Course detail
Game Theory
FIT-THEAcad. year: 2019/2020
The course deals with Mathematical game theory which is oftenly called the Theory of interactive decision making. The game theory became a popular tool for analysing of intelligent entities in many situations of competition or cooperation. This theory is being commonly applied in area of control, economic models, psychology, sociology, foreign affairs, evolutionary biology and informatics too. By computer science point of view, the game theory is an extension to artificial intelligence with algorithms of decision making, competing and bargaining. This also relates to multi-agent approaches. Games will be treated as models of real or fictitious situations with attributes of intelligence and competition. Students will go through basic terminology of games by the mechanism of their playing (sequential, strategic), by distribution of payoffs in a game (zero/nonzero sum games), by possible cooperation of players (cooperative, non-cooperative) and also by state of information in a game (complete/incomplete information). After the introduction, the games will be extended with possible repetition of moves (repeated games) and its effect to players behavior. In the second part of the semester, we will pay attention to game applications, mechanism design, auctions, social choice, economic and market models and others.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
In more general level, the study of rational decision making give a certain skills of problem analysis, selecting possible strategies and actions leading to its solving, assigning some utility to the strategies and finally, to accept a best decision in that situation. Mathematical game models also present clearly solutions to many problems in every day life. Moreover, the course introduces and plenty of applications of the computer science to natural and social sciences.
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
The minimal number of points which can be obtained from the final exam is 20. Otherwise, no points will be assigned to a student.
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading
Dorfman, R., Samuelson, P.A., Solow, R. M.: Linear Programming and Economic Analysis, Dover Publications, 1986
Dresher, M.: The Mathematics of Games of Strategy, Theory and Applications, Dover Publications, 1981
Dugatkin, L., Reeve, H.: Game Theory and Animal Behavior, Oxford University Press, 1988
Fudenberg, D., Tirole, J.: Game Theory, MIT Press, 1991
Gibbons, R.: Game Theory for Applied Economists, Princeton University Press, 1992
Gintis, H.: Game Theory Evolving, Princeton University Press, 2000
Hespanha, J. P.: Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists, Princeton University Press, 2017
Kreps, D.: Game Theory and Economic Modelling, Oxford University Press, 1990
Krishna, V.: Auction Theory, Elsevier, 2002
Mailath, G., Samuelson, L.: Repeated Games and Reputations, Oxford University Press, 2006
McCarty, N., Mierowitz, N.: Political Game Theory: An Introduction, Cambridge University Press, 2007
Miller, J.: Game Theory at Work, McGraw-Hill, 2003
Morrow, J.: Game Theory for Political Scientists, Princeton University Press, 1994
Osbourne, M.J., Rubinstein, A.: A Course in Game Theory, MIT Press, 1994
Rasmunsen, E.: Games and Information, Blackwell Publishing, 2007
Shubik, M.: Game Theory in the Social Sciences: Concepts and Solutions, MIT Press, 1984
Schelling, T. S. : The Strategy of Conflict, Harvard Press, 1980
Straffin, P.D.: Game Theory and Strategy, The Mathematical Association of America, 2003
various authors: Algorithmic Game Theory, edited by Noam Nisan, Cambridge University Press, 2006
various authors: Classics in Game Theory, edited by Harold W. Kuhn, Princetown University Press, 1997
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, Princeton University Press, 1944
Classification of course in study plans
- Programme IT-MSC-2 Master's
branch MMI , 0 year of study, winter semester, elective
branch MBI , 2 year of study, winter semester, compulsory
branch MSK , 1 year of study, winter semester, compulsory-optional
branch MMM , 0 year of study, winter semester, compulsory
branch MBS , 0 year of study, winter semester, elective
branch MPV , 0 year of study, winter semester, elective
branch MIS , 0 year of study, winter semester, elective
branch MIN , 0 year of study, winter semester, compulsory-optional
branch MGM , 0 year of study, winter semester, elective - Programme MITAI Master's
specialization NMAT , 0 year of study, winter semester, compulsory
specialization NBIO , 0 year of study, winter semester, elective
specialization NSEN , 0 year of study, winter semester, elective
specialization NVIZ , 0 year of study, winter semester, elective
specialization NGRI , 0 year of study, winter semester, elective
specialization NISD , 0 year of study, winter semester, elective
specialization NSEC , 0 year of study, winter semester, elective
specialization NCPS , 0 year of study, winter semester, elective
specialization NHPC , 0 year of study, winter semester, elective
specialization NNET , 0 year of study, winter semester, elective
specialization NMAL , 0 year of study, winter semester, elective
specialization NVER , 0 year of study, winter semester, elective
specialization NIDE , 0 year of study, winter semester, elective
specialization NEMB , 0 year of study, winter semester, elective
specialization NSPE , 0 year of study, winter semester, elective
specialization NADE , 0 year of study, winter semester, elective
specialization NISY , 0 year of study, winter semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Introduction, history of game theory, motivations to its study, theory of choice, basic terminology, basic classification of games, information in a game.
- Two player games with zero-sum payoffs: concept, saddle point, minimax theorem.
- Two player games with nonzero-sum payoffs: concept, strategy dominance, Nash equilibrium in pure and mixed strategies, basic algorithms to find the Nash equilibrium.
- Mathematical methods in nonzero-sum games: proof of Nashe's lemma of equilibrium existence in games with finite sets of strategies, algorithms to compute the equilibrium, graphical solution to games, linear programming.
- Sequential game with perfect/imperfect information: concept, applications, Stackelberg equilibrium, backward induction.
- Cooperative games and bargaining: presumptions for possible cooperation, bargaining in nonzero-sum games, Nash bargaining solution.
- Repeated games: concept (finite/infinite number of repetitions), solution. Applications of repeated games. Effect of repetitions to players behavior.
- Mechanism design: introduction to Mechanism design. Choice under uncertainty.
- Social choice, public voting: Arrow's paradox, mechanisms of voting.
- Auctions: study of rationality in auctions (mechanism with money). Business applications.
- Correlated equilibrium: effect of correlation to rational behavior, definition of correlated equilibrium and its relation to Nash equilibrium. Computing of correlated equilibria, applications.
- Evolutionary biology: strategic behavior in population of many entities, evolutionary stable strategy, case studies in the nature.
- Applications in economics and engineering: basic solution of oligopoly in analytic and numerical manner, nontrivial case study and its analysis. Application of game theory in computer networks. Applications in psychology, sociology and foreign affairs.
Project
Teacher / Lecturer
Syllabus
- Study - detail reading of given scientific paper and its analysis.
- Implementation - implementation of a given algorithm.
- Applications - a case-study and its model.