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 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 Econophysics of the Kolkata Restaurant Problem and Related Games written by Bikas K. Chakrabarti and published by Springer. This book was released on 2017-07-19 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first comprehensive introduction to multi-agent, multi-choice repetitive games, such as the Kolkata Restaurant Problem and the Minority Game. It explains how the tangible formulations of these games, using stochastic strategies developed by statistical physicists employing both classical and quantum physics, have led to very efficient solutions to the problems posed. Further, it includes sufficient introductory notes on information-processing strategies employing both classical statistical physics and quantum mechanics. Games of this nature, in which agents are presented with choices, from among which their goal is to make the minority choice, offer effective means of modeling herd behavior and market dynamics and are highly relevant to assessing systemic risk. Accordingly, this book will be of interest to economists, physicists, and computer scientists alike.

Download or read book Game Theoretical Models in Biology written by Mark Broom and published by CRC Press. This book was released on 2022-08-03 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology, Second Edition 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 Python 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 behaviour, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modelling. 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 modelling of these diverse biological phenomena. In this thoroughly revised new edition, the authors have added three new chapters on the evolution of structured populations, biological signalling games, and a topical new chapter on evolutionary models of cancer. There are also new sections on games with time constraints that convert simple games to potentially complex nonlinear ones; new models on extortion strategies for the Iterated Prisoner’s Dilemma and on social dilemmas; and on evolutionary models of vaccination, a timely section given the current Covid pandemic. Features Presents a wide range of biological applications of game theory. Suitable for researchers and professionals in mathematical biology and the life sciences, and as a text for postgraduate courses in mathematical biology. Provides numerous examples, exercises, and Python code.

Download or read book Essays in Evolutionary Game Theory written by Ratul Lahkar and published by . This book was released on 2007 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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 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 516 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.

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 Essays on Epistemology and Evolutionary Game Theory written by Elias Tsakas and published by . This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Advances in Dynamic and Evolutionary Games written by Frank Thuijsman and published by Birkhäuser. This book was released on 2016-04-07 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 16th Symposium of the International Society of Dynamic Games, held July 9-12, 2014, in Amsterdam. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. They discuss theoretical developments, algorithmic methods, issues relating to lack of information, and applications in areas such as biological or economical competition, stability in communication networks, and maintenance decisions in an electricity market, just to name a few. Advances in Dynamic and Evolutionary Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.

Download or read book Essays on Evolutionary Game Theory and Its Applications written by Shota Fujishima and published by . This book was released on 2013 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three essays on evolutionary game theory and its applications. The first essay considers mechanism design in the evolutionary game-theoretic framework. The second essay studies equilibrium selection of coordination games by using an evolutionary game-theoretic concept. The third essay formulates a multi-regional economic growth model as an evolutionary game and characterizes the stability of its equilibria under an evolutionary dynamic. The summaries of each essay are provided below. In the first essay, I consider an implementation problem in a class of congestion games with players that have heterogeneous costs of taking actions. One application is to traffic congestion with drivers having heterogeneous time costs. The planner would like to design a price scheme under which the economy converges to an epsilon-optimum from any initial state when he does not have full knowledge of the cost functions, and he can observe only the aggregate strategy distribution. Although the planner would like to internalize the externalities, the informational constraints compel him to estimate their values. Using the optimality and equilibrium conditions, I construct a practical estimation procedure that yields the true values of externalities in the long-run. Moreover, I show that our scheme makes the epsilon-optimum globally stable under the best response dynamic if the externalities among players taking the same action are sufficiently large relative to those among players taking different actions. In the second essay, I study the long-run outcomes of noisy asynchronous repeated games with players that are heterogeneous in in terms of their patience. The players repeatedly play a 2-by-2 coordination game with random pair-wise matching. The games are noisy because the players may make mistakes when choosing their actions and are asynchronous because only one player can move in each period. I characterize the long-run outcomes of Markov perfect equilibrium that are robust to the mistakes and show that if there is a sufficiently patient player, the efficient state can be the unique robust outcome even if it is risk-dominated. Because I need heterogeneity for the result, I argue that it enables the most patient player in effect to be the leader. In the third essay, I consider a microfounded urban growth model with two regions and a mass of mobile workers to study interactions among growth, agglomeration, and urban congestion. Unlike previous research in the urban growth literature, I formulate the model as a one-shot game and take an evolutionary game-theoretic approach for stability analysis. My approach enables us to analyze the stability of nonstationary equilibria in which populations of each region are not constant over time. I show that if both the expenditure share for housing and inter-regional transport cost are small, a stable stationary equilibrium does not exist. Moreover, in such a case, I show that there can exist a stable nonstationary equilibrium in which mobile workers agglomerate in one region at first but some of them migrate to the other region later. I argue that such a nonstationary location pattern is related to return migration.

Download or read book Game Equilibrium Models I written by Reinhard Selten and published by Springer. This book was released on 2010-12-01 with total page 330 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.

Download or read book Higher Order Game Dynamics in Population Games and Reinforcement Learning written by Bolin Gao and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary game theory is a game-theoretic framework which attempts to describe the outcomes of competitive scenarios involving large populations of anonymous agents, also known as population games. A significant portion of evolutionary game theory is devoted to the study of evolutionary game dynamics. These game dynamics are often posed as first-order ordinary differential equations (ODEs) in continuous-time, and the equilibria of these ODEs can coincide with certain solution concept associated with a game. Research into the class of higher-order game dynamics presents an opportunity to potentially significantly enlarge the set of well-behaved game dynamics and may reveal many features of game dynamics that are not present in their first-order counterparts. We begin our design and analysis of higher-order game dynamics using a novel control-theoretic approach. The utility of such a control approach manifests itself in three major ways. First, by representing the learning rule as a state-space system, we provide a generalization to the class of higher-order game dynamics previously considered in the literature, most of which were studied with respect to very specific forms of learning rules. Secondly, we can design control laws through well-established control techniques that allow us to overcome non-convergence issues associated with certain types of higher-order game dynamics. Last but not least, we show that by posing reinforcement learning schemes as feedback control systems, we are able to leverage a host of powerful tools from convex analysis, monotone operator theory, and Lyapunov theory to systematically design higher-order game dynamics with guaranteed convergence in large classes of games.

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 Essays in Evolutionary Game Theory written by Joerg Oechssler and published by . This book was released on 1994 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: