This book integrates the fundamentals, methodology, and major application fields of noncooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games including games represented by finite trees; matrix and bimatrix games as well as oligopolies; cooperative solution concepts; games under uncertainty; dynamic games and conflict resolution. The methodology is illustrated by carefully chosen examples, applications and case studies which are selected from economics, social sciences, engineering, the military and homeland security. This book is highly recommended to readers who are interested in the in-depth and up-to-date integration of the theory and ever-expanding application areas of game theory.

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 "2x2 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 2x2 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 2x2 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.

This wide-ranging and accessible book serves as a fascinating guide to the strategies and concepts that help us understand the boundaries between physics, on the one hand, and sociology, economics, and biology on the other. From cooperation and criticality to flock dynamics and fractals, the author addresses many of the topics belonging to the broad theme of complexity. He chooses excellent examples (requiring no prior mathematical knowledge) to illuminate these ideas and their implications. The lively style and clear description of the relevant models will appeal both to novices and those with an existing knowledge of the field.

This book covers the modelling of human behaviour in the education and labour markets, which due to their interdependency are viewed as one system. Important factors influencing the decision-making of individuals and firms in this system are discussed. The role of social environment and networks is stressed. The approach of agent-based modelling is presented and compared with standard economic modelling and other simulation techniques in the context of modelling complex adaptive systems. Practical questions in building agent-based models of labour-education market system with social networks are discussed. These questions include modelling the structure of education system and agent behaviour there; modelling and calibrating the labour market without and with firms; generating the social network, defining its behaviour and calibrating it; and embedding the resulting system into a larger model.

This textbook presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It is the second, revised version of the successful 2008 edition. The book covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book contains a problem section. Hints, answers and solutions are included.

Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a 'secret weapon' by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler's internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.

This is a textbook for university juniors, seniors, and graduate students majoring in economics, applied mathematics, and related fields. Each chapter is structured so that a core concept of that chapter is presented with motivations, useful applications are given, and related advanced topics are discussed for future study. Many helpful exercises at various levels are provided at the end of each chapter. Therefore, this book is most suitable for readers who intend to study non-cooperative game theory rigorously for both theoretical studies and applications. Game theory consists of non-cooperative games and cooperative games. This book covers only non-cooperative games, which are major tools used in current economics and related areas. Non-cooperative game theory aims to provide a mathematical prediction of strategic choices by decision makers (players) in situations of conflicting interest. Through the logical analyses of strategic choices, we obtain a better understanding of social (economic, business) problems and possible remedies. The book contains many well-known games such as the prisoner's dilemma, chicken (hawk-dove) game, coordination game, centipede game, and Cournot, Bertrand, and Stackelberg models in oligopoly. It also covers some advanced frameworks such as repeated games with non-simultaneous moves, repeated games with overlapping generations, global games, and voluntarily separable repeated prisoner's dilemma, so that readers familiar with basic game theory can expand their knowledge. The author's own research is reflected in topics such as formulations of information and evolutionary stability, which makes this book unique.

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.

These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on "Stochastics of Environmental and Financial Economics (SEFE)", being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.

Theory.- Review of Probability.- Conditional Expectation.- Martingales.- Markov Chains.- Game Theory.- House Advantage.- Gambler's Ruin.- Betting Systems.- Bold Play.- Optimal Proportional Play.- Card Theory.- Applications.- Slot Machines.- Roulette.- Keno.- Craps.- House-Banked Poker.- Video Poker.- Faro.- Baccarat.- Trente et Quarante.- Twenty-One.- Poker.

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

In economics agents are assumed to choose on the basis of rational calculations aimed at the maximization of their pleasure or profit. Formally, agents are said to manifest transitive and consistent preferences in attempting to maximize their utility in the presence of several constraints. They operate according to the choice imperative: given a set of alternatives, choose the best. This imperative works well in a static and simplistic framework, but it may fail or vary when 'the best' is changing continuously. This approach has been questioned by a descriptive approach that springing from the complexity theory tries to give a scientific basis to the way in which individuals really choose, showing that those models of human nature is routinely falsified by experiments since people are neither selfish nor rational. Thus inductive rules of thumb are usually implemented in order to make decisions in the presence of incomplete and heterogeneous information sets.

Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

The "Shapley value" of a finite multi- person game associates to each player the amount he should be willing to pay to participate. This book extends the value concept to certain classes of non-atomic games, which are infinite-person games in which no individual player has significance. It is primarily a book of mathematics--a study of non-additive set functions and associated linear operators. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This is a book on the basics of mathematics and computation and their uses in economics for modern day students and practitioners. The reader is introduced to the basics of numerical analysis as well as the use of computer programs such as Matlab and Excel in carrying out involved computations. Sections are devoted to the use of Maple in mathematical analysis. Examples drawn from recent contributions to economic theory and econometrics as well as a variety of end of chapter exercises help to illustrate and apply the presented concepts.

The mathematical theory of democracy deals with selection of representatives who make decisions on behalf of the whole society. In this book, the notion of representativeness is operationalized with the index of popularity (the average percentage of the population whose opinion is represented on a number of issues) and the index of universality (the frequency of cases when the opinion of a majority is represented). These indices are applied to evaluate and study the properties of single representatives (e.g. president) and representative bodies (e.g. parliament, magistrate, cabinet, jury, coalition). To bridge representative and direct democracy, an election method is proposed that is based not on voting but on indexing candidates with respect to the electorate's political profile. In addition, societal and non-societal applications are considered.

Tools and methods from complex systems science can have a considerable impact on the way in which the quantitative assessment of economic and financial issues is approached, as discussed in this thesis. First it is shown that the self-organization of financial markets is a crucial factor in the understanding of their dynamics. In fact, using an agent-based approach, it is argued that financial markets' stylized facts appear only in the self-organized state. Secondly, the thesis points out the potential of so-called big data science for financial market modeling, investigating how web-driven data can yield a picture of market activities: it has been found that web query volumes anticipate trade volumes. As a third achievement, the metrics developed here for country competitiveness and product complexity is groundbreaking in comparison to mainstream theories of economic growth and technological development. A key element in assessing the intangible variables determining the success of countries in the present globalized economy is represented by the diversification of the productive basket of countries. The comparison between the level of complexity of a country's productive system and economic indicators such as the GDP per capita discloses its hidden growth potential.

Mathematical demography is the centerpiece of quantitative social science. The founding works of this field from Roman times to the late Twentieth Century are collected here, in a new edition of a classic work by David R. Smith and Nathan Keyfitz. Commentaries by Smith and Keyfitz have been brought up to date and extended by Kenneth Wachter and Herve Le Bras, giving a synoptic picture of the leading achievements in formal population studies. Like the original collection, this new edition constitutes an indispensable source for students and scientists alike, and illustrates the deep roots and continuing vitality of mathematical demography.

This original and timely monograph describes a unique self-contained excursion that reveals to the readers the roles of two basic cognitive abilities, i.e. intention recognition and arranging commitments, in the evolution of cooperative behavior. This book analyses intention recognition, an important ability that helps agents predict others' behavior, in its artificial intelligence and evolutionary computational modeling aspects, and proposes a novel intention recognition method. Furthermore, the book presents a new framework for intention-based decision making and illustrates several ways in which an ability to recognize intentions of others can enhance a decision making process. By employing the new intention recognition method and the tools of evolutionary game theory, this book introduces computational models demonstrating that intention recognition promotes the emergence of cooperation within populations of self-regarding agents. Finally, the book describes how commitment provides a pathway to the evolution of cooperative behavior, and how it further empowers intention recognition, thereby leading to a combined improved strategy.

Transnational Cooperation: An Issue-Based Approach presents an analysis of transnational cooperation or collective action that stresses basic concepts and intuition. Throughout the book, authors Clint Peinhardt and Todd Sandler identify factors that facilitate and/or inhibit such cooperation. The first four chapters lay the analytical foundations for the book, while the next nine chapters apply the analysis to a host of exigencies and topics of great import. The authors use elementary game theory as a tool for illustrating the ideas put forth in the text. Game theory reminds us that rational actors (for example, countries, firms, or individuals) must account for the responses by other rational actors. The book assumes no prior knowledge of game theory; all game-theoretic concepts and analyses are explained in detail to the reader. Peinhardt and Sandler also employ paired comparisons in illustrating the book's concepts. The book is rich in applications and covers a wide range of topics, including superbugs, civil wars, money laundering, financial crises, drug trafficking, terrorism, global health concerns, international trade liberalization, acid rain, leadership, sovereignty, and many others. Students, researchers, and policymakers alike have much to gain from Transnational Cooperation. It is a crossover book for economics, political science, and public policy.

This second edition expands the first chapters, which focus on the approach to risk management issues discussed in the first edition, to offer readers a better understanding of the risk management process and the relevant quantitative phases. In the following chapters the book examines life insurance, non-life insurance and pension plans, presenting the technical and financial aspects of risk transfers and insurance without the use of complex mathematical tools. The book is written in a comprehensible style making it easily accessible to advanced undergraduate and graduate students in Economics, Business and Finance, as well as undergraduate students in Mathematics who intend starting on an actuarial qualification path. With the systematic inclusion of practical topics, professionals will find this text useful when working in insurance and pension related areas, where investments, risk analysis and financial reporting play a major role.

This book presents a rigorous treatment of the mathematical instruments available for dealing with income distributions, in particular Lorenz curves and related methods. The methods examined allow us to analyze, compare and modify such distributions from an economic and social perspective. Though balanced income distributions are key to peaceful coexistence within and between nations, it is often difficult to identify the right kind of balance needed, because there is an interesting interaction with innovation and economic growth. The issue of justice, as discussed in Thomas Piketty's bestseller "Capital in the Twenty-First Century" or in the important book "The Price of Inequality" by Nobel laureate Joseph Stiglitz, is also touched on. Further, there is a close connection to the issue of democracy in the context of globalization. One highlight of the book is its rigorous treatment of the so-called Atkinson theorem and some extensions, which help to explain under which type of societal utility functions nations tend to operate either in the direction of more balance or less balance. Finally, there are some completely new insights into changing the balance pattern of societies and the kind of coalitions between richer and poorer parts of society to organize political support in democracies in either case. Oxford University's Sir Tony Atkinson, well known for his so-called Atkinson theorem, writes in his foreword to the book: "[The authors] contribute directly to t he recent debates that are going on in politics. [...] with this book the foundation of arguments concerning a proper balance in income distribution in the sense of identifying an 'efficient inequality range' has got an additional push from mathematics, which I appreciate very much."

This is the first comprehensive monograph on the mathematical theory of the solitaire game "The Tower of Hanoi" which was invented in the 19th century by the French number theorist Edouard Lucas. The book comprises a survey of the historical development from the game's predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpinski graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the "Tower of London", are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement threshold and context of choice. The second edition has been updated to include the most recent developments and a new chapter on classic and new results for infinite sets.

Human development from birth through adulthood is a complex interplay of many interacting forces. Children's internal processes are manifest in behaviors that are sculpted by their experiences, most notably with primary caregivers. Because the discipline of psychology explores human behavior and cognition, the techniques employed for developmental analysis must be able to describe, depict, and quantify these complex processes. State Space Grids provides the framework, basic method, rationale, and advanced techniques for translating the behavior of children, adolescents, and parents into visible, traceable data. This seminar-between-covers takes readers step by step from conceptualization through implementation of projects, with examples from a range of current research within and outside child development. Links are included for the GridWare software program and related user resources. And although state space grids need not be used only to analyze dynamic systems, they serve as an excellent tool for honing systemic thinking. Key coverage in this volume includes: Dynamic systems and the origins of state space grids. The state of research using state space grids. Introducing GridWare and how it works. How to use state space grids, from idea through finished project. Within-grid and between-grid analysis. Conducting advanced analysis. State Space Grids is an essential reference for researchers across such disciplines as psychology, neuroscience, economics, computer science, and agricultural science.