Mathematical Game Theory

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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.

About the course

The choice may affect a small group of people or entire countries. In game theory, 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.

Instructors

Format

The course is taught completely online.

Requirements

The course is basic and does not require any special knowledge

Course program

Zero-sum Games

Noncooperative Games

Cooperative Games in Characteristic Function Form

Noncooperative Multistage Games

Cooperative Multistage Games

Differential Games

Learning outcomes

Upon completing the course "Mathematical Game Theory," learners will:

Grasp the fundamentals of game theory and its application to decision-making.
Analyze choices and strategies in different situations, considering both individual and collective interests.
Explore the reasons behind individuals and entities forming cooperative agreements.
Understand the dynamics of cooperation and the factors influencing the stability of such agreements.
Learn to quantify the profitability of interactions between different parties.
Analyze how economic incentives influence strategic choices.
Develop the ability to make decisions based on mathematical calculations rather than relying on intuition or fate.
Apply game theory principles to real-life situations for strategic advantage.

Competencies developed

The course is aimed at the formation of general learning competencies for Bachelor’s and Specialists’ programs, as well as other competencies included in the education program.

Формируемые компетенции:

1. способность к восприятию, обобщению, анализу информации, постановке цели и выбору путей её достижения (ОК-6)

2. способность использовать основные законы естественнонаучных дисциплин в профессиональной деятельности, применять методы математического анализа и моделирования, теоретического и экспериментального исследования (ОК-11)

3. способность использовать основные положения и методы гуманитарных и социально-экономических наук при решении профессиональных задач (ПК-12)

4. Способность применять известные математические методы для исследования и решения соответствующих задач (ПК-16.6)

5. Умение компьютерной реализации полученных решений (ПК-16.9)