Game Theory

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)