept is also revealed by the fact that the numerous refinements of the Nash equilibrium are often called ' solution concepts ' . Notwithstanding its increasing popularity , the concept of Nash equilibrium ...

Author: Alessandro Vercelli

Publisher: Cambridge University Press

ISBN: 0521392942

Category: Business & Economics

Page: 269

View: 788

An investigation of the methodological and epistemological foundations of macroeconomic theory. The author compares the two main alternative research programmes in macroeconomics: that outlined by Keynes in his 'General Theory', and that suggested by Lucas, the leader of the new classical economists. He concludes that a Keynesian conception of macroeconomics as a discipline autonomous from microeconomics and open to theoretical and methodological innovation should be defended.
Categories: Business & Economics

Game Theory Breakthroughs in Research and Practice

Game Theory  Breakthroughs in Research and Practice

Since the development of the Nash equilibrium concept, game theorists have proposed many related solution concepts, which refine the Nash equilibrium to overcome perceived flaws in the Nash concept. However, subsequent refinements and ...

Author: Management Association, Information Resources

Publisher: IGI Global

ISBN: 9781522525950

Category: Mathematics

Page: 505

View: 224

Developments in the use of game theory have impacted multiple fields and created opportunities for new applications. With the ubiquity of these developments, there is an increase in the overall utilization of this approach. Game Theory: Breakthroughs in Research and Practice contains a compendium of the latest academic material on the usage, strategies, and applications for implementing game theory across a variety of industries and fields. Including innovative studies on economics, military strategy, and political science, this multi-volume book is an ideal source for professionals, practitioners, graduate students, academics, and researchers interested in the applications of game theory.
Categories: Mathematics

Games And Dynamic Games

Games And Dynamic Games

Refinements. of. the. Equilibrium. Concepts. 4.1 Introduction In the previous chapter, we saw that the Nash-equilibrium solution concept has some limitations and drawbacks. For example, in bimatrix or m-matrix games, having multiple ...

Author: Haurie Alain

Publisher: World Scientific Publishing Company

ISBN: 9789814401340

Category: Mathematics

Page: 488

View: 761

Dynamic games arise between players (individuals, firms, countries, animals, etc.) when the strategic interactions among them recur over time and decisions made during one period affect both current and future payoffs. Dynamic games provide conceptually rich paradigms and tools to deal with these situations.This volume provides a uniform approach to game theory and illustrates it with present-day applications to economics and management, including environmental, with the emphasis on dynamic games.At the end of each chapter a case study called game engineering (GE) is provided, to help readers understand how problems of high social priority, such as environmental negotiations, exploitation of common resources, can be modeled as games and how solutions can be engineered.
Categories: Mathematics

Experimental Economics

Experimental Economics

In this case , the selection of a particular equilibrium requires a refinement of the Nash equilibrium concept . One very standard refinement is the notion of Pareto dominance : Participants will tend to coordinate on the Nash ...

Author: Douglas D. Davis

Publisher: Princeton University Press

ISBN: 9780691233376

Category: Business & Economics

Page: 584

View: 320

A small but increasing number of economists have begun to use laboratory experiments to evaluate economic propositions under carefully controlled conditions. Experimental Economics is the first comprehensive treatment of this rapidly growing area of research. While the book acknowledges that laboratory experiments are no panacea, it argues cogently for their effectiveness in selected situations. Covering methodological and procedural issues as well as theory, Experimental Economics is not only a textbook but also a useful introduction to laboratory methods for professional economists. Although the authors present some new material, their emphasis is on organizing and evaluating existing results. The book can be used as an anchoring device for a course at either the graduate or advanced undergraduate level. Applications include financial market experiments, oligopoly price competition, auctions, bargaining, provision of public goods, experimental games, and decision making under uncertainty. The book also contains instructions for a variety of laboratory experiments.
Categories: Business & Economics

Game Theory

Game Theory

Hence these refinements ( e.g. proper equilibria ) , like the Nash equilibrium project itself , seem to have to ... In other words , the attempt to bring greater determinacy to games by refining the Nash equilibrium concept is not ...

Author: Shaun Hargreaves Heap

Publisher: Psychology Press

ISBN: 0415250951

Category: Business & Economics

Page: 369

View: 313

Requiring no more than basic arithmetic, this book provides a careful and accessible introduction to the basic pillars of Game Theory, tracing its intellectual origins and philosophical premises.
Categories: Business & Economics