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.

The objective of this book is to provide a valuable compendium of problems as a reference for undergraduate and graduate students, faculty, researchers and practitioners of operations research and management science. These problems can serve as a basis for the development or study of assignments and exams. Also, they can be useful as a guide for the first stage of the model formulation, i.e. the definition of a problem. The book is divided into 11 chapters that address the following topics: Linear programming, integer programming, non linear programming, network modeling, inventory theory, queue theory, tree decision, game theory, dynamic programming and markov processes. Readers are going to find a considerable number of statements of operations research applications for management decision-making. The solutions of these problems are provided in a concise way although all topics start with a more developed resolution. The proposed problems are based on the research experience of the authors in real-world companies so much as on the teaching experience of the authors in order to develop exam problems for industrial engineering and business administration studies.

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.

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.

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.

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics' central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between 'soul and precision.'

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.

This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work's subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.

A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

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.

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.

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.

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.

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.

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 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.

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."

For decades, casino gaming has been steadily increasing in popularity worldwide. Blackjack is among the most popular of the casino table games, one where astute choices of playing strategy can create an advantage for the player. RISK AND REWARD analyzes the game in depth, pinpointing not just its optimal strategies but also its financial performance, in terms of both expected cash flow and associated risk. The book begins by describing the strategies and their performance in a clear, straightforward style. The presentation is self-contained, non-mathematical, and accessible to readers at all levels of playing skill, from the novice to the blackjack expert. Careful attention is also given to simplified, but still nearly optimal strategies that are easier to use in a casino. Unlike other books in the literature the author then derives each aspect of the strategy mathematically, to justify its claim to optimality. The derivations mostly use algebra and calculus, although some require more advanced analysis detailed in supporting appendices. For easy comprehension, formulae are translated into tables and graphs through extensive computation. This book will appeal to everyone interested in blackjack: those with mathematical training intrigued by its application to this popular game as well as all players seeking to improve their performance.

In his book "Marktform und Gleichgewicht", published initially in 1934, Heinrich von Stackelberg presented his groundbreaking leadership model of firm competition. In a work of great originality and richness, he described and analyzed a market situation in which the leader firm moves first and the follower firms then move sequentially. This game-theoretic model, now widely known as Stackelberg competition, has had tremendous impact on the theory of the firm and economic analysis in general, and has been applied to study decision-making in various fields of business. As the first translation of von Stackelberg's book into English, this volume makes his classic work available in its original form to an English-speaking audience for the very first time.

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.

This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

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.

The book is a benefit for graduate and postgraduate students in the areas of operations research, decision theory, optimization theory, linear algebra, interval analysis and fuzzy sets. The book will also be useful for the researchers in the respective areas. The first part of the book deals with decision making problems and procedures that have been established to combine opinions about alternatives related to different points of view. Procedures based on pairwise comparisons are thoroughly investigated. In the second part we investigate optimization problems where objective functions and constraints are characterized by extremal operators such as maximum, minimum or various triangular norms (t-norms). Matrices in max-min algebra are useful in applications such as automata theory, design of switching circuits, logic of binary relations, medical diagnosis, Markov chains, social choice, models of organizations, information systems, political systemsand clustering. The input data in real problems are usually not exact and can be characterized by interval values."

Market failure at medium intervals is inevitable in a capitalist economy. Such failures may not be seriously seen in the short run because market adjusts demand through hoarding of inventory or import of required goods and services. The market also adjusts demand in the long run through expansion of concerned industrial output and also by the entry of new firms. The crucial variable is price which also adjusts the commodity and the labor market. The problem comes when there are issues of overproduction, over capacity utilization of plants, over liquidation and excess supply of money, change in demand because of change in tastes and habits of consumers, households and the public. All these create knife edge disturbances in the economy. As a consequence they need adjustment through some variables such as employment and growth of population, saving propensity, technology, exhaustion of existing inventory, monetary and fiscal balancing. In this volume an attempt has been made to appraise the working of a market economy where short term disturbances may occur, market efficiency reduces, recessionary cycle emerges and after certain fundamental measures the market recovers. Starting with a brief recent history of the crisis and the recession, discussions in this volume turn to how deliberations in macroeconomics yield implications for specific policies, some of which have been tried and others still to be tested. Further in the volume we propose policies necessary for efficient regulation of the economic system, and give a brief assessment of the extent to which global policy coordination has been mulled in policy circles even if these are not seriously practiced.

This book is devoted to the study of dynamical models of decentralized economic systems. The models considered are based on the Leontief simple dynamic model with various mechanisms for decentralized planning and management. Branches of the economic system are treated as fully independent economic agents that plan their work according to their own purposes. It is shown that the lack of coordination between economic agents leads to a limit cycle for some economic indicators. Conversely, the exchange of information between the economic agents enables a move toward balanced growth. These results are generalized for the model with dynamics of the productive assets and for the model with the final consumption. The analysis also considers a problem of endogenous technological progress in a decentralized economy. The appendix includes a short review of non-negative matrices. The book offers a valuable resource for mathematical economists and graduate students specializing in mathematical economics.