Author | Maitra, Ashok P. author |
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Title | Discrete Gambling and Stochastic Games [electronic resource] / by Ashok P. Maitra, William D. Sudderth |
Imprint | New York, NY : Springer New York, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4002-0 |
Descript | XII, 244 p. online resource |
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 with lim 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