Discrete Mathematics and Game Theory

I. Vectors and Matrices.- 1. Algebraic Operations.- 2. Row Operations and the Solution of Systems of Linear Equations.- 3. Solution of General m×n Systems of Equations.- II. Linear Programming.- 1. Linear Programs.- 2. The Simplex Algorithm: Slack Variables.- 3. The Simplex Tableau.- 4. The Simplex Algorithm: Objectives.- 5. The Simplex Algorithm: Choice of Pivots.- 6. The Simplex Algorithm: Stage I..- 7. The Simplex Algorithm: Proof of Convergence.- 8. Equation Constraints.- 9. Degeneracy Procedures.- 10. Some Practical Comments.- 11. Duality.- 12. Transportation Problems.- 13. Assignment Problems.- III. The Theory of Probability.- 1. Probabilities.- 2. Discrete Probability Spaces.- 3. Conditional Probability.- 4. Compound Experiments.- 5. Bayes' Formula.- 6. Repetition of Simple Experiments; The Binomial Distribution.- 7. Drawings with and without Replacement.- 8. Random Variables.- 9. Expected Values. Means and Variances.- 10. Rules for Computing the Mean and Variance.- 11. Two Important Theorems.- 12. Markov Chains.- 13. Regular and Absorbing Markov Chains.- IV. The Theory of Games.- 1. Games: Extensive and Normal Form.- 2. Saddle Points.- 3. Mixed Strategies.- 4. Solution of 2×2 Games.- 5. 2×n and m×2 Games.- 6. Solutions by Linear Programming.- 7 Solution of Games by Fictitious Play.- 8. The von Neumann Model of an Expanding Economy.- 9. Existence of an Equilibrium Expansion Rate.- 10. Two-Person Non-Zero-Sum Games.- 11. Evolutionary Stable Systems.- V. Cooperative Games.- 1. n-Person Games.- 2. The Core.- 3. The Shapley Value.- 4. Voting Structures.- VI. Dynamic Programming.- 1. The Principle of Maximality.- 2. The Fixed-Charge Transportation Problem.- 3. Inventories.- 4. Stochastic Inventory Systems.- VII. Graphs and Networks.- 1. Introduction.- 2. CriticalPath Analysis.- 3. The Shortest Path through a Network.- 4. Minimal Spanning Trees.- 5. The Maximal Flow in a Network.