Download or read book Nonlinear Dynamics Of Cycles In Evolutionary Games written by Danielle Flora Pougoum Toupo and published by . This book was released on 2016 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary game theorists have devoted a great deal of effort to answering questions related to cooperation. They typically combine game theory with coupled nonlinear differential equations to create an evolutionary dynamic system. Indeed, cooperation, where individuals pay costs to benefit others, is a cornerstone of human civilization. The most common mathematical model used to study evolutionary dynamic systems is the replicator equation: a payoff matrix is defined such that strategies with a payoff above average are more and more prevalent over time while strategies with a payoff below average are less prevalent. Interestingly, many of the dynamics studied using the replicator equation have applications inside and outside the field of of biology, including the dynamics of sociological systems, the evolution of language, fashion, autocatalytic chemical networks, behavioral dynamics, and multi-agent decision making in social networks. Nonetheless, some non-trivial questions have not yet been explored. In our work, we explore the long term nonlinear dynamics of evolutionary dynamical systems with the replicator equation in which agents are allowed to mutate into each other using various graph-theoretic mutation patterns. Additionally, we introduce a minimal mathematical model to investigate which processes or strategies are favored by natural selection in a competitive environment where different levels of resources are available and agents have a choice between making long term rational decisions or quick and effortless decisions that focus on the present.

Download or read book Evolutionary Games and Population Dynamics written by Josef Hofbauer and published by Cambridge University Press. This book was released on 1998-05-28 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Essay on Nonlinear evolutionary game dynamics written by Marius Ionut Ochea and published by Rozenberg Publishers. This book was released on 2010 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Download or read book Symmetry and Collective Fluctuations in Evolutionary Games written by Eric Smith and published by Iop Expanding Physics. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary game theory has the potential to provide an integrated framework to model many aspects of evolution, development, and ecology. The reliable use of game models, however, requires an understanding of their behaviour when the number of players becomes very large, resulting in the emergence of thermodynamic limits. This behaviour is controlled by the symmetries that characterize the game, and the approach to the thermodynamic limit is governed by collective fluctuations in the actions of the players. In this book, the authors present methods to derive large-deviations limits for population processes, and apply these to game models illustrating the many roles of symmetry and collective fluctuations in evolutionary dynamics.

Download or read book Symmetry and Collective Fluctuations in Evolutionary Games written by Eric Smith and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary game theory has the potential to provide an integrated framework to model many aspects of evolution, development, and ecology. The reliable use of game models, however, requires an understanding of their behaviour when the number of players becomes very large, resulting in the emergence of thermodynamic limits. This behaviour is controlled by the symmetries that characterize the game, and the approach to the thermodynamic limit is governed by collective fluctuations in the actions of the players. In this book, the authors present methods to derive large-deviations limits for population processes, and apply these to game models illustrating the many roles of symmetry and collective fluctuations in evolutionary dynamics.

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 223 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.

Download or read book A Class of Evolutionary Models for Participation Games written by Pietro Dindo and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a framework to analyze the interaction of boundedly rational heterogeneous agents repeatedly playing a participation game with negative feedback. We assume that agents use different behavioral rules prescribing how to play the game conditionally on the outcome of previous rounds. We update the fraction of the population using each rule by means of a general class of evolutionary dynamics based on imitation, which contains both replicator and logit dynamics. Our model is analyzed by a combination of formal analysis and numerical simulations and is able to replicate results from the experimental and computational literature on these types of games. In particular, irrespective of the specific evolutionary dynamics and of the exact behavioral rules used, the dynamics of the aggregate participation rate is consistent with the symmetric mixed strategy Nash equilibrium, whereas individual behavior clearly departs from it. Moreover, as the number of players or speed of adjustment increase the evolutionary dynamics typically becomes unstable and leads to endogenous fluctuations around the steady state. These fluctuations are robust with respect to behavioral rules that try to exploit them. -- Participation games ; Heterogeneous behavioral rules ; Revision protocol ; Replicator Dynamics ; Logit Dynamics ; Nonlinear dynamics.

Download or read book Darwinian Dynamics written by Richard E. Michod and published by Princeton University Press. This book was released on 2021-01-12 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of fitness has long been a topic of intense debate among evolutionary biologists and their critics, with its definition and explanatory power coming under attack. In this book, Richard Michod offers a fresh, dynamical interpretation of evolution and fitness concepts. He argues that evolution has no enduring products; what matters is the process of genetic change. Whereas many biologists have focused on competition and aggression as determining factors in survival, Michod, by concentrating on the emergence of individuality at new and more complex levels, finds that cooperation plays even a greater role. Michod first considers the principles behind the hierarchically nested levels of organization that constitute life: genes, chromosomes, genomes, cells, multicellular organisms, and societies. By examining the evolutionary transitions from the molecular level up to the whole organism, the author explains how cooperation and conflict in a multilevel setting leads to new levels of fitness. He builds a model of fitness drawing on recent developments in ecology and multilevel selection theory and on new explanations of the origin of life. Michod concludes with a discussion of the philosophical implications of his theory of fitness, a theory that addresses the most fundamental and unique concept in all of biology.

Download or read book Foundations of Social Evolution written by Steven A. Frank and published by Princeton University Press. This book was released on 2019-12-31 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a masterly theoretical treatment of one of the central problems in evolutionary biology, the evolution of social cooperation and conflict. Steven Frank tackles the problem with a highly original combination of approaches: game theory, classical models of natural selection, quantitative genetics, and kin selection. He unites these with the best of economic thought: a clear theory of model formation and comparative statics, the development of simple methods for analyzing complex problems, and notions of information and rationality. Using this unique, multidisciplinary approach, Frank makes major advances in understanding the foundations of social evolution. Frank begins by developing the three measures of value used in biology--marginal value, reproductive value, and kin selection. He then combines these measures into a coherent framework, providing the first unified analysis of social evolution in its full ecological and demographic context. Frank also extends the theory of kin selection by showing that relatedness has two distinct meanings. The first is a measure of information about social partners, with close affinity to theories of correlated equilibrium and Bayesian rationality in economic game theory. The second is a measure of the fidelity by which characters are transmitted to future generations--an extended notion of heritability. Throughout, Frank illustrates his methods with many examples, including a complete reformulation of the theory of sex allocation. The book also provides a unique "how-to" guide for constructing models of social behavior. It is essential reading for evolutionary biologists and for economists, mathematicians, and others interested in natural selection.

Download or read book Nonlinear Parametric Excitation of an Evolutionary Dynamical System written by Rocio Esmeralda Ruelas and published by . This book was released on 2015 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary Dynamics is a field that combines Dynamical Systems with Game Theory. Game Theory studies the costs and benefits of competing strategies. This competition between strategies is called a "game" and is usually represented by a payoff matrix. The entries of the payoff matrix represent the loss or gain received when one type of strategy plays against another. Through the use of differential equations known as the replicator equations, we can use the information in the payoff matrix to model the change in relative population (or frequency) for all of the strategies. Once we have written the evolutionary equations we can study the dynamics using the methods and theorems developed in the field of Dynamical Systems. The Rock-Paper-Scissor model is used to describe systems where there are three strategies and where each strategy has an advantage over one strategy, but a disadvantage over the other strategy. The model is named after the classic game in which Rock beats Scissors, Scissors beats Paper, and Paper beats Rock. Using the replicator equations, we can model the changes that occur in the relative populations of the strategies. Strategies whose payoffs are relatively better will have increasing population frequencies while those with lower payoffs will have decreasing population frequencies. In this work, we consider a variation of the standard RPS game where the payoffs vary periodically in time.

Download or read book Evolutionary Game Theory Natural Selection and Darwinian Dynamics written by Thomas L. Vincent and published by Cambridge University Press. This book was released on 2012-08-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: All of life is a game, and evolution by natural selection is no exception. The evolutionary game theory developed in this 2005 book provides the tools necessary for understanding many of nature's mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher's Fundamental Theorem of Natural Selection, and the nature of life's evolutionary game.

Download or read book Evolutionary Games in Natural Social and Virtual Worlds written by Daniel Friedman and published by Oxford University Press. This book was released on 2016-02-01 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 25 years, evolutionary game theory has grown with theoretical contributions from the disciplines of mathematics, economics, computer science and biology. It is now ripe for applications. In this book, Daniel Friedman---an economist trained in mathematics---and Barry Sinervo---a biologist trained in mathematics---offer the first unified account of evolutionary game theory aimed at applied researchers. They show how to use a single set of tools to build useful models for three different worlds: the natural world studied by biologists; the social world studied by anthropologists, economists, political scientists and others; and the virtual world built by computer scientists and engineers. The first six chapters offer an accessible introduction to core concepts of evolutionary game theory. These include fitness, replicator dynamics, sexual dynamics, memes and genes, single and multiple population games, Nash equilibrium and evolutionarily stable states, noisy best response and other adaptive processes, the Price equation, and cellular automata. The material connects evolutionary game theory with classic population genetic models, and also with classical game theory. Notably, these chapters also show how to estimate payoff and choice parameters from the data. The last eight chapters present exemplary game theory applications. These include a new coevolutionary predator-prey learning model extending rock-paper-scissors; models that use human subject laboratory data to estimate learning dynamics; new approaches to plastic strategies and life cycle strategies, including estimates for male elephant seals; a comparison of machine learning techniques for preserving diversity to those seen in the natural world; analyses of congestion in traffic networks (either internet or highways) and the “price of anarchy”; environmental and trade policy analysis based on evolutionary games; the evolution of cooperation; and speciation. As an aid for instruction, a web site provides downloadable computational tools written in the R programming language, Matlab, Mathematica and Excel.

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.

Download or read book Replicator Dynamics with Alternate Growth Functions Delay and Quasiperiodic Forcing written by Elizabeth Nicholas Wesson and published by . This book was released on 2015 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary dynamics combines game theory and nonlinear dynamics to model competition in biological and social situations. The replicator equation is a standard paradigm in evolutionary dynamics. The growth rate of each strategy is its excess fitness: the deviation of its fitness from the average. The gametheoretic aspect of the model lies in the choice of fitness function, which is determined by a payoff matrix. Two well-known replicator systems are the threestrategy Rock-Paper-Scissors game and the two-strategy Hawk-Dove game. In this work, we analyze the dynamics of replicator systems with three different types of modifications. The first generalization of the replicator model is given by considering alternate growth functions. We find that in the Rock-Paper-Scissors game with a logistic growth function, there are several fixed points that do not exist in the standard replicator model. The system exhibits both periodic motion and convergence to attractors. We also analyze replicator systems with delayed interactions between strategies. We consider a symmetric delay model, in which the fitness of each strategy is its expected payoff delayed by a time interval; and an asymmetric model, in which same-strategy terms appearing in the fitness of a given strategy are not delayed. In both cases, limit cycles arise that cannot occur in the usual replicator model. Finally, we examine Rock-Paper-Scissors systems with quasiperiodic forcing of the payoff coefficients. This model may represent systems in which the competition is affected by cyclical processes on different time-scales. We find that the stability of the equilibrium state depends sensitively on the two forcing frequencies; in fact, the region of stability has fractal boundary.

Download or read book Games and Dynamics in Economics written by Ferenc Szidarovszky and published by Springer Nature. This book was released on 2020-04-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the latest advances in nonlinear dynamic modeling in economics and finance, mainly—but not solely—based on the description of strategic interaction by using concepts and methods from dynamic and evolutionary game theory. The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theory of dynamical systems is used to analyze the local and global bifurcations that characterize complex behaviors observed in social systems where heterogeneous and boundedly rational economic agents interact. Nonlinear dynamical systems, represented by difference and differential and functional equations, are extensively used to simulate the behavior of time-evolving economic systems, also in the presence of time lags, discontinuities, and hysteresis phenomena. In addition, some theoretical issues and particular applications are discussed, as well. The contributions gathered here offer an up-to-date review of the latest research in this rapidly developing research area.