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Lectures on the theory of decision making. Textbook. (Лекциї з теорії вибору та прийняття рішень. Навчальний посібник.) (Ukrainian) Zbl 1183.90003
Kyïv: Vydavnycho-Poligrafichnyĭ Tsentr, Kyïvskyĭ Universytet (ISBN 966-439-002-X). 256 p. (2007).
The book is written on the basis of lectures on the course “Theory of decision making” which the authors read for students of the Mechanics and Mathematics faculty of Taras Shevchenko National University of Kyïv.
Basic notions, theorems and results of linear programming are stated in chapter 1 “Problems of linear programming”. Main methods of problem solving such as the simplex method and the method of potentials are given. The second chapter “Elements of the game theory” deals with basic methods and theorems of antagonistic and cooperative game theory. The basic theorems of antagonistic game theory are proved. Properties of optimal strategies of players are studied. Basic notions, results and theorems of bimatrix games are described. Chapter 3 “Optimal statistical decisions” contains fundamental results of the theory of statistical decisions. The main attention is on the Bayesian methods in decision theory. Chapter 4 “Conjugate prior distributions” describes basic probability distributions used for the problem of the estimation of unknown parameters. Chapter 5 “Estimation” contains description of Bayesian approach to the problem of the estimation of unknown parameters. The main attention is on estimates that minimize the mean square and absolute errors. Chapter 6 “Dynamic programming” considers the Bellman dynamical programming principle and its application for solving some problems of microeconomics.
The textbook contains a series of examples of solutions of problems. A lot of problems are proposed for self-study.
MSC:
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
91-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance
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