Discrete Gambling and Stochastic Games

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9780387946283: Discrete Gambling and Stochastic Games

The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de- veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op- timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi- nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler "controls" the stochastic pro- cess of his or her successive fortunes by choosing which games to play and what bets to make.

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Contenuti:

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.

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Ashok P. Maitra/ William D. Sudderth
Editore: Springer Verlag (1996)
ISBN 10: 0387946284 ISBN 13: 9780387946283
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Descrizione libro Springer Verlag, 1996. Hardcover. Condizione libro: Brand New. 1st edition. 244 pages. 9.75x6.50x0.75 inches. In Stock. Codice libro della libreria __0387946284

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Descrizione libro Springer, 1996. Hardcover. Condizione libro: New. 1996. This item is printed on demand. Codice libro della libreria DADAX0387946284

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Descrizione libro Springer, 1996. Hardcover. Condizione libro: New. book. Codice libro della libreria 0387946284

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Descrizione libro Springer-Verlag New York Inc., United States, 1996. Hardback. Condizione libro: New. 1996 ed.. 236 x 156 mm. Language: English . Brand New Book. The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de- veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op- timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi- nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler controls the stochastic pro- cess of his or her successive fortunes by choosing which games to play and what bets to make. Codice libro della libreria LIB9780387946283

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A.P. Maitra, W.D. Sudderth
Editore: Springer-Verlag New York Inc., United States (1996)
ISBN 10: 0387946284 ISBN 13: 9780387946283
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Descrizione libro Springer-Verlag New York Inc., United States, 1996. Hardback. Condizione libro: New. 1996 ed.. 236 x 156 mm. Language: English . Brand New Book. The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de- veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op- timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi- nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler controls the stochastic pro- cess of his or her successive fortunes by choosing which games to play and what bets to make. Codice libro della libreria LIB9780387946283

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A.P. Maitra, W.D. Sudderth
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Descrizione libro Springer-Verlag New York Inc. 1996-03-14, New York, NY, 1996. hardback. Condizione libro: New. Codice libro della libreria 9780387946283

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Descrizione libro Springer, 1996. Condizione libro: New. Codice libro della libreria L9780387946283

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Descrizione libro Springer Mrz 1996, 1996. Buch. Condizione libro: Neu. 241x161x22 mm. Neuware - The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler 'controls' the stochastic pro cess of his or her successive fortunes by choosing which games to play and what bets to make. 244 pp. Englisch. Codice libro della libreria 9780387946283

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Ashok P. Maitra
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ISBN 10: 0387946284 ISBN 13: 9780387946283
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Descrizione libro Springer Mrz 1996, 1996. Buch. Condizione libro: Neu. 235x155x20 mm. Neuware - The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler 'controls' the stochastic pro cess of his or her successive fortunes by choosing which games to play and what bets to make. 260 pp. Englisch. Codice libro della libreria 9780387946283

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Ashok P. Maitra
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ISBN 10: 0387946284 ISBN 13: 9780387946283
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(Bergisch Gladbach, Germania)
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Descrizione libro Springer Mrz 1996, 1996. Buch. Condizione libro: Neu. 235x155x20 mm. Neuware - The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler 'controls' the stochastic pro cess of his or her successive fortunes by choosing which games to play and what bets to make. 260 pp. Englisch. Codice libro della libreria 9780387946283

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