# 460-4116/02 – Game Theory (TEH)

 Gurantor department Department of Computer Science Credits 4 Subject guarantor doc. Ing. Zdeněk Sawa, Ph.D. Subject version guarantor doc. Ing. Zdeněk Sawa, Ph.D. Study level undergraduate or graduate Requirement Choice-compulsory Year 2 Semester winter Study language English Year of introduction 2015/2016 Year of cancellation Intended for the faculties FEI Intended for study types Master, Follow-up Master
Instruction secured by
SAW75 doc. Ing. Zdeněk Sawa, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+0

### Subject aims expressed by acquired skills and competences

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.

Lectures
Tutorials

### Summary

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.

### Compulsory literature:

- 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

### Recommended literature:

- Kevin Leyton-Brown, Yoav Shoham: Essentials of Game Theory: A Concise, Multidisciplinary Introduction, Morgan and Claypool Publishers, 2008. - Martin J. Osborne, Ariel Rubinstein: A Course in Game Theory, MIT Press, 1994. - Drew Fudenberg, Jean Tirole: Game Theory, MIT Press, 1991. - Robert Gibbons: A Primer in Game Theory, Financial Times Prentice Hall,1992. - Algorithmic Game Theory, edited by Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani, Cambridge University Press, 2007. - J. D. Williams: The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy, The RAND Corporation, 1954.

### Way of continuous check of knowledge in the course of semester

Conditions for credit: There will be a test during semester. It is possible to get at most 30 points from this test. To obtain credit, it is necessary to get at least 10 points from the test. An exam: It is necessary to obtain at least 25 points (of 70 points) from the exam to pass the course.

### E-learning

No additional requirements are placed on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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

### Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 30 (30) 15
Test Written test 30  15
Examination Examination 70 (70) 30
Written exam Written examination 70  30
Mandatory attendence parzicipation: 80% attendance at the exercises

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Choice-compulsory study plan
2019/2020 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Choice-compulsory study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Choice-compulsory study plan
2018/2019 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Choice-compulsory study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Choice-compulsory study plan
2017/2018 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Choice-compulsory study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Choice-compulsory study plan
2016/2017 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Choice-compulsory study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P English Ostrava 2 Choice-compulsory study plan
2015/2016 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K English Ostrava 2 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner