456-0104/01 – Game Theory and Decision Making under Uncertainty (TEH)

Gurantor departmentDepartment of Computer ScienceCredits4
Subject guarantordoc. RNDr. Jaroslav MarklSubject version guarantordoc. RNDr. Jaroslav Markl
Study levelundergraduate or graduateRequirementChoice-compulsory
YearSemesterwinter
Study languageCzech
Year of introduction1997/1998Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
MAR37 doc. RNDr. Jaroslav Markl
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+0

Subject aims expressed by acquired skills and competences

To understand the basic concepts and methods of mathematical game theory and decision making under uncertainty. To gain basic experience with solving simple conflict and decision making problems by means of these methods. Acquaintance with fundamental ideas of game theory and ability using them in everyday informal decisions. Understanding the main formal models and methods of the game theory and mastering their using in practice. Gaining practical experience with program tools supporting game design, analysis and solution.

Teaching methods

Lectures
Tutorials

Summary

Game theory is a branch of mathematical analysis developed to study decision making in conflict situations. The course describes standard models of conflict situations and decision making and provides methods for their solutions. Many types of games are studied: with two or many participants, with constant sum or nonconstant-sum, with complete or uncomplete information, without or with random factors, cooperative or noncooperative.

Compulsory literature:

Hušek R., Maňas M.: Matematické modely v ekonomii. SNTL, Praha 1989. Černý M., Gluckaufová D.: Vícekriteriální rozhodování v podmínkách neurčitosti. Academia, Praha 1987. Markl J.: Teorie her. Učební texty v elektronické podobě. VŠB-TU Ostrava, 1999. Chobot M., Turnovec F., Ulašin V.: Teoria hier a rozhodovania. Bratislava, Alfa, 1991. Osborne M.J., Rubinstein A.: A course in game theory. MIT,1994. Slantchev B.I.: Basic Game Theory. Lecture notes, University of California, San Diego. 2002. http://polisci.ucsd.edu/~bslantch/courses/gt/ Möbius M.M.: Introduction to Game Theory. Lecture notes. Harvard University. 2003. http://www.courses.fas.harvard.edu/~ec1052/

Recommended literature:

http://www.gametheory.net/ - A resource for educators and students of game theory. Kaplan E.L.: Mathematical programming and games. New York, John Wiley, 1982. Fishburn P.C.: Decision and Value Theory. New York, John Wiley, 1984. Ferguson T.S.: Game theory. Lecture notes, University of California, Los Angeles. 2002. http://www.math.ucla.edu/~tom/GameTheory/intro.pdf J. van Benthem: Logic and Games. Lecture notes. University of Amsterdam. 2003. http://www.illc.uva.nl/lgc/lg.html Bialas W. : Game Theory. Lecture notes. University at Buffalo, State University of New York. 2003. http://www.acsu.buffalo.edu/~bialas/IE675.html

Way of continuous check of knowledge in the course of semester

Conditions for credit: There will be two exams: a midterm and a final examination. A number of homework assignments and eventually a term project can be completed. The weights given to these items in determining final grade are: - Midterm exam min. 10 - Homeworks and project min. 10, - Final exam min. 31.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Content and application area of game theory. Three main mathematical models of game: extensive form, normal (strategic) form, coalitional form. The strategic form of game. Basic notions: players, rules, outcomes, strategies of players, preference systems of players. The extensive form of game with perfect information and without random moves. Basic notions: positions, moves, move index, position graph, trajectories on graph. Normalization of the extensive form (transformation to the strategic form). The extensive form of game with imperfect information. Information sets. Normalization. The extensive form of game with random moves. The nature as a pseudoplayer. Transformation to normal form. Elements of utility theory. Ordinal and cardinal preference systems and corresponding utility functions. Normal form game with payoff functions (canonical form). Finite two-person games with zero-sum (matrix, antagonistic games) and with general-sum (bimatrix games). Conflict and cooperation. Cooperation with and without side payments. Antagonistic games. Equilibrium points. Pure and mixed equilibrium strategies. Elementary methods for antagonistic game solution if game matrix is of type 2x2 or 2xn or mx2. Fundamental theorem for antagonistic games. General solution by means of linear programming. Two-person games with general-sum. Finding Nash equilibria. Cooperative and noncooperative games. Cooperative games with transferable utility. Coalitional form of game. Game characteristic functions. Core. Stable coalition. Finding stable coalition structure. Decision under uncertainty. One-person games against nature. Multicriterial decisions. Ordering with respect to domination. Transformation to one criteral optimization. Exercises: solution of standard models of games and decision situation. Working with program systems supporting game The content of exercises is determined by the content of lectures. The main goals are: Recapitulation of some necessary prerequisities from probability theory, utility theory, linear programming,... Confirmate understanding of theoretical knowledge by means of simple examples solving. Master the basic set of methods for analysis and definition, analysis and solution

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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