Discrete Gambling And Stochastic Games

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Discrete Gambling and Stochastic Games

Author : Ashok P. Maitra
Publisher : Springer Science & Business Media
ISBN 13 : 1461240026
Total Pages : 249 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Discrete Gambling and Stochastic Games by : Ashok P. Maitra

Download or read book Discrete Gambling and Stochastic Games written by Ashok P. Maitra and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Games and Applications

Author : Abraham Neyman
Publisher : Springer Science & Business Media
ISBN 13 : 9401001898
Total Pages : 473 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Stochastic Games and Applications by : Abraham Neyman

Download or read book Stochastic Games and Applications written by Abraham Neyman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures given at the NATO Advanced Study Institute on "Stochastic Games and Applications," which took place at Stony Brook, NY, USA, July 1999. It gives the editors great pleasure to present it on the occasion of L.S. Shapley's eightieth birthday, and on the fiftieth "birthday" of his seminal paper "Stochastic Games," with which this volume opens. We wish to thank NATO for the grant that made the Institute and this volume possible, and the Center for Game Theory in Economics of the State University of New York at Stony Brook for hosting this event. We also wish to thank the Hebrew University of Jerusalem, Israel, for providing continuing financial support, without which this project would never have been completed. In particular, we are grateful to our editorial assistant Mike Borns, whose work has been indispensable. We also would like to acknowledge the support of the Ecole Poly tech nique, Paris, and the Israel Science Foundation. March 2003 Abraham Neyman and Sylvain Sorin ix STOCHASTIC GAMES L.S. SHAPLEY University of California at Los Angeles Los Angeles, USA 1. Introduction In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players.

A Course in Stochastic Game Theory

Author : Eilon Solan
Publisher : Cambridge University Press
ISBN 13 : 1316516334
Total Pages : 279 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis A Course in Stochastic Game Theory by : Eilon Solan

Download or read book A Course in Stochastic Game Theory written by Eilon Solan and published by Cambridge University Press. This book was released on 2022-05-26 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book for beginning graduate students presents a course on stochastic games and the mathematical methods used in their analysis.

Stochastic Games and Related Concepts

Author : T. Parthasarathy
Publisher : Springer Nature
ISBN 13 : 9811565775
Total Pages : 127 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Stochastic Games and Related Concepts by : T. Parthasarathy

Download or read book Stochastic Games and Related Concepts written by T. Parthasarathy and published by Springer Nature. This book was released on 2020-12-08 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses stochastic game theory and related concepts. Topics focused upon in the book include matrix games, finite, infinite, and undiscounted stochastic games, n-player cooperative games, minimax theorem, and more. In addition to important definitions and theorems, the book provides readers with a range of problem-solving techniques and exercises. This book is of value to graduate students and readers of probability and statistics alike.

Handbook of Game Theory

Author : Petyon Young
Publisher : Elsevier
ISBN 13 : 0444537678
Total Pages : 1024 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Handbook of Game Theory by : Petyon Young

Download or read book Handbook of Game Theory written by Petyon Young and published by Elsevier. This book was released on 2014-10-01 with total page 1024 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to understand and predict behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others, has been the domain of game theory since the 1950s. Developing the theories at the heart of game theory has resulted in 8 Nobel Prizes and insights that researchers in many fields continue to develop. In Volume 4, top scholars synthesize and analyze mainstream scholarship on games and economic behavior, providing an updated account of developments in game theory since the 2002 publication of Volume 3, which only covers work through the mid 1990s. Focuses on innovation in games and economic behavior Presents coherent summaries of subjects in game theory Makes details about game theory accessible to scholars in fields outside economics

Discrete-Time Markov Chains

Author : George Yin
Publisher : Springer Science & Business Media
ISBN 13 : 9780387219486
Total Pages : 372 pages
Book Rating : 4.2/5 (194 download)

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Book Synopsis Discrete-Time Markov Chains by : George Yin

Download or read book Discrete-Time Markov Chains written by George Yin and published by Springer Science & Business Media. This book was released on 2005 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from existing and emerging applications in optimization and control of complex hybrid Markovian systems in manufacturing, wireless communication, and financial engineering. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.

Stochastic and Differential Games

Author : Martino Bardi
Publisher : Springer Science & Business Media
ISBN 13 : 1461215927
Total Pages : 388 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic and Differential Games by : Martino Bardi

Download or read book Stochastic and Differential Games written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.

Further Topics on Discrete-Time Markov Control Processes

Author : Onesimo Hernandez-Lerma
Publisher : Springer Science & Business Media
ISBN 13 : 1461205611
Total Pages : 286 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Further Topics on Discrete-Time Markov Control Processes by : Onesimo Hernandez-Lerma

Download or read book Further Topics on Discrete-Time Markov Control Processes written by Onesimo Hernandez-Lerma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to MCPs with Borel state and control spaces. Although the book follows on from the author's earlier work, an important feature of this volume is that it is self-contained and can thus be read independently of the first. The control model studied is sufficiently general to include virtually all the usual discrete-time stochastic control models that appear in applications to engineering, economics, mathematical population processes, operations research, and management science.

Repeated Games

Author : Jean-François Mertens
Publisher : Cambridge University Press
ISBN 13 : 110703020X
Total Pages : 597 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Repeated Games by : Jean-François Mertens

Download or read book Repeated Games written by Jean-François Mertens and published by Cambridge University Press. This book was released on 2015-02-09 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This landmark work significantly advances the literature on game theory with a masterful conceptual presentation of the CORE working papers published in 1994.

Statistics, Probability, and Game Theory

Author : David Blackwell
Publisher : IMS
ISBN 13 : 9780940600423
Total Pages : 428 pages
Book Rating : 4.6/5 (4 download)

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Book Synopsis Statistics, Probability, and Game Theory by : David Blackwell

Download or read book Statistics, Probability, and Game Theory written by David Blackwell and published by IMS. This book was released on 1996 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the 26 papers are research reports on probability, statistics, gambling, game theory, Markov decision processes, set theory, and logic. But they also include reviews on comparing experiments, games of timing, merging opinions, associated memory models, and SPLIF's; historical views of Carnap, von Mises, and the Berkeley Statistics Department; and a brief history, appreciation, and bibliography of Berkeley professor Blackwell. A sampling of titles turns up The Hamiltonian Cycle Problem and Singularly Perturbed Markov Decision Process, A Pathwise Approach to Dynkin Games, The Redistribution of Velocity: Collision and Transformations, Casino Winnings at Blackjack, and Randomness and the Foundations of Probability. No index. Annotation copyrighted by Book News, Inc., Portland, OR

How to Gamble If You Must

Author : Lester E. Dubins
Publisher : Courier Corporation
ISBN 13 : 0486780643
Total Pages : 307 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis How to Gamble If You Must by : Lester E. Dubins

Download or read book How to Gamble If You Must written by Lester E. Dubins and published by Courier Corporation. This book was released on 2014-08-20 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic of advanced statistics is geared toward graduate-level readers and uses the concepts of gambling to develop important ideas in probability theory. The authors have distilled the essence of many years' research into a dozen concise chapters. "Strongly recommended" by the Journal of the American Statistical Association upon its initial publication, this revised and updated edition features contributions from two well-known statisticians that include a new Preface, updated references, and findings from recent research. Following an introductory chapter, the book formulates the gambler's problem and discusses gambling strategies. Succeeding chapters explore the properties associated with casinos and certain measures of subfairness. Concluding chapters relate the scope of the gambler's problems to more general mathematical ideas, including dynamic programming, Bayesian statistics, and stochastic processes. Dover (2014) revised and updated republication of the 1976 Dover edition entitled Inequalities for Stochastic Processes. See every Dover book in print at www.doverpublications.com

Handbook of Markov Decision Processes

Author : Eugene A. Feinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461508053
Total Pages : 560 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Handbook of Markov Decision Processes by : Eugene A. Feinberg

Download or read book Handbook of Markov Decision Processes written by Eugene A. Feinberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eugene A. Feinberg Adam Shwartz This volume deals with the theory of Markov Decision Processes (MDPs) and their applications. Each chapter was written by a leading expert in the re spective area. The papers cover major research areas and methodologies, and discuss open questions and future research directions. The papers can be read independently, with the basic notation and concepts ofSection 1.2. Most chap ters should be accessible by graduate or advanced undergraduate students in fields of operations research, electrical engineering, and computer science. 1.1 AN OVERVIEW OF MARKOV DECISION PROCESSES The theory of Markov Decision Processes-also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming-studiessequential optimization ofdiscrete time stochastic systems. The basic object is a discrete-time stochas tic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. The goal is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types ofimpacts: (i) they cost orsavetime, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view offuture events. MDPs model this paradigm and provide results on the structure and existence of good policies and on methods for their calculation.

Two-Scale Stochastic Systems

Author : Yuri Kabanov
Publisher : Springer Science & Business Media
ISBN 13 : 3662132427
Total Pages : 266 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Two-Scale Stochastic Systems by : Yuri Kabanov

Download or read book Two-Scale Stochastic Systems written by Yuri Kabanov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.

Stochastic Networks and Queues

Author : Philippe Robert
Publisher : Springer Science & Business Media
ISBN 13 : 3662130521
Total Pages : 406 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Stochastic Networks and Queues by : Philippe Robert

Download or read book Stochastic Networks and Queues written by Philippe Robert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks. In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.

Stochastic Simulation: Algorithms and Analysis

Author : Søren Asmussen
Publisher : Springer Science & Business Media
ISBN 13 : 0387690336
Total Pages : 476 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Stochastic Simulation: Algorithms and Analysis by : Søren Asmussen

Download or read book Stochastic Simulation: Algorithms and Analysis written by Søren Asmussen and published by Springer Science & Business Media. This book was released on 2007-07-14 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.

Stochastic Control of Hereditary Systems and Applications

Author : Mou-Hsiung Chang
Publisher : Springer Science & Business Media
ISBN 13 : 038775816X
Total Pages : 406 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Stochastic Control of Hereditary Systems and Applications by : Mou-Hsiung Chang

Download or read book Stochastic Control of Hereditary Systems and Applications written by Mou-Hsiung Chang and published by Springer Science & Business Media. This book was released on 2008-01-03 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops the Hamilton-Jacobi-Bellman theory via dynamic programming principle for a class of optimal control problems for stochastic hereditary differential equations (SHDEs) driven by a standard Brownian motion and with a bounded or an infinite but fading memory. These equations represent a class of stochastic infinite-dimensional systems that become increasingly important and have wide range of applications in physics, chemistry, biology, engineering and economics/finance. This monograph can be used as a reference for those who have special interest in optimal control theory and applications of stochastic hereditary systems.

Stochastic Integration and Differential Equations

Author : Philip Protter
Publisher : Springer
ISBN 13 : 3662100614
Total Pages : 430 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Stochastic Integration and Differential Equations by : Philip Protter

Download or read book Stochastic Integration and Differential Equations written by Philip Protter and published by Springer. This book was released on 2013-12-21 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.