M7190 Game Theory

Faculty of Science
Spring 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.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Thu 16:00–17:50 M3,01023, 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
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.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Mon 1. 3. to Fri 14. 5. Fri 8:00–9:50 online_M2, 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
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.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Mon 18. 2. to Fri 17. 5. Fri 8:00–9:50 M4,01024, 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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
spring 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:
M7190/01: Wed 12:00–13:50 M2,01021, 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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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/T01: Wed 8. 3. to Mon 22. 5. Wed 10:00–12:00 114, R. Štěpánek, Nepřihlašuje se. Určeno pro studenty se zdravotním postižením.
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Thu 12:00–13:50 M2,01021, 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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Wed 14:00–14:50 M6,01011, D. Kruml
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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Wed 13:00–13:50 M2,01021, D. Kruml
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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Fri 16:00–16:50 M2,01021, 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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Tue 16:00–16:50 M2,01021, 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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Fri 12:00–12:50 M2,01021, M. Panák
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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Mon 17:00–17:50 M1,01017, L. Polák
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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Mon 17:00–17:50 M4,01024, L. Polák
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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Mon 17:00–17:50 N41, L. Polák
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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Mon 17:00–17:50 N41, L. Polák
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Mon 17:00–17:50 N41, L. Polák
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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:
M7190/01: Tue 16:00–16:50 N41, L. Polák
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Autumn 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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
spring 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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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
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
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.

M7190 Game Theory

Faculty of Science
Spring 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
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023, Spring 2025.
  • Enrolment Statistics (recent)