# Game Theory

- Credits: 4
- Ending: Examination
- Range: 2P + 2C
- Semester: winter
- Year: 1
- Faculty of Business Economics with seat in Košice

## Teachers

## Included in study programs

**Teaching results**

The aim of the course is to provide students with basic knowledge of game theory. The student will gain an overview of the basic types of games that can be applied to real situations, he will be able to find optimal strategies in various decision-making situations, whether it will be a situation corresponding to non-cooperative games or cooperative games, in which he also learns to work in team. Students will also practice the connection of game theory with real situations in voting games, where it is important to know which coalitions are advantageous and why. The student will get acquainted with the basic models of the market and with the basic types of auctions.

Knowledge:

At the theoretical level student has the necessary knowledge of the basic definitions of game theory, he knows ways to find optimal strategies, methods how to solve matrix and bimatrix games, he has an overview of possible solutions in situations corresponding to decision-making for risks and uncertainties, he knows definitions and principles of non-cooperative and cooperative games and has knowledge of coalition formation, the basic market models and the basic types of auctions.

Skills:

The student is able to apply the concepts of game theory to real situations, to solve basic types of games, to find the optimal solution of matrix games, non-cooperative and cooperative games. He is able to decide in situations corresponding to games against nature. The student's ability to work in a team will be used in solving cooperative games and creating coalitions.

Competences:

After completing the course, student has basic knowledge of game theory and their use in solving specific tasks, especially those of an economic nature, which he demonstrates by the project developing and its subsequent presentation. Student is able to apply the gained knowledge in real situations such as the selection of a suitable partner in the company, the selection of a suitable location for the company or the selection of a suitable strategy for the competition fight on the market.

**Indicative content**

Lectures:

1. Basic concepts of modeling conflict situations.

2. Games in normal form, games in extensive form, non-conflict decision situations.

3. Two player games. Definition of antagonistic conflict. Matrix games and methods of their solution. Optimal player strategies, their existence and properties. Fictitious game method, dominance in matrix games.

4. Bimatrix games.

5. Endless antagonistic conflicts - finding a balanced strategy of the game.

6. Von Neumann-Morgenstern utility function.

7. Decision making for risks and uncertainties. Games against nature.

8. Non-cooperative games of n players. Equilibrium points in pure and mixed strategies. Optimal decision making in non-cooperative games.

9. Cooperative games of n players. Coalitions and their characteristic functions. The core of the game. Shapley's value of the game.

10. Voting games. Shapley force index. Banzhaf's strength index. Coalition formation theory.

11. Market models in game theory. Monopoly, duopoly, oligopoly.

12. Introduction to auction theory.

13. Applications of game theory in the economic environment, paradoxes of economic laws.

Seminars:

1. Basic concepts of modeling conflict situations.

2. Games in normal form, games in extensive form, non-conflict decision situations.

3. Two player games. Definition of antagonistic conflict. Matrix games and methods of their solution. Optimal player strategies, their existence and properties. Fictitious game method, dominance in matrix games.

4. Bimatrix games.

5. Endless antagonistic conflicts - finding a balanced strategy of the game.

6. Von Neumann-Morgenstern utility function.

7. Decision making for risks and uncertainties. Games against nature.

8. Non-cooperative games of n players. Equilibrium points in pure and mixed strategies. Optimal decision making in non-cooperative games.

9. Cooperative games of n players. Coalitions and their characteristic functions. The core of the game. Shapley's value of the game.

10. Voting games. Shapley force index. Banzhaf's strength index. Coalition formation theory.

11. Test.

12. Projects presentations.

13. Projects presentations.

**Support literature**

Elementary literature:

1. BONANNO, Giacomo. Game theory: Parts I and II-with 88 solved exercises. An open access textbook. Working Paper, 2015.

2. JIMÉNEZ-MARTÍNEZ, Antonio. Game Theory and its Applications.

3. MASCHLER, Michael; ZAMIR, Shmuel; SOLAN, Eilon. Game theory. Cambridge University Press, 2020.

4. MUNOZ-GARCIA, F. – TORO-GONZALES, D. 2016. Strategy and Game Theory:Practice Excercises with Answers. Springer International Publishing Switzerland. 2016. ISBN: 978-3319329628.

5. OWEN, G. 1995. Game theory. Academic Press, London, 1995.

6. PETROSYAN, L. A.- ZENKEVICH, N. A. 2016. Game Theory. Second Edition. World Scientific Publishing. 2016.

Supplementary literature:

7. CORCHÓN, L. C. – MARINI, M. A. 2018. Handbook of Game Theory and Industrial Organization, Volume I. Edward Elgar Publishing. 2018. ISBN: 978-1-78536-327-6

8. CORCHÓN, L. C. – MARINI, M. A. 2018. Handbook of Game Theory and Industrial Organization, Volume II. Edward Elgar Publishing. 2018. ISBN: 978- 1-78811-277-2

9. KUHN, H. W. (ed.) 1997. Classics in Game Theory. Princeton : Princeton University Press, 1997.

10. MUROS, F. J. 2018. Cooperative Game Theory Tools in Coalitional Control Networks.Springer, Cham. 2018. ISBN: 978-3-030-10489-4

11. PETERSON, M. 2010. An Introduction to Decision Theory. Cambridge University Press, 2010.

**Syllabus**

Lectures: 1. Basic concepts of modeling conflict situations. 2. Games in normal form, games in extensive form, non-conflict decision situations. 3. Two player games. Definition of antagonistic conflict. Matrix games and methods of their solution. Optimal player strategies, their existence and properties. Fictitious game method, dominance in matrix games. 4. Bimatrix games. 5. Endless antagonistic conflicts - finding a balanced strategy of the game. 6. Von Neumann-Morgenstern utility function. 7. Decision making for risks and uncertainties. Games against nature. 8. Non-cooperative games n players. Equilibrium points in pure and mixed strategies. Optimal decision making in non-cooperative games. 9. Cooperative games n players. Coalitions and their characteristic functions. The core of the game. Shapley's value of the game. 10. Voting games. Shapley force index. Banzhaf's strength index. Coalition formation theory. 11. Market models in game theory. Monopoly, duopoly, oligopoly. 12. Introduction to auction theory. 13. Applications of game theory in the economic environment, paradoxes of economic laws. Seminars: 1. Basic concepts of modeling conflict situations. 2. Games in normal form, games in extensive form, non-conflict decision situations. 3. Two player games. Definition of antagonistic conflict. Matrix games and methods of their solution. Optimal player strategies, their existence and properties. Fictitious game method, dominance in matrix games. 4. Bimatrix games. 5. Endless antagonistic conflicts - finding a balanced strategy of the game. 6. Von Neumann-Morgenstern utility function. 7. Decision making for risks and uncertainties. Games against nature. 8. Non-cooperative games n players. Equilibrium points in pure and mixed strategies. Optimal decision making in non-cooperative games. 9. Cooperative games n players. Coalitions and their characteristic functions. The core of the game. Shapley's value of the game. 10. Voting games. Shapley force index. Banzhaf's strength index. Coalition formation theory. 11. Test. 12. Projects presentations. 13. Projects presentations.

**Requirements to complete the course**

project, test

written exam

• project – 20 %

• test 20 – %

• written exam – 60 %

**Student workload**

• participation in lectures - 26 hours

• participation in seminars - 26 hours

• preparation for seminars - 10 hours

• preparation for the semester test - 10 hours

• project processing - 10 hours

• preparation for the exam - 22 hours

Total: 104 hours

**Language whose command is required to complete the course**

English

Date of approval: 20.02.2023

Date of the latest change: 03.05.2024