M7190 Game Theory
Faculty of ScienceSpring 2025
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- Mgr. David Kruml, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- The course provides an introduction to game theory and explains its basic concepts and results. Games in a normal form are studied more intensively, then the topic is developed to iterated and extensive form games. Furthermore, coalition games are studied. We focus on applications of the theory for practically oriented problems. This is reflected by a form of examination.
- Learning outcomes
- After passing the course the student will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. The student will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria. The student will get an intuition for ways how the players think, how the games could turn out, and an ability for detailed solving.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, iterated games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance. In 2021, the course will be given in online form and both parts will be recorded.
- Assessment methods
- A written exam consists of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given.
- Language of instruction
- Czech
- Further Comments
- The course is taught once in two years.
The course is taught: every week.
M7190 Game Theory
Faculty of ScienceSpring 2023
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 8:00–9:50 M2,01021
- Timetable of Seminar Groups:
- Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- The course provides an introduction to game theory and explains its basic concepts and results. Games in a normal form are studied more intensively, then the topic is developed to iterated and extensive form games. Furthermore, coalition games are studied. We focus on applications of the theory for practically oriented problems. This is reflected by a form of examination.
- Learning outcomes
- After passing the course the student will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. The student will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria. The student will get an intuition for ways how the players think, how the games could turn out, and an ability for detailed solving.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, iterated games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance. In 2021, the course will be given in online form and both parts will be recorded.
- Assessment methods
- A written exam consists of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught once in two years.
M7190 Game Theory
Faculty of ScienceSpring 2021
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 1. 3. to Fri 14. 5. Tue 10:00–11:50 online_M2
- Timetable of Seminar Groups:
- Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- The course provides an introduction to game theory and explains its basic concepts and results. Games in a normal form are studied more intensively, then the topic is developed to iterated and extensive form games. Furthermore, coalition games are studied. We focus on applications of the theory for practically oriented problems. This is reflected by a form of examination.
- Learning outcomes
- After passing the course the student will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. The student will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria. The student will get an intuition for ways how the players think, how the games could turn out, and an ability for detailed solving.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, iterated games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance. In 2021, the course will be given in online form and both parts will be recorded.
- Assessment methods
- A written exam consists of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught once in two years.
M7190 Game Theory
Faculty of ScienceSpring 2019
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 18. 2. to Fri 17. 5. Thu 16:00–17:50 M5,01013
- Timetable of Seminar Groups:
- Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- After passing the course the students will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. Moreover, the students will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of Sciencespring 2018
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Wed 8:00–9:50 M2,01021
- Timetable of Seminar Groups:
- Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- After passing the course the students will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. Moreover, the students will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2017
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
Mgr. Roman Štěpánek (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 20. 2. to Mon 22. 5. Tue 16:00–17:50 M4,01024
- Timetable of Seminar Groups:
M7190/01: Mon 20. 2. to Mon 22. 5. Fri 8:00–9:50 M5,01013, D. Kruml - Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- After passing the course the students will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. Moreover, the students will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2016
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Wed 14:00–15:50 M1,01017
- Timetable of Seminar Groups:
- Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- After passing the course the students will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. Moreover, the students will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2015
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 14:00–15:50 M2,01021
- Timetable of Seminar Groups:
M7190/02: Tue 16:00–16:50 M2,01021, L. Polák - Prerequisites
- ( M1100 Mathematical Analysis I || FI:MB201 Linear models B || FI:MB000 Calculus I ) && ( M1110 Linear Algebra I || FI:MB202 Calculus B || FI:MB003 Linear Algebra and Geometry I )
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-MA)
- Course objectives
- After passing the course the students will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. Moreover, the students will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2014
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Thu 16:00–17:50 M4,01024
- Timetable of Seminar Groups:
- Prerequisites
- ( M1100 Mathematical Analysis I || FI:MB201 Linear models B || FI:MB000 Calculus I ) && ( M1110 Linear Algebra I || FI:MB202 Calculus B || FI:MB003 Linear Algebra and Geometry I )
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-MA)
- Course objectives
- After passing the course the students will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. Moreover, the students will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2013
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Fri 14:00–15:50 M2,01021
- Timetable of Seminar Groups:
- Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 6 fields of study the course is directly associated with, display
- Course objectives
- Basic course on Game Theory with the stress on applications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria and their existence are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-our lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2012
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 14:00–15:50 M2,01021
- Timetable of Seminar Groups:
- Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 6 fields of study the course is directly associated with, display
- Course objectives
- Basic course on Game Theory with the stress on applications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria and their existence are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-our lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2011
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. Martin Panák, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 14:00–15:50 M1,01017
- Timetable of Seminar Groups:
M7190/02: Mon 16:00–16:50 M1,01017, L. Polák - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-AM)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on applications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria and their existence are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-our lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2010
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 15:00–16:50 M1,01017
- Timetable of Seminar Groups:
M7190/02: Wed 13:00–13:50 M4,01024, D. Kruml - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-AM)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on applications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria and their existence are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-our lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2009
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 15:00–16:50 M1,01017
- Timetable of Seminar Groups:
M7190/02: Thu 11:00–11:50 M2,01021, D. Kruml - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-AM)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods
- a standard lecture with a seminar, written exam
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- Information on completion of the course: Studenti Ma-Ek mají tento předmět zakončen kolokviem (3kredity) a ostatní studenti odborného studia mají zakončeni zkouskou (5 kreditu). Další studenti (FI,...) si mohou vybrat.
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2008
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (assistant) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 15:00–16:50 N41
- Timetable of Seminar Groups:
M7190/02: Mon 17:00–17:50 N21, D. Kruml - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Informatics (programme FI, M-IN)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods (in Czech)
- standardní přednáška se cvičením, písemná zkouška
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2007
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc. - Timetable
- Mon 15:00–16:50 N41
- Timetable of Seminar Groups:
M7190/02: Mon 18:00–18:50 N41, D. Kruml - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:M000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:M003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:M001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 6 fields of study the course is directly associated with, display
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods (in Czech)
- standardní přednáška se cvičením, písemná zkouška
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2006
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc. - Timetable
- Mon 15:00–16:50 N41
- Timetable of Seminar Groups:
M7190/02: Mon 18:00–18:50 N41, D. Kruml - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:M000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:M003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:M001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 6 fields of study the course is directly associated with, display
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods (in Czech)
- standardní přednáška se cvičením; ukončení písemným kolokviem nebo poněkud náročnější písemnou zkouškou
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2005
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc. - Timetable
- Tue 14:00–15:50 N41
- Timetable of Seminar Groups:
- Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:M000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:M003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:M001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 6 fields of study the course is directly associated with, display
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods (in Czech)
- standardní přednáška se cvičením, písemná zkouška
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
- Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2004
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc. - Timetable of Seminar Groups
- M7190/01: No timetable has been entered into IS.
M7190/02: No timetable has been entered into IS.
M7190/03: No timetable has been entered into IS. - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:M000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:M003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:M001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Informatics (programme FI, M-IN)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods (in Czech)
- standardní přednáška se cvičením, písemná zkouška
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
- Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceAutumn 2002
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc. - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:M000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:M003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:M001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Informatics (programme FI, M-IN)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods (in Czech)
- standardní přednáška se cvičením, písemná zkouška
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2024
The course is not taught in Spring 2024
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- Mgr. David Kruml, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- The course provides an introduction to game theory and explains its basic concepts and results. Games in a normal form are studied more intensively, then the topic is developed to iterated and extensive form games. Furthermore, coalition games are studied. We focus on applications of the theory for practically oriented problems. This is reflected by a form of examination.
- Learning outcomes
- After passing the course the student will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. The student will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria. The student will get an intuition for ways how the players think, how the games could turn out, and an ability for detailed solving.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, iterated games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance. In 2021, the course will be given in online form and both parts will be recorded.
- Assessment methods
- A written exam consists of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given.
- Language of instruction
- Czech
- Further Comments
- The course is taught once in two years.
The course is taught: every week.
M7190 Game Theory
Faculty of ScienceSpring 2022
The course is not taught in Spring 2022
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- The course provides an introduction to game theory and explains its basic concepts and results. Games in a normal form are studied more intensively, then the topic is developed to iterated and extensive form games. Furthermore, coalition games are studied. We focus on applications of the theory for practically oriented problems. This is reflected by a form of examination.
- Learning outcomes
- After passing the course the student will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. The student will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria. The student will get an intuition for ways how the players think, how the games could turn out, and an ability for detailed solving.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, iterated games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance. In 2021, the course will be given in online form and both parts will be recorded.
- Assessment methods
- A written exam consists of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given.
- Language of instruction
- Czech
- Further Comments
- The course is taught once in two years.
The course is taught: every week.
M7190 Game Theory
Faculty of ScienceSpring 2020
The course is not taught in Spring 2020
- Extent and Intensity
- 2/2/0. 6 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- Mgr. David Kruml, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 8 fields of study the course is directly associated with, display
- Course objectives
- The course provides an introduction to game theory and explains its basic concepts and results. Games in a normal form are studied more intensively, then the topic is developed to iterated and extensive form games. Furthermore, coalition games are studied. We focus on applications of the theory for practically oriented problems. This is reflected by a form of examination.
- Learning outcomes
- After passing the course the student will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. The student will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria. The student will get an intuition for ways how the players think, how the games could turn out, and an ability for detailed solving.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, iterated games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consists of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given.
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week.
M7190 Game Theory
Faculty of Sciencespring 2012 - acreditation
The information about the term spring 2012 - acreditation is not made public
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear Algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-AM)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on applications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria and their existence are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-our lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2011 - only for the accreditation
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:MB000 Calculus I )) && ( M1110 Linear algebra I || ( FI:MB003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:MB001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-AM)
- Informatics (programme FI, N-IN)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Basic course on Game Theory with the stress on applications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria and their existence are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Teaching methods
- A classical two-our lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance.
- Assessment methods
- A written exam consisting of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week. - Teacher's information
- http://www.math.muni.cz/~polak
M7190 Game Theory
Faculty of ScienceSpring 2008 - for the purpose of the accreditation
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Libor Polák, CSc. (lecturer)
Mgr. David Kruml, Ph.D. (seminar tutor) - Guaranteed by
- doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Libor Polák, CSc. - Prerequisites
- ( M1100 Mathematical Analysis I || ( FI:M000 Calculus I )) && ( M1110 Linear algebra I || ( FI:M003 Linear Algebra and Geometry I )) && ( M2100 Mathematical Analysis II || ( FI:M001 Calculus II ))
Basics of linear algebra and calculus. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 6 fields of study the course is directly associated with, display
- Course objectives
- Basic course on Game Theory with the stress on aplications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria are discussed. Numerous practical problems are solved.
- Syllabus
- n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square,multi-stage games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
- Literature
- G. Owen, Game Theory, Sounders Company 1983
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North Holland, 1999, xxvi, 733. ISBN 0444880984. info
- Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
- Assessment methods (in Czech)
- standardní přednáška se cvičením, písemná zkouška
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week. - Teacher's information
- http://www.math.muni.cz/~polak
- Enrolment Statistics (recent)