Course details

# Game Theory

THE Acad. year 2019/2020 Winter semester 5 credits

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Subject specific learning outcomes and competences

Generic learning outcomes and competences

Learning objectives

Why is the course taught

Prerequisite kwnowledge and skills

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

Fundamental literature

- various authors: Classics in Game Theory, edited by Harold W. Kuhn, Princetown University Press, 1997
- Cesa-Bianci, 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, McGraw-Hill, 2003
- Straffin, P.D.: Game Theory and Strategy, The Mathematical Association of America, 2003
- Rasmunsen, E.: Games and Information, Blackwell Publishing, 2007
- Hespanha, J. P.: Noncooperative Game Theory: An Introduction for Engineers and Computer Scientists, Princeton University Press, 2017

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 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.

Syllabus - others, projects and individual work of students

- Study - detail reading of given scientific paper and its analysis.
- Implementation - implementation of a given algorithm.
- Applications - a case-study and its model.

Controlled instruction

**The minimal number of points which can be obtained from the final exam is 20. Otherwise, no points will be assigned to a student.**

Exam prerequisites

Schedule

Course inclusion in study plans

- Programme IT-MSC-2, field MBI, 2nd year of study, Compulsory
- Programme IT-MSC-2, field MBS, MGM, MIS, MMI, MPV, any year of study, Elective
- Programme IT-MSC-2, field MIN, any year of study, Compulsory-Elective group S
- Programme IT-MSC-2, field MMM, any year of study, Compulsory
- Programme IT-MSC-2, field MSK, 1st year of study, Compulsory-Elective group M
- Programme MITAI, specialisation NADE, NBIO, NCPS, NEMB, NGRI, NHPC, NIDE, NISD, NISY, NMAL, NNET, NSEC, NSEN, NSPE, NVER, NVIZ, any year of study, Elective
- Programme MITAI, specialisation NMAT, any year of study, Compulsory