Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Mathematical game theory (17.IAM005)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Master Academic Studies	Engineering Animation (Year: 1, Semester: Summer)
Master Academic Studies	Mathematics in Engineering (Year: 1, Semester: Summer)

General information:

Category	Theoretical-methodological
Scientific or art field	Teorijska i primenjena matematika
ECTS	5

The educational objective of the course is to introduce basic concept of combinatorial game theory, with a special emphasis on the positional game theory. Suggested topics have both theoretical and practical importance. The knowledge of mathematical game theory contributes to the full understanding of the designing process, implementation and game design within computer animation.

Acquisition of basic knowledge in the field of mathematical (combinatorial) games. Introduction to tools and techniques used in this field, as well as to possibilities and methods of their application.

1. Introduction concepts. Types of combinatorial games. Strategy. Game tree. Total min-max game tree search. Stealing the strategy. Probability approach. 2. Some combinatorial games. 3. Positional games. Definition. X and O. Pairing strategy. Strong and weak games. Maker-Breaker games. Basic concepts in the graph theory 5. Graphs games Part of the lectures consists of numerical simulation and possible writing of the term paper.

Lectures, Audio Practice and Consultations. During the Audio-Practice, the contents from the lectures are applied and exercised. During the semester, each student has to write the term paper worth 30% of the points. Parts of the course which represent a logical whole may be passed through two colloquiums. If the student wins at least 30% of possible points at each colloquium, it is considered that he passed the examination. At the examination the student may win up to 30% of the points. The course grade is formed based on the points won at the term paper, colloquiums and the knowledge demonstrated at the examination.

Authors	Title	Year	Publisher	Language
Rida Laraki, Jérôme Renault, et al.	Mathematical Foundations of Game Theory	2019	Springer	English
Saul Stahl	A Gentle Introduction to Game Theory	1998	American Mathematical Society	English
John Maynard Smith	Evolution and the Theory of Games	1982	Cambridge University Press	English
E.R. Berlekamp, J.H.Conway, R.K. Guy	Winning Ways	1982	Academic Press, London	English
Michael H. Albert, Richard J. Nowakowski, et al.	Lessons in Play: An Introduction to Combinatorial Game Theory	2019	A K Peters	English
Vladimir Mazalov	Mathematical Game Theory and Applications	2014	Wiley	English
J. Beck	Foundations of positional games	1996		English