Three leading experts have produced a landmark work based on a set of working papers published by the Center for Operations Research and Econometrics (CORE) at the Universite Catholique de Louvain in 1994 under the title 'Repeated Games', which holds almost mythic status among game theorists. Jean-Francois Mertens, Sylvain Sorin and Shmuel Zamir have significantly elevated the clarity and depth of presentation with many results presented at a level of generality that goes far beyond the original papers - many written by the authors themselves. Numerous results are new, and many classic results and examples are not to be found elsewhere. Most remain state of the art in the literature. This book is full of challenging and important problems that are set up as exercises, with detailed hints provided for their solutions. A new bibliography traces the development of the core concepts up to the present day.

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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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.

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.

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 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."

Three leading experts have produced a landmark work based on a set of working papers published by the Center for Operations Research and Econometrics (CORE) at the Universite Catholique de Louvain in 1994 under the title 'Repeated Games', which holds almost mythic status among game theorists. Jean-Francois Mertens, Sylvain Sorin and Shmuel Zamir have significantly elevated the clarity and depth of presentation with many results presented at a level of generality that goes far beyond the original papers - many written by the authors themselves. Numerous results are new, and many classic results and examples are not to be found elsewhere. Most remain state of the art in the literature. This book is full of challenging and important problems that are set up as exercises, with detailed hints provided for their solutions. A new bibliography traces the development of the core concepts up to the present day.

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.

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.

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."

Political Game Theory, first published in 2007, is a self-contained introduction to game theory and its applications to political science. The book presents choice theory, social choice theory, static and dynamic games of complete information, static and dynamic games of incomplete information, repeated games, bargaining theory, mechanism design and a mathematical appendix covering, logic, real analysis, calculus and probability theory. The methods employed have many applications in various disciplines including comparative politics, international relations and American politics. Political Game Theory is tailored to students without extensive backgrounds in mathematics, and traditional economics, however there are also many special sections that present technical material that will appeal to more advanced students. A large number of exercises are also provided to practice the skills and techniques discussed.

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.

This book provides the current status of research on the application of OR methods to solve emerging and relevant operations management problems. Each chapter is a selected contribution of the IO2021 - XXI Congress of APDIO, the Portuguese Association of Operational Research, held in Figueira da Foz from 7 to 8 November 2021. Under the theme of analytics for a better world, the book presents interesting results and applications of OR cutting-edge methods and techniques to various real-world problems. Of particular importance are works applying nonlinear, multi-objective optimization, hybrid heuristics, multicriteria decision analysis, data envelopment analysis, simulation, clustering techniques and decision support systems, in different areas such as supply chain management, production planning and scheduling, logistics, energy, telecommunications, finance and health. All chapters were carefully reviewed by the members of the scientific program committee.

Selected papers submitted by participants of the international Conference "Stochastic Analysis and Applied Probability 2010" ( www.saap2010.org ) make up the basis of this volume.

The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was organized by the "Applied Mathematics & Mathematical Physics" research unit of the preparatory institute to the military academies of Sousse (Tunisia), chaired by Mounir Zili.

The papers cover theoretical, numerical and applied aspects of stochastic processes and stochastic differential equations. The study of such topic is motivated in part by the need to model, understand, forecast and control the behavior of many natural phenomena that evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few.

As this book emphasizes the importance of numerical and theoretical studies of the stochastic differential equations and stochastic processes, it will be useful for a wide spectrum of researchers in applied probability, stochastic numerical and theoretical analysis and statistics, as well as for graduate students.

To make it more complete and accessible for graduate students, practitioners and researchers, the editors Mounir Zili and Daria Filatova have included a survey dedicated to the basic concepts of numerical analysis of the stochastic differential equations, written by Henri Schurz.

These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for "pure" mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.

This book provides a comprehensive study of asymmetric territorial conflict combining game theory, statistical empirical analysis and historiographic analysis. Using the Israeli-Palestine conflict as a case study, it tests the model on a database of almost four hundred territorial conflicts.

The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

Drawing on a wealth of new archival material, including personal correspondence and diaries, Robert Leonard tells the fascinating story of the creation of game theory by Hungarian Jewish mathematician John von Neumann and Austrian economist Oskar Morgenstern. Game theory first emerged amid discussions of the psychology and mathematics of chess in Germany and fin-de-siecle Austro-Hungary. In the 1930s, on the cusp of anti-Semitism and political upheaval, it was developed by von Neumann into an ambitious theory of social organization. It was shaped still further by its use in combat analysis in World War II and during the Cold War. Interweaving accounts of the period s economics, science, and mathematics, and drawing sensitively on the private lives of von Neumann and Morgenstern, Robert Leonard provides a detailed reconstruction of a complex historical drama.

Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.

Broad and diverse ranges of activities are conducted within and by organized groups of individuals, including political, economic and social activities. These activities have become a subject of intense interest in economics and game theory. Some of the topics investigated in this collection are models of networks of power and privilege, trade networks, co-authorship networks, buyer-seller networks with differentiated products, and networks of medical innovation and the adaptation of new information. Other topics are social norms on punctuality, clubs and the provision of club goods and public goods, research and development and collusive alliances among corporations, and international alliances and trading agreements. While relatively recent, the literature on game theoretic studies of group formation in economics is already vast. This volume provides an introduction to this important literature on game-theoretic treatments of situations with networks, clubs, and coalitions, including some applications.