1 Introduction. - 1. 1 Preview. - 1. 2 Prerequisites. - 1. 3 Numbering. - 2 Gambling Houses and the Conservation of Fairness. - 2. 1 Introduction. - 2. 2 Gambles Gambling Houses and Strategies. - 2. 3 Stopping Times and Stop Rules. - 2. 4 An Optional Sampling Theorem. - 2. 5 Martingale Convergence Theorems. - 2. 6 The Ordinals and Transfinite Induction. - 2. 7 Uncountable State Spaces and Continuous-Time. - 2. 8 Problems for Chapter 2. - 3 Leavable Gambling Problems. - 3. 1 The Fundamental Theorem. - 3. 2 The One-Day Operator and the Optimality Equation. - 3. 3 The Utility of a Strategy. - 3. 4 Some Examples. - 3. 5 Optimal Strategies. - 3. 6 Backward Induction: An Algorithm for U. - 3. 7 Problems for Chapter 3. - 4 Nonleavable Gambling Problems. - 4. 1 Introduction. - 4. 2 Understanding u(?). - 4. 3 A Characterization of V. - 4. 4 The Optimality Equation for V. - 4. 5 Proving Optimality. - 4. 6 Some Examples. - 4. 7 Optimal Strategies. - 4. 8 Another Characterization of V. - 4. 9 An Algorithm for V. - 4. 10 Problems for Chapter 4. - 5 Stationary Families of Strategies. - 5. 1 Introduction. - 5. 2 Comparing Strategies. - 5. 3 Finite Gambling Problems. - 5. 4 Nonnegative Stop-or-Go Problems. - 5. 5 Leavable Houses. - 5. 6 An Example of Blackwell and Ramakrishnan. - 5. 7 Markov Families of Strategies. - 5. 8 Stationary Plans in Dynamic Programming. - 5. 9 Problems for Chapter 5. - 6 Approximation Theorems. - 6. 1 Introduction. - 6. 2 Analytic Sets. - 6. 3 Optimality Equations. - 6. 4 Special Cases of Theorem 1. 2. - 6. 5 The Going-Up Property of $$ \overline M $$. - 6. 6 Dynamic Capacities and the Proof of Theorem 1. 2. - 6. 7 Approximating Functions. - 6. 8 Composition Closure and Saturated House. - 6. 9 Problems for Chapter 6. - 7 Stochastic Games. - 7. 1 Introduction. - 7. 2 Two-Person Zero-Sum Games. - 7. 3 The Dynamics of Stochastic Games. - 7. 4 Stochastic Games withlim sup Payoff. - 7. 5 Other Payoff Functions. - 7. 6 The One-Day Operator. - 7. 7 Leavable Games. - 7. 8 Families of Optimal Strategies for Leavable Games. - 7. 9 Examples of Leavable Games. - 7. 10 A Modification of Leavable Games and the Operator T. - 7. 11 An Algorithm for the Value of a Nonleavable Game. - 7. 12 The Optimality Equation for V. - 7. 13 Good Strategies in Nonleavable Games. - 7. 14 Win Lose or Draw. - 7. 15 Recursive Matrix Games. - 7. 16 Games of Survival. - 7. 17 The Big Match. - 7. 18 Problems for Chapter 7. - References. - Symbol Index. Language: English