Graphs, Dynamic Programming and Finite Games
Published on 1. January 1967
481 pages
978-0-08-095543-8 (ISBN)
Description
Graphs, Dynamic Programming and Finite Games
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Arnold Kaufmann
Graphs, Dynamic Programming and Finite Games
Book
10/1967
Academic Press
€73.67
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Content
- Front Cover
- Graphs, Dynamic Programming, and Finite Games
- Copyright Page
- Contents
- Foreword
- Foreword to the French Edition
- Preface to the French Edition
- Part 1. Methods and Models
- Chapter I. Graphs
- 1. Introduction
- 2. The Use of Points and Arcs to Represent Structures
- 3. Principal Concepts Used in the Theory of Graphs
- 4. Scheduling and Sequencing Problems
- 5. Tree of a Graph
- 6. Search for an Optimal Flow in a Network. The Ford-Fulkerson Algorithm
- 7. Application of the Theory of Graphs to Psychosociology
- 8. Automatic Textual Emendation. Search for Lost Manuscripts
- Chapter II. Dynamic Programming
- 9. Introduction
- 10. Bellman's Theorem of Optimality
- 11. First Example of Multistage Optimization
- 12. Distribution of Investments
- 13. A Purchasing Problem
- 14. Decisions in the Face of Uncertainty
- 15. Two Examples of Dynamic Programming in the Face of an Uncertain Future
- 16. Theorem of Optimality in the Case of Uncertainty. Discrete Systems
- 17. Interval of Anticipation. Dynamic Programming with Adaptation
- 18. Effect of Introducing a Rate of Interest
- Chapter III. The Theory of Games of Strategy
- 19. Introduction
- 20. Game on a Rectangular Matrix
- 21. Point of Equilibrium of a Rectangular Game
- 22. Pure Strategy and Mixed Strategy
- 23. Various Properties
- 24. Use in Concrete Cases of Competition
- 25. Use in Cases of a "Struggle against Nature
- 26. Choice of a Criterion
- 27. The Theory of Statistical Decision
- 28. Multistage Games with Two Players
- Part II. Mathematical Developments
- Symbols for the Theory of Sets Used in Part II
- Chapter IV. The Principal Properties of Graphs
- 29. Introduction
- 30. Definition and Figure
- 31. Oriented Concepts
- 32. Nonoriented Concepts
- 33. Product and Sum of Graphs
- 34. Various Generalizations
- 35. Typical Numbers in a p-Graph
- 36. Separation or Shortest Path in a Graph
- 37. Transport Network
- 38. Linking Two Disjoint Sets
- 39. Hamiltonian Path and Circuit
- 40. Center and Radius of a Graph
- 41. Network (Strongly Connected Graph without a Loop)
- 42. Matrix Associated with a Graph
- 43. Incidence Matrix
- 44. Tree. Arborescence
- 45. Eulerian Chain and Cycle
- 46. Point and Set of Articulation. Connectivity Number
- 47. Planar Graphs
- 48. Mapping a Graph into a Graph
- Chapter V. Mathematical Properties of Dynamic Programming
- 49. Introduction
- 50. Formulas for Multistage Optimization
- 51. Convergence of a Dynamic Program in a Limited Future
- 52. Difficulty of the Final Calculations
- 53. Uncertain Development Using a Markovian Chain
- 54. The z-Transform
- 55. Using the z-Transform to Study Markovian Chains
- 56. Markovian Chain with Transition Values
- 57. Study of Some Important Special Cases
- 58. Dynamic Programming in a Case of Uncertainty
- 59. Dynamic Program with Markovian Chain
- 60. Long Term Situation (Case of a Fully Ergodic Matrix)
- 61. Iterative Optimization
- 62. Long Term Strategy When the Chain Is Not Fully Ergodic
- 63. Discounted Value of the Revenue
- 64. Applying Dynamic Programming to a Real Problem
- Chapter VI. Mathematical Properties of Games of Strategy
- 65. Introduction
- 66. Various Properties Connected with the Maximal and Minimal Values of Functions
- 67. Fundamental Theorem for Games of Strategy
- 68. Various Proofs
- 69. Calculating the Numerical Solution of a Rectangular Game
- 70. Reducing a Rectangular Game to a Linear Program
- 71. Reducing a Linear Program to a Rectangular Game
- 72. Evaluation by Multistage Adaptation
- 73. Finding Bayes's Optimal Strategy in a "Game against Nature
- 74. Game with a Continuous Function
- 75. Games with n Players and a Zero Sum (n & 2)
- 76.Games with n Players (n = 2) with a Nonzero Sum
- Conclusion
- Bibliography
- IX. Theory of Graphs and Their Applications
- X. Dynamic Programming
- XI. Theory of Games of Strategy
- Subject Index
