| Preface List of Notations | |
| Linear Programming: Examples, Definitions, and Statements of the Principal Theorems | |
| Examples The diet problem The transportation problem Production to meet given demand at minimum cost Production to maximize income from given resources | |
| Duality and prices | |
| Further interpretation of duality | |
| Price equilibrium Bibliographical notes Exercises | |
| Real Linear Algebra | |
| Vector | |
| Scalar product, matrices, linear equations | |
| Real linear equations and inequalities | |
| Basic solutions of equations | |
| Geometry of linear inequalities. Convex cones | |
| Extreme vectors and extreme solutions | |
| Convex sets and polytopes Bibliographical notes Exercises | |
| The Theory of Linear Programming | |
| Definitions | |
| The duality theorems | |
| The equilibrium theorems | |
| Basic solutions | |
| An application: allocation of resources in a competitive economy Bibliographical notes Exercises | |
| Computation. The Simplex Method | |
| Solving simultaneous equations and inverting a matrix | |
| The simplex method for linear programming. Discussion | |
| Theory of the simplex method | |
| Some numerical examples | |
| Nonnegative solutions of linear equations | |
| Solving linear inequalities | |
| Degeneracy. The generalized simplex method Bibliographical notes Exercises | |
| Integral Linear Programming | |
| Examples Transportation problem with indivisible commodity The optimal-assignment problem The loading problem | |
| Flows in networks | |
| The simple-assignment problem | |
| The transshipment problem | |
| The optimal-assignment problem | |
| A problem related to optimal assignment. Price equilibrium | |
| The transportation problem | |
| Other examples: shortest route; the caterer | |
| Concluding remarks and open questions Bibliographical notes Exercises | |
| Two-person Games: Examples, Definitions, and Elementary Theory | |
| First examples and definitions Odds and evens (matching pennies) Morra | |
| Further examples of matrix games Goofspiel Bluffing A, B, C | |
| Solutions of games. Mixed strategies | |
| Value of a game and optimal strategies | |
| Some infinite games Continuous bluffing Duels The oil prospector (a game against nature) The bomber and the submarine High number Low number | |
| Saddle points and minimax | |
| Symmetric games | |
| Proof of the fundamental theorem Appendix to | |
| A geometric "proof" of the fundamental theorem of game theory Bibliographical notes Exercises | |
| Solutions of Matrix Games | |
| Relation between matrix games and linear programming | |
| Solving games by the simplex method | |
| Optimal strategies | |
| Solutions | |
| Examples | |
| The structure of symmetric games | |
| Constructing a game with prescribed solutions | |
| Basic optimal strategies | |
| A method of "learning" a game | |
| Convergence of the learning method Bibliographical notes Exercises | |
| Linear Models of Exchange | |
| Examples The simple exchange model. The price problem The simple linear model of international trade | |
| Equilibrium for the exchange model | |
| Dynamic theory | |
| Dynamics in the reducible case | |
| Price equilibrium for linear exchange models | |
| An example of price equilibrium | |
| Uniqueness of equilibrium prices Bibliographical notes Exercises | |
| Linear Models of Production | |
| The simple linear production model | |
| A dynamic property of the simple model | |
| The Leontief model | |
| The general linear production model. Efficient points | |
| Von Neumann's expanding model | |
| Some examples | |
| The expanding simple model | |
| Bibliographical notes Exercises | |
| Bibliography | |
| Index | |
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