Course details

Game Theory

THE Acad. year 2010/2011 Winter semester 4 credits

Current academic year

Guarantor

Hrubý Martin, Ing., Ph.D. (DITS)

Language of instruction

Czech

Completion

Credit+Examination

Time span

  • 26 hrs lectures
  • 13 hrs projects

Department

Department of Intelligent Systems (UITS)

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

  • různí autoři: 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
  • různí autoři: 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

Syllabus of lectures

  1. Introduction, history of game theory, motivations to its study, theory of choice, basic terminology, basic classification of games, information in a game.
  2. Two player games with zero-sum payoffs: concept, saddle point, minimax theorem.
  3. Two player games with nonzero-sum payoffs: concept,  strategy dominance, Nash equilibrium in pure and mixed strategies, basic algorithms to find the Nash equilibrium.
  4. 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 equilibria, graphical solution to games, linear programming.
  5. Sequential game with perfect/imperfect information: concept, applications, Stackelberg equilibrium, backward induction.
  6. Cooperative games and bargaining: presumptions for possible cooperation, bargaining in nonzero-sum games, Nash  bargaining solution.
  7. Repeated games: concept (finite/infinite number of repetitions), solution. Applications of repeated games.  Effect of repetitions to players behavior.
  8. Mechanism design: introduction to Mechanism design. Choice under uncertainty.
  9. Social choice, public voting: Arrow's paradox, mechanisms of voting.
  10. Auctions: study of rationality in auctions (mechanism with money). Business applications.
  11. Correlated ekvilibrium: effect of correlation to rational behavior, definition of correlated equilibrium and its relation to Nash equilibrium. Computing of correlated equilibria, applications.
  12. Evolutionary biology: strategic behavior in population of many entities, evolutionary stable strategy, case studies in the nature.
  13. Applications in economics and engineering: basic solutio 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.

Course inclusion in study plans

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