Geometry, Language and Strategy


Book Description

Geometry, Language and Strategy is a way of looking at game theory or strategic decision-making from a scientific perspective, using standard equations from the fields of engineering and physics. To better approximate reality, it extends game theory beyond the two-player set piece. The book begins where former game theory literature ends OCo with multi-person games on a world stage. It encompasses many of the variables encountered in strategic planning, using mathematics borrowed from physics and engineering, rather than the economic models which have not proven to be good in predicting reality. Sample Chapter(s). Chapter 1: Introduction (1,364 KB). Contents: Rules-of-the-Game; Flow of Strategic-Mass; Game Symmetries; Analysis; Graphical Presentation; Applications and Open Problems; Appendices: Thermodynamics; Symmetry in Differential Geometry; Central Strategies; Single Strategy Model; Single Strategy Numerical Solutions; Streamlines; Player Fluid. Readership: Mathematicians and scientists who wish to broaden their understanding of economic possibilities using game theory."




Geometry, Language and Strategy


Book Description

Geometry, Language and Strategy is a way of looking at game theory or strategic decision-making from a scientific perspective, using standard equations from the fields of engineering and physics. To better approximate reality, it extends game theory beyond the two-player set piece.The book begins where former game theory literature ends ? with multi-person games on a world stage. It encompasses many of the variables encountered in strategic planning, using mathematics borrowed from physics and engineering, rather than the economic models which have not proven to be good in predicting reality.




Geometry, Language And Strategy: The Dynamics Of Decision Processes - Volume 2


Book Description

The first volume, Geometry, Language and Strategy, extended the concepts of Game Theory, replacing static equilibrium with a deterministic dynamic theory. The first volume opened up many applications that were only briefly touched on. To study the consequences of the deterministic approach in contrast to standard Bayesian approaches, the richness of applications, requires an engineering foundation and discipline, which this volume supplies. It provides a richer list of applications, such as the Prisoner's Dilemma, which extends the resonant behavior of Vol. 1 to more general time-dependent and transient behaviors.







Linguistic Geometry


Book Description

Linguistic Geometry: From Search to Construction is the first book of its kind. Linguistic Geometry (LG) is an approach to the construction of mathematical models for large-scale multi-agent systems. A number of such systems, including air/space combat, robotic manufacturing, software re-engineering and Internet cyberwar, can be modeled as abstract board games. These are games with moves that can be represented by the movement of abstract pieces over locations on an abstract board. The purpose of LG is to provide strategies to guide the games' participants to their goals. Traditionally, discovering such strategies required searches in giant game trees. These searches are often beyond the capacity of modern and even conceivable future computers. LG dramatically reduces the size of the search trees, making the problems computationally tractable. LG provides a formalization and abstraction of search heuristics used by advanced experts including chess grandmasters. Essentially, these heuristics replace search with the construction of strategies. To formalize the heuristics, LG employs the theory of formal languages (i.e. formal linguistics), as well as certain geometric structures over an abstract board. The new formal strategies solve problems from different domains far beyond the areas envisioned by the experts. For a number of these domains, Linguistic Geometry yields optimal solutions.




The Britannica Guide to Geometry


Book Description

More than a study of shapes and angles, geometry reflects an amalgamation of discoveries over time. This book not only provides readers with a comprehensive understanding of geometric shapes, axioms, and formulas, it presents the field’s brilliant minds—from Euclid to Wendelin Werner and many in between—whose works reflect a progression of mathematical thought throughout the centuries and have helped produce the various branches of geometry as they are known today. Detailed diagrams illustrate various concepts and help make geometry accessible to all.




The Geometry of Strategy


Book Description

To excel in today’s exacting world, organizations need to combine strategic planning and strategic thinking. Strategic planning is a formal activity carried out periodically by top managers, but it is vulnerable to change. Strategic thinking is an informal activity that occurs intermittently throughout an organization, but it tends to be non-cumulative. Keidel offers a framework for integrating strategic planning and strategic thinking that leverages the strengths of both. The key to his work is the application of simple geometric forms—especially, 2x2 grids and triangles—that help organizational leaders and strategists structure their thinking and planning. Keidel introduces four strategic categories—persona (organizational identity), performance (what is measured), puzzle (dilemmas that are faced), and pattern (how to compete, grow, & organize). Each category matches a specific geometry of thinking—point, linear, angular, and triangular. The payoff? A novel way to develop strategy, as well as a set of conceptual lenses for "reading" any other organization’s strategy—or any strategic argument. Keidel’s work is illustrated with case studies from his own consulting practice and grounded in the theoretical literature underlying the various geometries of thinking. This book will be a valuable resource for managerial and executive education in strategy, as well as a provocative reading for organizational strategy consultants and thoughtful practitioners.







Geometry, Language and Strategy


Book Description

"The first volume, Geometry, Language and Strategy, extended the concepts of Game Theory, replacing static equilibrium with a deterministic dynamic theory. The first volume opened up many applications that were only briefly touched on. To study the consequences of the deterministic approach in contrast to standard Bayesian approaches, the richness of applications, requires an engineering foundation and discipline, which this volume supplies. It provides a richer list of applications, such as the Prisoner's Dilemma, which extends the resonant behavior of Vol. 1 to more general time-dependent and transient behaviors."--Publisher's website.




Problem-Solving Strategies


Book Description

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.