"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Game Theory |
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| Teaching Staff in Charge |
Prof. KASSAY Gabor, Ph.D., kassay math.ubbcluj.ro |
| Aims |
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Exposition of the most important minimax theorems and various methods for proving them, and the presentation of some algorithms for solving matrix games. |
| Content |
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Classical minimax theorems; recently published minimax theorems; methods: fixed point, separation of convex sets with hyperplanes (Hahn-Banach's theorem), elementary methods (the level set method of Istvan Joo). Applications to noncooperative matrix and nonmatrix games. Methods for solving games, examples. The connection between minimax theorems and duality theory in optimization. |
| References |
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1. KASSAY G.: The Equilibrium Problem and Related Topics. Cluj-Napoca: Editura Risoprint, 2000.
2. KASSAY G. et al.: Lectures on Nonlinear Analysis and its Applications. Cluj-Napoca: Scientia Publishing House, 2003. 3. BRECKNER W. W.: Cercetare operationala. Cluj-Napoca: Universitatea Babes-Bolyai, 1981. 4. SZÉP J., FORGÓ F.: Introduction to the Theory of Games. Budapest: Akadémiai Kiadó, 1985. 5. KASSAY G., KOLUMBÁN J.: On a generalized sup-inf problem. J. Optim. Theory Appl., 91 (1996), 651-670. 6. FRENK J. B. G., KASSAY G.: Minimax results and finite dimensional separation. J. Optim. Theory Appl., 113 (2002), nr. 2, 409-421. 7. FRENK J. B. G., KASSAY G., KOLUMBÁN J.: Equivalent results in minimax theory. European J. Oper. Res., 157 (2004), 46-58. 8. KAS P., KASSAY G., BORATAS-SENSOY Z.: On generalized equilibrum points. J. Math. Anal. Appl., 296 (2004), 619-633. |
| Assessment |
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Exam |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |