The theory of linear economic models /
David Gale.
- Chicago : The University of Chicago Press, 1989.
- xxi, 330 páginas ; : tablas, gráficas ; 23 cm.
- Economics. Mathematics. .
Incluye referencias bibliográficas (páginas 323-326) e índice
Chapter 1. Linear programming: examples, definitions, and statements of the principal theorems: 1. Examples ; 2. Duality and prices ; 3. Further interpretation of duality ; 4. Price equilibrium -- Chapter 2. Real linear algebra: 1. Vectors ; 2. Scalar product, matrices, linear equations ; 3. The theory of linear programming:1. Definitions ; 2. The duality theorems ; 3. The equilibrium theorems ; 4. Basic solutions ; 5. An application: allocations of resources in a competitive economy -- Chapter 4. Computation. The simples method: 1. Solving simultaneous equations and inverting a matrix ; 2. The simplex method for linear programming ; 3. Theory of the simplex methods ; 4. Some numerical examples ; 5. Nonnegative solutions of linear equations ; 6 Solving linear inequalities ; 7. Degeneracy. The generalized simplex method – Chapter 5. Integral linear programming: 1. Examples ; 2. Flows in networks ; 3. The simple-assignment problem ; 4. The transshipment problem ; 5. The optimal-assignment problem ; 6. A problem related to optimal assignment ; 7. The transportation problem ; 8. Other examples: shortest rote ; the caterer ; 9. Concluding remarks and open questions -- Chapter 6: Two-person games: examples: definitions, and elementary theory: 1. Fist examples and definitions ; 2. Further examples of matrix games ; 3. Solutions of games ; 4. Value of game and optimal strategies ; 5. Some infinite games ; 6. Saddle points and minimax ; 7. Symmetric games ; 8. Proof of the fundamental theorem -- Chapter 7. Solutions of matrix games: 1. Relation between matrix games and linear programming ; 2. Solving games by the simplex method ; 3. Optimal strategies ; 4. Solutions ; 5. Examples ; 6. The structure of symmetric games ; 7. Constructing a game with prescribed solutions ; 8. Basic optimal strategies ; 9. A method of “learning” a game ; 10. Convergence of the learning method -- Chapter 8. Linear models of exchange: 1. Examples ; 2. Equilibrium for the exchange model ; 3. Dynamic theory ; 4. Dynamics in the reducible case ; 5. Price equilibrium for linear exchange models ; 7. Uniqueness of equilibrium prices -- Chapter 9. Linear models of production: 1. The simple linear production model ; 2. A dynamic property of the simple model ; 3. The Leontief model ; 4. The general linear production model ; 5. Von Neumann’s expanding model ; 6. Some examples ; 7. The expanding simple model.