Theory Of Games And Statistical Decisions

Evaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory. The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games to normal forms, the minimax theorem, and the utility theorem. With this introduction, Blackwell and Professor Girshick look at: Values and Optimal Strategies in Games; General Structure of Statistical Games; Utility and Principles of Choice; Classes of Optimal Strategies; Fixed Sample-Size Games with Finite Ω and with Finite A; Sufficient Statistics and the Invariance Principle; Sequential Games; Bayes and Minimax Sequential Procedures; Estimation; and Comparison of Experiments. A few topics not directly applicable to statistics, such as perfect information theory, are also discussed. Prerequisites for full understanding of the procedures in this book include knowledge of elementary analysis, and some familiarity with matrices, determinants, and linear dependence. For purposes of formal development, only discrete distributions are used, though continuous distributions are employed as illustrations. The number and variety of problems presented will be welcomed by all students, computer experts, and others using statistics and game theory. This comprehensive and sophisticated introduction remains one of the strongest and most useful approaches to a field which today touches areas as diverse as gambling and particle physics.

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INTRODUCES THE FUNDAMENTALS OF PROBABILITY, STATISTICS, DECISION THEORY, AND GAME THEORY, AND FEATURES INTERESTING EXAMPLES OF GAMES OF CHANCE AND STRATEGY TO MOTIVATE AND ILLUSTRATE ABSTRACT MATHEMATICAL CONCEPTS Covering both random and strategic games, Probability, Decisions and Games features a variety of gaming and gambling examples to build a better understanding of basic concepts of probability, statistics, decision theory, and game theory. The authors present fundamental concepts such as random variables, rational choice theory, mathematical expectation and variance, fair games, combinatorial calculus, conditional probability, Bayes Theorem, Bernoulli trials, zero-sum games and Nash equilibria, as well as their application in games such as Roulette, Craps, Lotto, Blackjack, Poker, Rock-Paper-Scissors, the Game of Chicken and Tic-Tac-Toe. Computer simulations, implemented using the popular R computing environment, are used to provide intuition on key concepts and verify complex calculations. The book starts by introducing simple concepts that are carefully motivated by the same historical examples that drove their original development of the field of probability, and then applies those concepts to popular contemporary games. The first two chapters of Probability, Decisions and Games: A Gentle Introduction using R feature an introductory discussion of probability and rational choice theory in finite and discrete spaces that builds upon the simple games discussed in the famous correspondence between Blaise Pascal and Pierre de Fermat. Subsequent chapters utilize popular casino games such as Roulette and Blackjack to expand on these concepts illustrate modern applications of these methodologies. Finally, the book concludes with discussions on game theory using a number of strategic games. This book: · Features introductory coverage of probability, statistics, decision theory and game theory, and has been class-tested at University of California, Santa Cruz for the past six years · Illustrates basic concepts in probability through interesting and fun examples using a number of popular casino games: roulette, lotto, craps, blackjack, and poker · Introduces key ideas in game theory using classic games such as Rock-Paper-Scissors, Chess, and Tic-Tac-Toe. · Features computer simulations using R throughout in order to illustrate complex concepts and help readers verify complex calculations · Contains exercises and approaches games and gambling at a level that is accessible for readers with minimal experience · Adopts a unique approach by motivating complex concepts using first simple games and then moving on to more complex, well-known games that illustrate how these concepts work together Probability, Decisions and Games: A Gentle Introduction using R is a unique and helpful textbook for undergraduate courses on statistical reasoning, introduction to probability, statistical literacy, and quantitative reasoning for students from a variety of disciplines. ABEL RODRÍGUEZ, PhD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC), CA, USA. The author of 40 journal articles, his research interests include Bayesian nonparametric methods, machine learning, spatial temporal models, network models, and extreme value theory. BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz, CA, USA. BRUNO MENDES, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of Cal

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.