Game theory with examples from the game Magic: the Gathering

Learning outcomes at the level of the programme to which the course contributes

• Apply specific knowledge and skills from selected disciplines constituting cognitive science.
• Integrate insights, methods, and levels of analysis across different disciplines into a unified framework for understanding the human mind and cognition in general.
• Participate in data-driven innovation projects and apply appropriate data science tools.
• Employ diverse disciplinary tools in exploring and describing the nature of cognitive processes.

Course content (syllabus)

1. Introduction to basic concepts from logic and the theory of probability.
2. Basic concepts of game theory, types of games, examples from practice.
3. Introduction to the game Magic: the Gathering, history and rules of the game.
4. Archetypes of decks and their position in a competitive environment.
5. Formalization of games, games in extensive and normal form, matrix games.
6. Formalized situations from the game Magic: the Gathering.
7. Games with perfect and imperfect information, games with complete and incomplete information.
8. Zero and non-zero sum games.
9. Pure and mixed strategies, elimination of dominated strategies.
10. Application of linear programming in the game theory.
11. Problems of equilibrium, J. Nash's contribution to game theory, Nash's criterion, Nash's equilibrium.
12. Bargaining Model. Solving Bargaining Games.
13. Draft format.
14. Alternative game formats of Magic: the Gathering.
15. Application of game theory in cognitive science.