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Lecturer(s)
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Volek Josef, doc. Ing. CSc.
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Course content
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Decision making and Theory of Games, history, subject of the discipline, John von Neumann formulation of the Theory of Games problem. Classification of decision situations. Basic notions and definitions I, matrix game, symmetric games, pure strategy, mixed strategy. Basic notions and definitions II, optimal strategy, skin game, paper, rock and scissor game, basic theorem of matrix games, mini max. Matrix games I, control of the game, domination, solution of matrix games by using linear programming. Matrix games II, method of fictive game (Brown method), graphical method, 2n/m2 games. Finite games, non antagonistic conflict of two players, cooperative theory, non cooperative theory, games with/without transfer of winnings. Positional games I, general model of n players in normal form, finite game of n persons in normal and developed form. Positional games II, information and information sets, attendance of nature, classification of finite games of n players in developed form. Positional games III, pure, mixed strategies and strategy of behavior, non cooperative and cooperative theory. Games against nature with risk, games against nature within uncertainty. Application of the Theory of Games in practice, optimal strategy in auction, two cooperating investors, general model.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Demonstration, Projection, Skills training
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Learning outcomes
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The aim of the subject is to acquaint the students with an important discipline of operational research that is Theory of Games and Decision Making Optimization. Using simple two players antagonistic decision situations the principles of mathematical modelling of general decision situations will be explained and appropriate mmethods of solution will be presented. Except static games the subject includes dynamic decision making situations inclusive presence of neture or casual mechanism. From the branch of non antagonistic decision making situations the attention will be payed to cooperative and not cooperative games. The study plan of the subject also includes games with uncertainty and games with risk.
Successfully passing the subject exam student masters philosophy and approaches towards mathematical models design of concrete decision situations is able to use mathematical methods for solving them and determine optimal strategies of all participants (players) of the decision situation.
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Prerequisites
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Basic knowledge of the Theory of probability and Linear programming in scale usual at universities of economic orientation.
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Assessment methods and criteria
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Oral examination, Written examination
The examination comprises of two parts - theoretical part and practical exercises - at least 51% success rate in each part is required.
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Recommended literature
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Baye, M. R. Managerial Economics and Business Strategy. McGraw-Hill, 2001, 2001.
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Baye,M.R. Managerial economics and business strategy. McGraw-Hill,2001, 2001.
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Chobot, M.,Turnovcová, A. Modely rozhodovania v konfliktných situáciách a za neurčitosti. VŠE Bratislava, 2004.
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Chobot,M. Teória hier. VŠE Bratislava, 2003.
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J. Von Neumann, Morgenstern O. Theory of Games and Eeconomic Behaviour. Princenton University Press, 2004.
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Jones, A.J. Game Theory: Mathematical Models of Conflict. J. Wiley, New York 1980, 1980.
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Maňas, M. Teorie her a její aplikace. SNTL, Praha 1992, 1992.
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Volek, J. Operační výzkum IV - Teorie her a optimální rozhodování. Univerzita Pardubice, skripta DFJP, 2004.
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