Introduction to the Theory of Games (Hardcover)

1. On equilibrium of systems.- 1.1. Basic ideas.- 1.2. Chains and traversable regions.- 1.3. Equilibrium point, stability set, equilibrium set.- 1.4. "Equilibrium properties" of equilibrium points and equilibrium sets.- 1.5. On the existence of an equilibrium point.- 1.6. On the existence of stability sets.- 2. The n-person game.- 3. Existence theorems of equilibrium points.- 4. Special n-person games and methods to solve them.- 4.1. Mathematical programming methods for the solution of n-person concave games.- 4.2. Generalized polyhedral games.- 4.3. Solution of n-person zero-sum concave-convex games.- 4.4. Concave games with unique equilibrium points.- 5. The Scarf-Hansen algorithm for approximating an equilibrium point of a finite n-person game.- 6. The oligopoly game.- 6.1. The reduction principle.- 6.2. The general multiproduct case.- 6.3. The general linear case.- 6.4. The single-product case.- 7. Two-person games.- 8. Bimatrix games.- 8.1. Basic definitions and some simple properties of bimatrix games.- 8.2. Methods for solving bimatrix games.- 8.3. Examples.- 9. Matrix games.- 9.1. Equilibrium and the minimax principle.- 9.2. The set of equilibrium strategies.- 10. Symmetric games.- 11. Connection between matrix games and linear programming.- 12. Methods for solving general matrix games.- 12.1 Solution of matrix games by linear programming.- 12.2. Method of fictitious play.- 12.3. von Neumann's method.- 13. Some Special Games and methods.- 13.1. Matrices with saddle-points.- 13.2. Dominance relations.- 13.3. 2 x n games.- 13.4. Convex (concave) matrix games.- 14. Decomposition of matrix games.- 15. Examples of matrix games.- 15.1. Example 1.- 15.2. Example 2.- 16. Games played over the unit square.- 17. Some special classes of games on the unit square.- 18. Approximate solution of two- person zero-sum games played over the unit square.- 19. Two-person zero-sum games over metric spaces sequential games.- 20. Sequential games.- 20.1. Shapley's stochastic game.- 20.2. Recursive games.- 21. Games against nature.- 22. Cooperative games in characteristic function form.- 23. Solution concepts for n-person cooperative games.- 23.1. The von Neumann-Morgenstern solution.- 23.2. The core.- 23.3. The strong e-core.- 23.4. The kernel.- 23.5. The nucleolus.- 23.6. The Shapley-value.- 24. Stability of pay-off configurations.- 25. A bargaining model of cooperative games.- 26. The solution concept of nash for n-person cooperative games.- 27. Examples of cooperative games.- 27.1. A linear production game.- 27.2. A market game.- 27.3. The cooperative oligopoly game.- 27.4. A game theoretic approach for cost allocation: a case.- 27.5. Committee decision making as a game.- 28. Game theoretical treatment of multicriteria decision making.- 29. Games with incomplete information.- 29.1. The Harsanyi-model.- 29.2. The Selten-model.- 29.3. Dynamic processes and games with limited information about the pay-off function.- Epilogue.- References.- Name Index.