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