Mathematical Game Theory

Every day, almost every minute we make a choice. Right now you have made the choice to read this text instead of scrolling further. Choices can be insignificant: to go by tram or by bus, to take an umbrella or not. Sometimes they can be very significant and even crucial: the choice of University, life partner. However, the importance of choice may not be realized initially. Sometimes a decision "not to take an umbrella" radically changes everything. The choice may affect a small group of people or entire countries. In game тtheory, we call it the choice of strategy. Constantly interacting with society and adopting certain strategies, many of us wonder: why can't everyone exist peacefully and cooperate with each other? Why do those who have agreed to cooperate, suddenly break the agreement? What if one is cooperative and the other is not? How profitable should the interaction be for the opponent to change his opinion? When are long-term stable prospects better than short-term benefits, and when not? The answers to these and other questions you will find out in our course. This course will be useful for those who want to make choices based on mathematical calculations rather than relying on fate. Who is interested in world politics and at least once heard about the "Prisoner's Dilemma". The course is basic and does not require any special knowledge. In several sections, definitions and theorems from mathematical analysis and elements of probability theory will be used.