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This monograph develops a method of creating convenient coordinate systems for game theory that will allow readers to more easily understand, analyze, and create games at various levels of complexity. By identifying the unique characterization of games that separates the individual's strategic interests from the group's collective behavior, the authors construct a single analytical methodology that readers will be able to apply to a wide variety of games. With its emphasis on practicality and approachability, readers will find this book an invaluable tool, and a viable alternative to the ad hoc analytical approach that has become customary for researchers utilizing game theory.The introductory chapters serve two important purposes: they review several games of fundamental importance, and also introduce a dynamic that is inherent in games, but has gone unexplored until now. After this has been established, readers will advance from simple 2 x 2 games to games with more player strategies and dynamics. For interested readers, a rigorous treatment of the underlying mathematics is conveniently gathered at the end of the book. Additional topics of interest, such as extensive form and coalitional games, are presented to help readers visualize more complex settings that will be vital in aiding the understanding of advanced topics, such as coalition-free Nash points, multi-player repeated games, and more.Coordinate Systems for Games is ideal for a wide variety of researchers interested in game theory, including social scientists, economists, mathematicians, computer scientists, and more. The authors'approachable style also makes this accessible to an audience at any scale of experience, from beginning non-specialists to more practiced researchers.

This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.

A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi­ cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing'spline'curves can be extended to allow us to compute'spline'surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi­ nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav­ els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.

Communication networks are very complex and interdependent systems requiring complicated management and control operations under strict resource and time constraints. A finite number of network components with limited capacities need to be shared for dynamically allocating a high number of traffic demands. Moreover, coordination of peer provider is required whenever these demands span domains controlled by distinct operators. In this context, traditional human-driven management is becoming increasingly inadequate to cope with the growing heterogeneity of actors, services and technologies populating the current deregulated market. This book proposes a novel approach to improve multi-provider interactions based on the coordination of autonomous and self-motivated software entities acting on behalf of distinct operators. Coordination is achieved by means of distributed constraint satisfaction techniques integrated within economic mechanisms, which enable automated negotiations to take place. This allows software agents to find efficient allocations of service demands spanning several networks without having to reveal strategic or confidential data. In addition, a novel way of addressing resource allocation and pricing in a compact framework is made possible by the use of powerful resource abstraction techniques. The book is addressed to researchers in the area of agent technology, automated negotiation, distributed constraint satisfaction, and networking, in particular for what concerns resource allocation and pricing. Furthermore, it should be a valuable resource for both network and service providers

Presenting mobile software agents for Internet service monitoring, this research monograph discusses newly standardized Internet technologies that allow service providers to offer secured Internet services with quality guarantees. Yet, today the customers of such services have no independent tool to verify (monitor) the service quality. This book shows why mobile software agents are best fit to fill the gap. Key features: - An introduction to standard Internet service enabling and managing technology such as IPSec, DiffServ and SNMP - A generic service monitoring architecture based on mobile agents - An object-oriented implementation of the architecture based on the Java programming language - Several implementations of mobile software agents that can monitor new and emerging Internet services such as virtual private networks (VPN) The book is addressed to mobile agent researchers looking for new and fruitful application areas. It will also be a valuable resource for innovative internet providers who are looking for a service monitoring infrastructure going beyond monthly reports.

Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry. Mathematical advances have been made both analytically and numerically in finding practical solutions. This book provides a comprehensive overview of existing and original material, about what mathematics when allied with Mathematica can do for finance. Sophisticated theories are presented systematically in a user-friendly style, and a powerful combination of mathematical rigor and Mathematica programming. Three kinds of solution methods are emphasized: symbolic, numerical, and Monte-- Carlo. Nowadays, only good personal computers are required to handle the symbolic and numerical methods that are developed in this book. Key features: • No previous knowledge of Mathematica programming is required • The symbolic, numeric, data management and graphic capabilities of Mathematica are fully utilized • Monte--Carlo solutions of scalar and multivariable SDEs are developed and utilized heavily in discussing trading issues such as Black--Scholes hedging • Black--Scholes and Dupire PDEs are solved symbolically and numerically • Fast numerical solutions to free boundary problems with details of their Mathematica realizations are provided • Comprehensive study of optimal portfolio diversification, including an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics is presented The book is designed for the academic community of instructors and students, and most importantly, will meet the everyday trading needs of quantitatively inclined professional and individual investors.