SUBJECT
Game theory
lecture
master
3
Semesters 1-4
Autumn/Spring semester
Matrix games. Optimal strategies for matrix games with saddle point. Mixed strategies, expected yield. Neumann minimax theorem. Solving matrix games with linear programming. Nash equilibrium. Sperner lemma. The first and second Knaster-Kuratowski-Mazurkiewicz theorems. The Brower and Kakutani fixed-point theorems. Shiffmann minimax theorem. Arrow-Hurwitz and Arrow-Debreu theorems. The Arrow-Hurwitz-Uzawa condition. The Arrow-Hurwitz and Uzawa algorithms. Applications of games in environment protection, health sciences and psichology.
- Forgó F., Szép J., Szidarovszky F., Introduction to the theory of games: concepts, methods, applications, Kluwer Academic Publishers, Dordrecht, 1999.
- Osborne, M. J., Rubinstein A., A course in game theory, The MIT Press, Cambridge, 1994.
- J. P. Aubin: Mathematical Methods of Game and Economic Theor. North-Holland, Amsterdam, 1982.