Game Theory: Mathematical Models of Conflict (Horwood Series in Mathematics & Applications)

Biography (John Nash). First printing, full number line. Book fine and clean, inside and out. dust jacket near fine, light edge wear, price clipped Written engagingly and with agreeable humour, this book balances a light touch with a rigorous yet economical account of the theory of games and bargaining models. It provides a precise interpretation, discussion and mathematical analysis for a wide range of “game-like” problems in economics, sociology, strategic studies and war.

There is first an informal introduction to game theory, which can be understood by non-mathematicians, which covers the basic ideas of extensive form, pure and mixed strategies and the minimax theorem. The general theory of non-cooperative games is then given a detailed mathematical treatment in the second chapter. Next follows a “first class” account of linear programming, theory and practice, terse, rigorous and readable, which is applied as a tool to matrix games and economics from duality theory via the equilibrium theorem, with detailed explanations of computational aspects of the simplex algorithm.

The remaining chapters give an unusually comprehensive but concise treatment of cooperative games, an original account of bargaining models, with a skillfully guided tour through the Shapley and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.

• Balances a light touch with a rigorous yet economical account of the theory of games and bargaining models
• Shows basic ideas of extensive form, pure and mixed strategies, the minimax theorem, non-cooperative and co-operative games, and a ‘‘first class’’ account of linear programming, theory and practice
• Based on a series of lectures given by the author in the theory of games at Royal Holloway College

"This book balances a light touch with a rigorous yet economical account of the theory of games and bargaining models. It provides a precise interpretation, discussion and mathematical analysis for a wide range of "game-like" problems in economics, sociology, strategic studies and war." "There is first an informal introduction to game theory, which can be understood by non-mathematicians, which covers the basic ideas of extensive form, pure and mixed strategies and the minimax theorem. The general theory of non-cooperative games is then given a detailed mathematical treatment in the second chapter. Next follows a "first class" account of linear programming, theory and practice, terse, rigorous and readable, which is applied as a tool to matrix games and economics from duality theory via the equilibrium theorem, with detailed explanations of computational aspects of the simplex algorithm." "The remaining chapters give an unusually comprehensive but concise treatment of cooperative games, an original account of bargaining models, with a skillfully guided tour through the Shapley and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies."--Jacket. In this biography, Sylvia Nasar re-creates the life of a mathematical genius whose brilliant career was cut short by schizophrenia and who, after three decades of devastating mental illness, miraculously recovered and was honored with a Nobel Prize. A Beautiful Mind traces the meteoric rise of John Forbes Nash, Jr., from his lonely childhood in West Virginia to his student years at Princeton, where he encountered Albert Einstein, John von Neumann, and a host of other mathematical luminaries. At twenty-one, the handsome, ambitious, eccentric graduate student invented what would become the most influential theory of rational human behavior in modern social science. Nash's contribution to game theory would ultimately revolutionize the field of economics. At thirty, Nash was poised to take his dreamed-of place in the pantheon of history's greatest mathematicians. Then Nash suffered a catastrophic mental breakdown A biography of John Nash, who suffered a breakdown at the peak of a dazzling mathematical career and spent decades as a silent, ghost-like figure haunting the campus of Princeton University. When he was 61 a remission of his illness and the receipt of a Nobel Prize restored him to the world. Tells the life story of mathmatical genius John Nash, his descent into schizophrenia and his subsequent triumph over the illness and winning of the Nobel Prize; This title is also available as a film Relates how mathematical genius John Forbes Nash, Jr., suffered a breakdown at age thirty-one and was diagnosed with schizophrenia, but experienced a remission of his illness thirty years later.