Game Theoretical Foundations Of Evolutionary Stability

Author : Immanuel M. Bomze
Publisher : Springer Science & Business Media
ISBN 13 : 364245660X
Total Pages : 152 pages
Book Rating : 4.02/5 ( download)

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Download or read book Game Theoretical Foundations of Evolutionary Stability written by Immanuel M. Bomze and published by Springer Science & Business Media. This book was released on 2013-12-19 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes arose from discussions we had over a working paper written by the first author in fall 1987. We decided then to write a short paper about the basic structure of evolutionary stability and found ourselves ending up with a book manuscript. Parts of the material contained herein were presented in a seminar at the Department of Mathematics at the University of Vienna, as well as at a workshop on evolutionary game theory in Bielefeld. The final version of the manuscript has certainly benefitted from critical comments and suggestions by the participants of both the seminar and the workshop. Thanks are also due to S. Bomze-de Barba, R. Burger, G. Danninger, J. Hofbauer, R. Selten, K. Sigmund, G. Stiastny and F. Weising. The co-operation of W. Muller from Springer Verlag, Heidelberg, is gratefully acknowledged. Vienna, November 1988 Immanuel M. Bomze Benedikt M. Potscher III Contents 1. Introduction 1 2. Strategies and payoffs 5 2. 1. A general setting for evolutionary game theory 6 2. 2. Mixed strategies and population games 8 2. 3. Finite number of strategies . . . . . 13 2. 4. Infinitely many (pure) strategies 15 2. 5. Structured populations: asymmetric contests and multitype games 17 2. 6. Additional remarks . . . . . . . . . . . . . . . . . . . . . 21 3. Evolutionary stability 25 3. 1. Definition of evolutionary stability 25 3. 2. Evolutionary stability and solution concepts in classical game theory 30 3. 3. Conditions for evolutionary stability based on the normal cone 31 3. 4.

Author : Ross Cressman
Publisher : Springer Science & Business Media
ISBN 13 : 3642499813
Total Pages : 137 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Stability Concept of Evolutionary Game Theory written by Ross Cressman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Notes grew from my research in evolutionary biology, specifically on the theory of evolutionarily stable strategies (ESS theory), over the past ten years. Personally, evolutionary game theory has given me the opportunity to transfer my enthusiasm for abstract mathematics to more practical pursuits. I was fortunate to have entered this field in its infancy when many biologists recognized its potential but were not prepared to grant it general acceptance. This is no longer the case. ESS theory is now a rapidly expanding (in both applied and theoretical directions) force that no evolutionary biologist can afford to ignore. Perhaps, to continue the life-cycle metaphor, ESS theory is now in its late adolescence and displays much of the optimism and exuberance of this exciting age. There are dangers in writing a text about a theory at this stage of development. A comprehensive treatment would involve too many loose ends for the reader to appreciate the central message. On the other hand, the current central message may soon become obsolete as the theory matures. Although the restricted topics I have chosen for this text reflect my own research bias, I am confident they will remain the theoretical basis of ESS theory. Indeed, I feel the adult maturity of ESS theory is close at hand and I hope the text will play an important role in this achievement.

Author : Jörgen W. Weibull
Publisher : MIT Press
ISBN 13 : 9780262731218
Total Pages : 292 pages
Book Rating : 4.15/5 ( download)

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Download or read book Evolutionary Game Theory written by Jörgen W. Weibull and published by MIT Press. This book was released on 1997 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Reinhard Selten
Publisher : Springer Science & Business Media
ISBN 13 : 3662026740
Total Pages : 338 pages
Book Rating : 4.48/5 ( download)

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Download or read book Game Equilibrium Models I written by Reinhard Selten and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two main approaches towards the phenotypic analysis of frequency dependent natural selection. First, there is the approach of evolutionary game theory, which was introduced in 1973 by John Maynard Smith and George R. Price. In this theory, the dynamical process of natural selection is not modeled explicitly. Instead, the selective forces acting within a population are represented by a fitness function, which is then analysed according to the concept of an evolutionarily stable strategy or ESS. Later on, the static approach of evolutionary game theory has been complemented by a dynamic stability analysis of the replicator equations. Introduced by Peter D. Taylor and Leo B. Jonker in 1978, these equations specify a class of dynamical systems, which provide a simple dynamic description of a selection process. Usually, the investigation of the replicator dynamics centers around a stability analysis of their stationary solutions. Although evolutionary stability and dynamic stability both intend to characterize the long-term outcome of frequency dependent selection, these concepts differ considerably in the 'philosophies' on which they are based. It is therefore not too surprising that they often lead to quite different evolutionary predictions (see, e. g. , Weissing 1983). The present paper intends to illustrate the incongruities between the two approaches towards a phenotypic theory of natural selection. A detailed game theoretical and dynamical analysis is given for a generic class of evolutionary normal form games.

Author : J. McKenzie Alexander
Publisher : Cambridge University Press
ISBN 13 : 1009380583
Total Pages : 115 pages
Book Rating : 4.84/5 ( download)

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Download or read book Evolutionary Game Theory written by J. McKenzie Alexander and published by Cambridge University Press. This book was released on 2023-03-31 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary game theory originated in population biology from the realisation that frequency-dependent fitness introduced a strategic element into evolution. Since its development, evolutionary game theory has been adopted by many social scientists, and philosophers, to analyse interdependent decision problems played by boundedly rational individuals. Its study has led to theoretical innovations of great interest for the biological and social sciences. For example, theorists have developed a number of dynamical models which can be used to study how populations of interacting individuals change their behaviours over time. In this introduction, this Element covers the two main approaches to evolutionary game theory: the static analysis of evolutionary stability concepts, and the study of dynamical models, their convergence behaviour and rest points. This Element also explores the many fascinating, and complex, connections between the two approaches.

Author : John Maynard Smith
Publisher : Cambridge University Press
ISBN 13 : 9780521288842
Total Pages : 244 pages
Book Rating : 4.43/5 ( download)

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Download or read book Evolution and the Theory of Games written by John Maynard Smith and published by Cambridge University Press. This book was released on 1982-10-21 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1982 book is an account of an alternative way of thinking about evolution and the theory of games.

Author : Larry Samuelson
Publisher : MIT Press
ISBN 13 : 9780262692199
Total Pages : 332 pages
Book Rating : 4.98/5 ( download)

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Download or read book Evolutionary Games and Equilibrium Selection written by Larry Samuelson and published by MIT Press. This book was released on 1997 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jun Tanimoto
Publisher : Springer
ISBN 13 : 4431549625
Total Pages : 214 pages
Book Rating : 4.28/5 ( download)

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Download or read book Fundamentals of Evolutionary Game Theory and its Applications written by Jun Tanimoto and published by Springer. This book was released on 2015-10-23 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​This book both summarizes the basic theory of evolutionary games and explains their developing applications, giving special attention to the 2-player, 2-strategy game. This game, usually termed a "2×2 game” in the jargon, has been deemed most important because it makes it possible to posit an archetype framework that can be extended to various applications for engineering, the social sciences, and even pure science fields spanning theoretical biology, physics, economics, politics, and information science. The 2×2 game is in fact one of the hottest issues in the field of statistical physics. The book first shows how the fundamental theory of the 2×2 game, based on so-called replicator dynamics, highlights its potential relation with nonlinear dynamical systems. This analytical approach implies that there is a gap between theoretical and reality-based prognoses observed in social systems of humans as well as in those of animal species. The book explains that this perceived gap is the result of an underlying reciprocity mechanism called social viscosity. As a second major point, the book puts a sharp focus on network reciprocity, one of the five fundamental mechanisms for adding social viscosity to a system and one that has been a great concern for study by statistical physicists in the past decade. The book explains how network reciprocity works for emerging cooperation, and readers can clearly understand the existence of substantial mechanics when the term "network reciprocity" is used. In the latter part of the book, readers will find several interesting examples in which evolutionary game theory is applied. One such example is traffic flow analysis. Traffic flow is one of the subjects that fluid dynamics can deal with, although flowing objects do not comprise a pure fluid but, rather, are a set of many particles. Applying the framework of evolutionary games to realistic traffic flows, the book reveals that social dilemma structures lie behind traffic flow.

Author : Mark Broom
Publisher : CRC Press
ISBN 13 : 1439853215
Total Pages : 522 pages
Book Rating : 4.14/5 ( download)

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Download or read book Game-Theoretical Models in Biology written by Mark Broom and published by CRC Press. This book was released on 2013-03-27 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well. The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner’s dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use MATLAB® to solve various games. Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behavior, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modeling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modeling of these diverse biological phenomena.

Author : American Mathematical Society. Short Course
Publisher : American Mathematical Soc.
ISBN 13 : 0821853260
Total Pages : 186 pages
Book Rating : 4.69/5 ( download)

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Download or read book Evolutionary Game Dynamics written by American Mathematical Society. Short Course and published by American Mathematical Soc.. This book was released on 2011-10-27 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures delivered at the 2011 AMS Short Course on Evolutionary Game Dynamics, held January 4-5, 2011 in New Orleans, Louisiana. Evolutionary game theory studies basic types of social interactions in populations of players. It combines the strategic viewpoint of classical game theory (independent rational players trying to outguess each other) with population dynamics (successful strategies increase their frequencies). A substantial part of the appeal of evolutionary game theory comes from its highly diverse applications such as social dilemmas, the evolution of language, or mating behaviour in animals. Moreover, its methods are becoming increasingly popular in computer science, engineering, and control theory. They help to design and control multi-agent systems, often with a large number of agents (for instance, when routing drivers over highway networks or data packets over the Internet). While these fields have traditionally used a top down approach by directly controlling the behaviour of each agent in the system, attention has recently turned to an indirect approach allowing the agents to function independently while providing incentives that lead them to behave in the desired way. Instead of the traditional assumption of equilibrium behaviour, researchers opt increasingly for the evolutionary paradigm and consider the dynamics of behaviour in populations of agents employing simple, myopic decision rules.