简介
This book is an introduction to mathematical game theory, which might better be called the mathematical theory of conflict and cooperation. It is applicable whenever two individuals - or companies, or political parties, or nations - confront situations where the outcome for each depends on the behavior of all. What are the best strategies in such situations? If there are chances of cooperation, with whom should you cooperate, and how should you share the proceeds of cooperation? Since its creation by John von Neumann and Oskar Morgenstern in 1944, game theory has shed new light on business, politics, economics, social psychology, philosophy, and evolutionary biology. In this book its fundamental ideas are developed with mathematics at the level of high school algebra and applied to many of these fields (see the table of contents). Ideas like "fairness" are presented via axioms that fair allocations should satisfy; thus the reader is introduced to axiomatic thinking as well as to mathematical modeling of actual situations. - Cover.
目录
Two-Person Zero-Sum Games
The nature of games
Matrix games: dominance and saddle points
Matrix games: mixed strategies
Application to anthropology: Jamaican fishing
Application to warfare: guerillas, police, and missiles
Application to philosophy: Newcomb's problem and free will
Game trees
Application to business: competitive decision making
Utility theory
Games against nature
Two-Person Non-Zero-Sum Games
Nash equilibria and non-cooperative solutions
The prisoner's dilemma
Application to social psychology: trust, suspicion, and the F-Scale
Strategic moves
Application to biology: evolutionarily stable strategies
The Nash arbitration scheme and cooperative solutions
Application to business: management-labor arbitration
Application to economics: the duopoly problem
N-Person Games
An introduction to N-Person games
Applications to politics: strategic voting
N-Person prisoner's dilemma
Application to athletics: prisoner's dilemma and the football draft
Imputations, domination, and stable set
Application to anthropology: pathan organization
The core
The shapley value
Application to politics: the Shapley-Shubik power Index
Application to politics: the Banzhaf Index and the Canadian constitution
Bargaining sets
Application to politics: parliamentary coalitions
The nucleolus and the Gately point
Application to economics: cost allocations in India
The value of game theory
The nature of games
Matrix games: dominance and saddle points
Matrix games: mixed strategies
Application to anthropology: Jamaican fishing
Application to warfare: guerillas, police, and missiles
Application to philosophy: Newcomb's problem and free will
Game trees
Application to business: competitive decision making
Utility theory
Games against nature
Two-Person Non-Zero-Sum Games
Nash equilibria and non-cooperative solutions
The prisoner's dilemma
Application to social psychology: trust, suspicion, and the F-Scale
Strategic moves
Application to biology: evolutionarily stable strategies
The Nash arbitration scheme and cooperative solutions
Application to business: management-labor arbitration
Application to economics: the duopoly problem
N-Person Games
An introduction to N-Person games
Applications to politics: strategic voting
N-Person prisoner's dilemma
Application to athletics: prisoner's dilemma and the football draft
Imputations, domination, and stable set
Application to anthropology: pathan organization
The core
The shapley value
Application to politics: the Shapley-Shubik power Index
Application to politics: the Banzhaf Index and the Canadian constitution
Bargaining sets
Application to politics: parliamentary coalitions
The nucleolus and the Gately point
Application to economics: cost allocations in India
The value of game theory
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