| Course Unit Code | 460-4116/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| SAW75 | doc. Ing. Zdeněk Sawa, Ph.D. |
| Summary |
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The course presents basic notions of the mathematical game theory. Different types of games are discussed together with different possibilities how to formalize them mathematically and how to solve them algorithmically. At the beginning, the combinatorial games are discussed, i.e., games played by two players with perfect information. Then the games in the games in the standard (strategic) and in the extensive form are studied, where we start with two-person zero-sum games (that can be solved in a finite case by transformation to the linear programming problem), and then we continue with two-person general-sum games. When the general-sum games are discussed, there are distinguished two case: non-cooperative games, where existence of Nash equilibria is studied, and cooperative games, where we distinguish variants with transferable utility and with nontransferable utility. When studying both zero-sum and general-sum games, the variants of the games extended with
probabilistic moves and an incomplete information are also studied.
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| Learning Outcomes of the Course Unit |
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To understand the basic concepts and methods of mathematical game theory.
To gain basic experience with solving simple conflict and decision making problems by means of these methods.
Acquaintance with fundamental ideas of game theory and ability using them in everyday informal decisions.
Understanding the main formal models and methods of the game theory and mastering their using in practice. Gaining practical experience with program tools supporting game design, analysis and solution.
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| Course Contents |
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Lectures:
1 introduction
2 combinatorial games, graph games
3 the game of NIM, the Sprague-Grundy function
4 sums of games and their solution using the Sprague-Grundy function
5 two-person zero-sum games in the strategic form, matrix games
6 dominated strategies, saddle points, mixed strategies
7 solving matrix games by transformation to a linear programming problem
8 linear programming
9 two-person zero-sum games in the extensive form, Kuhn tree, chance moves, games of imperfect information
10 two-person general-sum games in the strategic form, bimatrix games, Nash equilibria
11 cooperative games with transferable utility
12 games in coalitional form
Tutorials:
the content of tutorials corresponds to the content of lectures |
| Recommended or Required Reading |
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| Required Reading: |
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[1] Thomas S. Ferguson – Game Theory — syllabus the game theory course teached at UCLA (University of California, Los Angeles), http://www.math.ucla.edu/~tom/math167.html
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[1] Thomas S. Ferguson – Game Theory — výukové texty k předmětu Game Theory vyučovaném na UCLA (University of California, Los Angeles), http://www.math.ucla.edu/~tom/math167.html
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| Recommended Reading: |
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[2] Kevin Leyton-Brown, Yoav Shoham: Essentials of Game Theory: A Concise, Multidisciplinary Introduction, Morgan and Claypool Publishers, 2008.
[3] Algorithmic Game Theory, edited by Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani, Cambridge University Press, 2007.
[4] Martin J. Osborne, Ariel Rubinstein: A Course in Game Theory, MIT Press, 1994.
[5] Drew Fudenberg, Jean Tirole: Game Theory, MIT Press, 1991.
[6] Robert Gibbons: A Primer in Game Theory, Financial Times Prentice Hall, 1992. |
[2] Kevin Leyton-Brown, Yoav Shoham: Essentials of Game Theory: A Concise, Multidisciplinary Introduction, Morgan and Claypool Publishers, 2008.
[3] Algorithmic Game Theory, edited by Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani, Cambridge University Press, 2007.
[4] Martin J. Osborne, Ariel Rubinstein: A Course in Game Theory, MIT Press, 1994.
[5] Drew Fudenberg, Jean Tirole: Game Theory, MIT Press, 1991.
[6] Robert Gibbons: A Primer in Game Theory, Financial Times Prentice Hall, 1992. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 (30) | 15 |
| Zápočtová písemka | Written test | 30 | 15 |
| Examination | Examination | 70 (70) | 30 |
| Zkoušková písemka | Written examination | 70 | 30 |