Title:  Game Theory 

Code:  THE 

Ac.Year:  2017/2018 

Term:  Winter 

Curriculums:  

Language of Instruction:  Czech 

Private info:  http://www.fit.vutbr.cz/study/courses/THE/private/ 

Credits:  4 

Completion:  credit+exam (written&verbal) 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  26  0  0  0  13 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  60  0  0  0  40 



Guarantor:  Hrubý Martin, Ing., Ph.D., DITS 

Lecturer:  Hrubý Martin, Ing., Ph.D., DITS 
Faculty:  Faculty of Information Technology BUT 

Department:  Department of Intelligent Systems FIT BUT 

 Learning objectives: 

  The THE course is going to give the students certain education in area of rational strategic decision making in conflict situations, to learn them creating models of such situations, to analyze the situations through the models and in some cases to predict future evolution of the modeled systems. The course extends the education of artificial intelligence with strategic decision making. Applications and use will be oriented to the computer science (control, decisions, safety and security, games, networking) and also to social sciences like economics, sociology and political sciences.  Description: 

  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 multiagent 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, noncooperative) 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.  Knowledge and skills required for the course: 

  Students should have a basic knowledge of discrete mathematics, algebra and mathematical analysis, as they are basic tools to describe the studied problems. Basics of artificial intelligence and computer modelling are also required.  Subject specific learning outcomes and competences: 

  Students will get a wide knowledge of game theory and a plenty of its applications in engineering and social sciences. When passed the course, the students will be able to create a simple model of given game situation and predict its probable future evolution.  Generic learning outcomes and competences: 

  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.  Syllabus of lectures: 


 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 zerosum payoffs: concept, saddle point, minimax theorem.
 Two player games with nonzerosum payoffs: concept, strategy dominance, Nash equilibrium in pure and mixed strategies, basic algorithms to find the Nash equilibrium.
 Mathematical methods in nonzerosum 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 nonzerosum 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.
 Syllabus  others, projects and individual work of students: 

 Students will be given an individual project to solve. The project is going to be one of these areas:
 Study  detail reading of given scientific paper and its analysis.
 Implementation  implementation of a given algorithm.
 Applications  a casestudy and its model.
 Fundamental literature: 


 various authors: Classics in Game Theory, edited by Harold W. Kuhn, Princetown University Press, 1997
 CesaBianci, N., Lugosi, G.: Prediction, Learning, and Games, Cambridge University Press, 2006
 Shubik, M.: Game Theory in the Social Sciences: Concepts and Solutions, MIT Press, 1984
 Dresher, M.: The Mathematics of Games of Strategy, Theory and Applications, Dover Publications, 1981
 McCarty, N., Mierowitz, N.: Political Game Theory: An Introduction, Cambridge University Press, 2007
 various authors: Algorithmic Game Theory, edited by Noam Nisan, Cambridge University Press, 2006
 Osbourne, M.J., Rubinstein, A.: A Course in Game Theory, MIT Press, 1994
 Fudenberg, D., Tirole, J.: Game Theory, MIT Press, 1991
 Dorfman, R., Samuelson, P.A., Solow, R. M.: Linear Programming and Economic Analysis, Dover Publications, 1986
 Schelling, T. S. : The Strategy of Conflict, Harvard Press, 1980
 Dugatkin, L., Reeve, H.: Game Theory and Animal Behavior, Oxford University Press, 1988
 Morrow, J.: Game Theory for Political Scientists, Princeton University Press, 1994
 Kreps, D.: Game Theory and Economic Modelling, Oxford University Press, 1990
 von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, Princeton University Press, 1944
 Mailath, G., Samuelson, L.: Repeated Games and Reputations, Oxford University Press, 2006
 Krishna, V.: Auction Theory, Elsevier, 2002
 Gintis, H.: Game Theory Evolving, Princeton University Press, 2000
 Miller, J.: Game Theory at Work, McGrawHill, 2003
 Straffin, P.D.: Game Theory and Strategy, The Mathematical Association of America, 2003
 Rasmunsen, E.: Games and Information, Blackwell Publishing, 2007
 Study literature: 


 Straffin, P.D.: Game Theory and Strategy, The Mathematical Association of America, 2003
 Gibbons, R.: Game Theory for Applied Economists, Princeton University Press, 1992
 Osbourne, M.J., Rubinstein, A.: A Course in Game Theory, MIT Press, 1994
 Controlled instruction: 

  Individual project and final exam. The final exam has two alternativies. The minimal number of points which can be obtained from the final exam is 25. Otherwise, no points will be assigned to a student.
 Exam prerequisites: 

  Students have to release a individually made project which will be evaluated at least with one half of points (20 points from 40).  
