The course presents basic notions of the mathematical game theory. Different types of games are discussed together with different possibilities how to formalize them mathematically and how to solve them algorithmically.
At the beginning, the combinatorial games are discussed, i.e., games played by two players with perfect information.
Then the games in the standard (strategic) form and in the extensive form are studied, where we start with two-person zero-sum games (that can be solved in a finite case by transformation to the linear programming problem), and then we continue with
two-person general-sum games.
When the general-sum games are discussed, there are distinguished two case: non-cooperative games, where existence of Nash equilibria is studied, and cooperative games, where we distinguish variants with transferable utility and with nontransferable utility.
When studying both zero-sum and general-sum games, the variants of the games extended with probabilistic moves and an incomplete information are also studied.
Results of learning:
- To understand the basic concepts and methods of mathematical game theory.
- To gain basic experience with solving simple conflict and decision making problems by means of these methods.
- Acquaintance with fundamental ideas of game theory and ability using them in in complicated decision situation (conflicting situations, with randomness, incomplete information, ...).
- Understanding the main formal models and methods of the game theory and mastering their use in practice. To be able to solve standard problems of game theory (knowledge of corresponding algorithms).