Course: Theory of Games

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Course title Theory of Games
Course code UMKM/PTH
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Zahrádka Jaromír, RNDr. Ph.D.
  • Volek Josef, doc. Ing. CSc.
  • Linda Bohdan, doc. RNDr. CSc.
Course content
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.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
Learning outcomes
The goal of the subject is to acquaint university students with important discipline of operational research-Theory of games and optimal decision making. On simple paradigms of matrix games will be explained procedure of mathematical models design of decision situations and methods of solution.
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.
Prerequisites
Basic knowledge of the Theory of probability and Linear programming in scale usual at universities of economic orientation.

Assessment methods and criteria
Oral examination, Written examination, Student performance assessment

The examination comprises of two parts - theoretical part and practical exercises - at least 51% success rate in each part is required.
Recommended literature
  • . ..
  • Baye,M.R. Managerial economics and business strategy. McGraw-Hill,2001, 2001.
  • Chobot, M.,Turnovcová, A. Modely rozhodovania v konfliktných situáciách a za neurčitosti. VŠE Bratislava, 2004.
  • Chobot,M. Teória hier. VŠE Bratislava, 2003.
  • J. Von Neumann, Morgenstern O. Theory of Games and Eeconomic Behaviour. Princenton University Press, 2004.
  • Jones, A.J. Game Theory: Mathematical Models of Conflict. J. Wiley, New York 1980, 1980.
  • Volek, J. Operační výzkum IV - Teorie her a optimální rozhodování. Univerzita Pardubice, skripta DFJP, 2004.


Study plans that include the course