Code: 01TEH Game Theory
Lecturer: Mgr. Jan Volec Ph.D. Weekly load: 2+0 Completion: EX
Department: 14101 Credits: 2 Semester: S
Description:
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.
Contents:
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.
Recommended literature:
Course textbook:
[1] Devos M., Kent D.: Game theory - A Playful Introduction, American Mathematical Society, 2016

Additional material:
[2] Maschler M., Solan E., Zamir S.: Game theory, Cambridge University Press, 2013
[3] von Neumann J., Morgenstern O.: Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944
Keywords:
Game theory, Hales-Jewett theorem, combinatorial games, strategical games, Nash equilibrium, coalitional games.

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