The textbook bridges the gap between pure mathematics and applied operations research. It is specifically tailored for undergraduate and postgraduate students in mathematics, computer science, and engineering. Key Features of the Book:
The text provides a rigorous yet accessible account of linear programming (LP) and its applications in game theory, specifically for undergraduate and postgraduate levels. Typically available in paperback with approximately Core Content & Topics
Explores the mathematical relationship between the "Primal" problem (e.g., maximizing profit) and its "Dual" (e.g., minimizing resource costs), proving that both yield the same optimal value.
The book "Linear Programming and Game Theory" by Ghosh and Chakraborty is a comprehensive textbook that covers the fundamental concepts of Linear Programming and Game Theory. The book is written in a clear and concise manner, making it accessible to students and practitioners alike. The authors have provided numerous examples, illustrations, and case studies to facilitate a deeper understanding of the subject matter. Linear Programming And Game Theory Ghosh Chakraborty Pdf
The connection between Linear Programming and Game Theory is deeply rooted in John von Neumann's . Any two-person zero-sum game lacking a saddle point can be transformed into a pair of primal and dual Linear Programming problems. Transformation Methodology
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Visualizing and solving 2 × n or m × 2 games. The textbook bridges the gap between pure mathematics
Detailed explanations of the Big-M Method and the Two-Phase Method used when initial basic feasible solutions are not readily available (e.g., when constraints involve ≥is greater than or equal to
Solving games where players choose strategies probabilistically.
Linear programming (LP) is a method used to optimize a linear objective function, subject to a set of linear constraints. It is a powerful tool for making decisions in a wide range of fields, including finance, marketing, and supply chain management. The general form of an LP problem is: number of units to produce).
: Duality theory, sensitivity analysis, revised simplex method, and integer programming. Game Theory
The book is structured to be accessible to those with at least one year of college-level mathematics, avoiding overly complex vector space notation in favor of linear simultaneous equations.
Offer a wealth of solved engineering and economic problems tailored for university examinations. Accessing Educational Resources Legally
: The unknown quantities you want to determine (e.g., number of units to produce).
To solve a game without a saddle point, you can set up an LP model where the objective is to maximize the expected value of the game for the row player.