Evolutionary Games And The Replicator Dynamics
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Evolutionary Games And The Replicator Dynamics
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Author : Saul Mendoza-Palacios
language : en
Publisher: Cambridge University Press
Release Date : 2024-06-06
Evolutionary Games And The Replicator Dynamics written by Saul Mendoza-Palacios and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Business & Economics categories.
This Element introduces the replicator dynamics for symmetric and asymmetric games where the strategy sets are metric spaces. Under this hypothesis the replicator dynamics evolves in a Banach space of finite signed measures. The authors provide a general framework to study the stability of the replicator dynamics for evolutionary games in this Banach space. This allows them to establish a relation between Nash equilibria and the stability of the replicator for normal a form games applicable to oligopoly models, theory of international trade, public good models, the tragedy of commons, and War of attrition game among others. They also provide conditions to approximate the replicator dynamics on a space of measures by means of a finite-dimensional dynamical system and a sequence of measure-valued Markov processes.
Evolutionary Games In Natural Social And Virtual Worlds
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Author : Daniel Friedman
language : en
Publisher: Oxford University Press
Release Date : 2016
Evolutionary Games In Natural Social And Virtual Worlds written by Daniel Friedman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Business & Economics categories.
Authors Daniel Friedman and Barry Sinervo show how to use theoretical developments in evolutionary game theory to build useful models describing parts of the worlds we live in --- the natural world of biology, the social world of politics and economics, and the virtual world that is emerging from our connected electronic devices.
Evolutionary Games And Population Dynamics
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Author : Josef Hofbauer
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-28
Evolutionary Games And Population Dynamics written by Josef Hofbauer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-28 with Mathematics categories.
Every form of behaviour is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realised how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centred not on the concept of rational players but on the population dynamics of behavioural programmes. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behaviour, and of the closely related interactions between species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions which can alter the basis of their success, i.e. to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions which punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.
Evolutionary Game Dynamics
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Author : American Mathematical Society. Short Course
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-10-27
Evolutionary Game Dynamics written by American Mathematical Society. Short Course and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-27 with Mathematics categories.
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.
Game Equilibrium Models I
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Author : Reinhard Selten
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Game Equilibrium Models I written by Reinhard Selten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Game Theory Evolving
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Author : Herbert Gintis
language : en
Publisher: Princeton University Press
Release Date : 2009-01-26
Game Theory Evolving written by Herbert Gintis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-26 with Business & Economics categories.
Since its original publication in 2000, Game Theory Evolving has been considered the best textbook on evolutionary game theory. This completely revised and updated second edition of Game Theory Evolving contains new material and shows students how to apply game theory to model human behavior in ways that reflect the special nature of sociality and individuality. The textbook continues its in-depth look at cooperation in teams, agent-based simulations, experimental economics, the evolution and diffusion of preferences, and the connection between biology and economics. Recognizing that students learn by doing, the textbook introduces principles through practice. Herbert Gintis exposes students to the techniques and applications of game theory through a wealth of sophisticated and surprisingly fun-to-solve problems involving human and animal behavior. The second edition includes solutions to the problems presented and information related to agent-based modeling. In addition, the textbook incorporates instruction in using mathematical software to solve complex problems. Game Theory Evolving is perfect for graduate and upper-level undergraduate economics students, and is a terrific introduction for ambitious do-it-yourselfers throughout the behavioral sciences. Revised and updated edition relevant for courses across disciplines Perfect for graduate and upper-level undergraduate economics courses Solutions to problems presented throughout Incorporates instruction in using computational software for complex problem solving Includes in-depth discussions of agent-based modeling
Evolutionary Game Theory
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Author : Jörgen W. Weibull
language : en
Publisher: MIT Press
Release Date : 1997
Evolutionary Game Theory written by Jörgen W. Weibull and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Business & Economics categories.
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.
Fundamentals Of Evolutionary Game Theory And Its Applications
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Author : Jun Tanimoto
language : en
Publisher: Springer
Release Date : 2015-10-23
Fundamentals Of Evolutionary Game Theory And Its Applications written by Jun Tanimoto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-23 with Business & Economics categories.
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.
Evolutionary Games And Equilibrium Selection
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Author : Larry Samuelson
language : en
Publisher: MIT Press
Release Date : 1997
Evolutionary Games And Equilibrium Selection written by Larry Samuelson and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Business & Economics categories.
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.
Dynamic Evolutionary Game Related To Elementary Large Games And Replicator Dynamics
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Author : Krzysztof Argasiński
language : en
Publisher:
Release Date : 2003
Dynamic Evolutionary Game Related To Elementary Large Games And Replicator Dynamics written by Krzysztof Argasiński and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.