What if life is a game? Are you winning? Have you even decided what 'winning' is? Game design could be defined in many ways, but here the term is used to denote the practice of creating choices. Designing a game, in this sense, involves crafting limits, rewards, incentives, and risks in such a way that the person who interacts with the game - the player - makes choices that have consequences. Edward Castronova urges readers to think about the fundamentals of the human condition and compare them to different games that we all know. In some ways, life is like an idle game: providing unchallenging distractions that fit easily into a person's daily routine. In other ways, life is like the game Minesweeper: You poke in different places to learn about what you don't know, taking care to avoid big explosions. Or, life is like a role-playing game: You adopt a persona and speak your part, always seeking adventure. Bringing together questions relating to diverse fields - such as politics, economics, sociology and philosophy - Castronova persuades readers to broaden the scope of game design to answer questions about life's everyday obstacles. The object of this book is to take seriously the idea that life is a game. The goal is not to make readers wealthier or healthier. Its goal is to go on a journey into the human condition, with game design as a guide.

This proceedings volume convenes selected, peer-reviewed papers presented at the 3rd International Conference on Mathematics and its Applications in Science and Engineering - ICMASE 2022, which was held on July 4-7, 2022 by the Technical University of Civil Engineering of Bucharest, Romania. Works in this volume cover new developments in applications of mathematics in science and engineering, with emphasis on mathematical and computational modeling of real-world problems. Topics range from the use of differential equations to model mechanical structures to the employ of number theory in the development of information security and cryptography. Educational issues specific to the acquisition of mathematical competencies by engineering and science students at all university levels are also touched on. Researchers and university students are the natural audiences for this book, which can be equally appealing to practitioners seeking up-to-date techniques in mathematical applications to different contexts and disciplines.

DLP denotes a dynamic-linear modeling and optimization approach to computational decision support for resource planning problems that arise, typically, within the natural resource sciences and the disciplines of operations research and operational engineering. It integrates techniques of dynamic programming (DP) and linear programming (LP) and can be realized in an immediate, practical and usable way. Simultaneously DLP connotes a broad and very general modeling/ algorithmic concept that has numerous areas of application and possibilities for extension. Two motivating examples provide a linking thread through the main chapters, and an appendix provides a demonstration program, executable on a PC, for hands-on experience with the DLP approach.

This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.

Game theory has revolutionized economics research and teaching during the past two decades. There are few undergraduate or graduate courses in which it does not form a core component. Game theory is the study of multi-decision problems and such problems occur frequently in economics. Industrial organization provides many examples where firms must consider the reactions of others. But there are many other areas in which it is applicable - from individual workers vying for promotion to countries competing or colluding to choose trade policies.

Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampere equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton-Jacobi-Bellman equations Improving policies for Hamilton-Jacobi-Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton-Jacobi-Bellman equations based on diagonally implicit symplectic Runge-Kutta methods Numerical solution of the simple Monge-Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton-Jacobi-Bellman equation within the European Union Emission Trading Scheme

Co-opetition offers a new way of thinking that combines competition and cooperation. It is the first book to adapt game theory to the needs of CEOs, managers and entrepreneurs. Though often compared to games like chess or poker, business is different - people are free to change the rules, the players, the boundaries, even the game itself. The essence of business success lies in making sure you are in the right game. Actively shaping which game you play, and how you play it, is the core of the innovative business strategy laid out in Co-opetition. Barry Nalebuff and Adam Brandenburger, professors at Yale and Harvard, are pioneers in the practice of applying the science of game theory to the art of corporate strategy. They have devised a practice-oriented model to help you break out of the traditional win-lose or lose-lose situations. Dozens of companies - including Intel, Nintendo, American Express and Nutrasweet - have been using the strategies of co-opetition to change their game and enjoy the benefits of win-win opportunities.

This Palgrave Pivot uses a simple model from game theory to explain the behavior of countries disputing ownership of resources and of small islands in the South China Sea. It argues that the rapid transformation of the region's economy - the rise of Factory Asia - is not being acknowledged, leading countries to take chances beyond what a rational picture of costs and benefits would suggest. Regional economic cooperation may be a viable alternative to the present conflicts. However, the varied experience of regional initiatives in Southeast Asia provides a cautionary note that, while there is the potential for peaceful development of the South China Sea, there are significant challenges to structuring successful programs.

This monograph deals with problems of dynamical reconstruction of unknown variable characteristics (distributed or boundary disturbances, coefficients ofoperator etc.) for various classes of systems with distributed parameters (parabolic and hyperbolic equations, evolutionary variational inequalities etc.).

This monograph collects cutting-edge results and techniques for solving nonlinear partial differential equations using critical points. Including many of the author's own contributions, a range of proofs are conveniently collected here, Because the material is approached with rigor, this book will serve as an invaluable resource for exploring recent developments in this active area of research, as well as the numerous ways in which critical point theory can be applied. Different methods for finding critical points are presented in the first six chapters. The specific situations in which these methods are applicable is explained in detail. Focus then shifts toward the book's main subject: applications to problems in mathematics and physics. These include topics such as Schroedinger equations, Hamiltonian systems, elliptic systems, nonlinear wave equations, nonlinear optics, semilinear PDEs, boundary value problems, and equations with multiple solutions. Readers will find this collection of applications convenient and thorough, with detailed proofs appearing throughout. Critical Point Theory will be ideal for graduate students and researchers interested in solving differential equations, and for those studying variational methods. An understanding of fundamental mathematical analysis is assumed. In particular, the basic properties of Hilbert and Banach spaces are used.

The book presents new developments in the dynamic modeling and optimization methods in environmental economics and provides a huge range of applications dealing with the economics of natural resources, the impacts of climate change and of environmental pollution, and respective policy measures. The interrelationship between economic activities and environmental quality, the development of cleaner technologies, the switch from fossil to renewable resources and the proper use of policy instruments play an important role along the path towards a sustainable future. Biological, physical and economic processes are naturally involved in the subject, and postulate the main modelling, simulation and decision-making tools: the methods of dynamic optimization and dynamic games.

Thomas Schelling won the Nobel Prize in economics "for having enhanced our understanding of conflict and cooperation through game-theory analysis." This came after he had taught a course in game theory and rational choice to advanced students and government officials for 45 years. In this book, Robert Dodge provides in language for a broad audience, the concepts that Schelling taught. Armed with Schelling's understanding of game theory methods and his approaches to problems, the general reader can improve daily decision making. Mathematics often make game theory challenging but was not a major part of Schelling's course and is even less of a factor in this book. Along with a summary of the material Schelling presented, included are problems from the course and similar less challenging questions. While considerable analysis is done with the basic game theory tool - the two-by-two matrix - much of the book is descriptive and rational decision-making is explained with stories. Chapter supplements are added to illuminate points presented by Schelling, including writings by Paul Krugman, Thomas Friedman, Steven Levitt, and others.

This book addresses the perennial question of how to promote Africa's indigenous languages as medium of instruction in educational systems. Breaking with the traditional approach to the continent's language question by focusing on the often overlooked issue of the link between African languages and economic development, Language Policy and Economics argues that African languages are an integral part of a nation's socio-political and economic development. Therefore, the book argues that any language policy designed to promote these languages in such higher domains as the educational system in particular must have economic advantages if the intent is to succeed, and proposes Prestige Planning as the way to address this issue. The proposition is a welcome break away from language policies which pay lip-service to the empowerment of African languages while, by default, strengthening the stranglehold of imported European languages.

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications.

The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.

This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.

During the past 20 years, behavioral and social scientists following advances in physics and mathematics have shown an increasing interest in complex, adaptive, self-organizing, dynamic systems. The appeal of this perspective is fueled by the fact that there are a handful of properties that are common to all dynamic systems that can be used to explain the spontaneous emergence of novel forms, the mechanisms of continuity and change, and the dynamics of a large number of interacting factors. From animal population dynamics to human neural processes, there is growing evidence that human individual and social interactions may be understood as a dynamic system. In the field of psychology, there was a flurry of books during the early 1990s that explored the dynamic human system. These titles, and those that have been published since, fall into two general categories: those that integrate dynamic systems ideas into psychological theories and those that provide methods of modeling dynamic human systems (see list of competitive titles below).

Despite the enrichment that dynamic systems principles have afforded psychological theories, the methods provided to test these theoretical assumptions have not been readily adopted. The reason is that, unlike the physical scientists, social scientists are not as familiar with the mathematical formulations (i.e., differential and difference equations) required for these methods, nor are their data particularly amenable to such manipulations or models. Furthermore, the psychological relevance of some of the parameters extracted from these methods (i.e., Lyupanov exponents, chaotic attractors) is very difficult to interpret. What is needed is a methodological middle road to bridge theory and analysis. The proposed book on the state space grid method is perfectly poised to provide that bridge.

State space grids were first developed by Marc Lewis and colleagues (Lewis, Lamey, and Douglas, 1999) to depict sequences of infant attention and distress. This technique has since been applied to the study of parent-child interactions (Granic & Lamey, 2002; Granic, Hollenstein, Dishion, & Patterson, 2003; Hollenstein, Granic, Stoolmiller, & Snyder, 2005; Hollenstein & Lewis, under review; Lewis, Zimmerman, Hollenstein, & Lamey, 2004), and peer interactions (Dishion, Nelson, Bullock, & Winter, 2005; Martin, Fabes, Hanish, & Hollenstein, 2005). At this time, there are projects in progress that extend this work into the study of marital interactions, young adult group drinking patterns, eye gaze and eye contact in response to questioning, diary studies, and peer pressure dynamics.
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This book offers the first systematic analysis of economic thought concerning war. It retraces debates on war from the formation of European states, the rise of Mercantilism, to Colonialism, Imperialism, the World Wars and the Cold War. Allio shows different economic perspectives from which it is possible to study war as a tool to achieve economic ends: causes, consequences, costs, funding methods, and effects on the economic status of the state and on the well-being of citizens. Examining interpretations from Smith, Hobson, Keynes, Kalecki, Stiglitz and many more, this important volume addresses the economic implications of war from the perspectives of many who bore the costs of wars in reality.

Individuals, firms, governments and nations behave strategically, for good and bad. Over the last few decades, game theory has been constructed and progressively refined to become the major tool used by social scientists to understand, predict and regulate strategic interaction among agents who often have conflicting interests. In the surprisingly anodyne jargon of the theory, they play games . This book offers an introduction to the basic tools of game theory and an overview of a number of applications to real-world cases, covering the areas of economics, politics and international relations. Each chapter is accompanied by some suggestions about further reading.

In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. The problems of numerical approximation of tabulated functions and numerical solution of overdetermined systems of linear algebraic equations and some systems of nonlinear equations are solved by separable convex unconstrained minimization problems. Some properties of the Knapsack polytope are also studied. This second edition includes a substantial amount of new and revised content. Three new chapters, 15-17, are included. Chapters 15-16 are devoted to the further analysis of the Knapsack problem. Chapter 17 is focused on the analysis of a nonlinear transportation problem. Three new Appendices (E-G) are also added to this edition and present technical details that help round out the coverage. Optimization problems and methods for solving the problems considered are interesting not only from the viewpoint of optimization theory, optimization methods and their applications, but also from the viewpoint of other fields of science, especially the artificial intelligence and machine learning fields within computer science. This book is intended for the researcher, practitioner, or engineer who is interested in the detailed treatment of separable programming and wants to take advantage of the latest theoretical and algorithmic results. It may also be used as a textbook for a special topics course or as a supplementary textbook for graduate courses on nonlinear and convex optimization.

The rise of game theory has made bargaining one of the core issues in economic theory. Written at a theoretical and conceptual level, the book develops a framework for the analysis of bargaining processes. The framework focuses on the dynamic of the bargaining process, which is in contrast to much previous theoretical work on the subject, and most notably to the approaches stemming from game theory. Chapters include: * Decision-Making and Expectations in Theories of Bargaining * Decision-Making and Expectations in a Game Theory Model * Limitations of the Environment Concept * Game Theory as a Basis for a Theory of Bargaining * The Decision/Expectation/adjustment Approach * The Adjustment Process * Direct Interdependence and the Consistency of Decisions

This book describes highly applicable mathematics without using calculus or limits in general. The study agrees with the opinion that the traditional calculus/analysis is not necessarily the only proper grounding for academics who wish to apply mathematics. The choice of topics is based on a desire to present those facets of mathematics which will be useful to economists and social/behavioral scientists. The volume is divided into seven chapters. Chapter I presents a brief review of the solution of systems of linear equations by the use of matrices. Chapter III introduces the theory of probability. The rest of the book deals with new developments in mathematics such as linear and dynamic programming, the theory of networks and the theory of games. These developments are generally recognized as the most important field in the new mathematics' and they also have specific applications in the management sciences.

Dynamic optimization is rocket science and more. This volume teaches how to harness the modern theory of dynamic optimization to solve practical problems, not only from space flight but also in emerging social applications such as the control of drugs, corruption, and terror. These innovative domains are usefully thought about in terms of populations, incentives, and interventions, concepts which map well into the framework of optimal dynamic control. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. We celebrate Pontryagin s Maximum Principle that crowning intellectual achievement of human understanding and push its frontiers by exploring models that display multiple equilibria whose basins of attraction are separated by higher-dimensional DNSS "tipping points." That rich theory is complemented by numerical methods available through a companion web site."

Linear programming (LP), modeling, and optimization are very much the fundamentals of OR, and no academic program is complete without them. No matter how highly developed one 's LP skills are, however, if a fine appreciation for modeling isn t developed to make the best use of those skills, then the truly best solutions are often not realized, and efforts go wasted.

Katta Murty studied LP with George Dantzig, the father of linear programming, and has written the graduate-level solution to that problem. While maintaining the rigorous LP instruction required, Murty's new book is unique in his focus on developing modeling skills to support valid decision making for complex real world problems. He describes the approach as 'intelligent modeling and decision making' to emphasize the importance of employing the best expression of actual problems and then applying the most computationally effective and efficient solution technique for that model.

This book is focused on the discussion of the traffic assignment problem, the mathematical and practical meaning of variables, functions and basic principles. This work gives information about new approaches, methods and algorithms based on original methodological technique, developed by authors in their publications for the past several years, as well as corresponding prospective implementations. The book may be of interest to a wide range of readers, such as civil engineering students, traffic engineers, developers of traffic assignment algorithms etc. The obtained results here are to be used in both practice and theory. This book is devoted to the traffic assignment problem, formulated in a form of nonlinear optimization program. The most efficient solution algorithms related to the problem are based on its structural features and practical meaning rather than on standard nonlinear optimization techniques or approaches. The authors have carefully considered the meaning of the traffic assignment problem for efficient algorithms development.

Providing readers with a detailed examination of resilient controls in risk-averse decision, this monograph is aimed toward researchers and graduate students in applied mathematics and electrical engineering with a systems-theoretic concentration. This work contains a timely and responsive evaluation of reforms on the use of asymmetry or skewness pertaining to the restrictive family of quadratic costs that have been appeared in various scholarly forums. Additionally, the book includes a discussion of the current and ongoing efforts in the usage of risk, dynamic game decision optimization and disturbance mitigation techniques with output feedback measurements tailored toward the worst-case scenarios. This work encompasses some of the current changes across uncertainty quantification, stochastic control communities, and the creative efforts that are being made to increase the understanding of resilient controls. Specific considerations are made in this book for the application of decision theory to resilient controls of the linear-quadratic class of stochastic dynamical systems. Each of these topics are examined explicitly in several chapters. This monograph also puts forward initiatives to reform both control decisions with risk consequences and correct-by-design paradigms for performance reliability associated with the class of stochastic linear dynamical systems with integral quadratic costs and subject to network delays, control and communication constraints.