Game Theory
Code | Completion | Credits | Range |
---|---|---|---|
01TEH | ZK | 2 | 2+0 |
- Garant předmětu:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Mathematics
- Synopsis:
-
1. Combinatorial games, normal games - impartial and partizan games.
2. Multidimensional tic-tac-toe, Hales Jewett theorem.
3. Game tree, Zermelo's Theorem, Strategy stealing.
4. Arithmetic on normal games, equivalence on games, MEX principle, Sprague-Grundy theorem.
5. Strategic games, pure and mixed strategies, dominated strategies.
6. Zero-sum games, MAX-min principle, von Neumann theorem.
7. Nash equilibrium, Nash theorem.
8. Cooperation of two players, Nash arbitration.
9. Coalitional games, Shapley value.
- Requirements:
-
Basic knowledge of discrete mathematics and linear programming.
- Syllabus of lectures:
-
1. Combinatorial games, normal games - impartial and partizan games.
2. Multidimensional tic-tac-toe, Hales Jewett theorem.
3. Game tree, Zermelo's Theorem, Strategy stealing.
4. Arithmetic on normal games, equivalence on games, MEX principle, Sprague-Grundy theorem.
5. Strategic games, pure and mixed strategies, dominated strategies.
6. Zero-sum games, MAX-min principle, von Neumann theorem.
7. Nash equilibrium, Nash theorem.
8. Cooperation of two players, Nash arbitration.
9. Coalitional games, Shapley value.
- Syllabus of tutorials:
- Study Objective:
-
Acquired knowledge: basic mathematical forms of games, their solutions and computational algorithms
Acquired skills: familiarity with game-theoretic models and their applications.
- Study materials:
-
Compulsory literature:
Devos M., Kent D.: Game theory - A Playful Introduction, American Mathematical Society, 2016
Optional literature:
Maschler M., Solan E., Zamir S.: Game theory, Cambridge University Press, 2013
von Neumann J., Morgenstern O.: Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944
- Note:
- Further information:
- http://honza.ucw.cz/TEH
- No time-table has been prepared for this course
- The course is a part of the following study plans:
-
- Aplikované matematicko-stochastické metody (elective course)
- Matematická informatika (elective course)