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 (Godina: 1, Summer)
Master Academic Studies	Mathematics in Engineering (Godina: 1, Summer)

General information:

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

Educational goal:

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.

Educational outcome:

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.

Course content:

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.

Teaching methods:

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.

Literature:

Authors	Title	Year	Publisher	Language
E.R. Berlekamp, J.H.Conway, R.K. Guy	Winning Ways	1982	Academic Press, London	English
Rida Laraki, Jérôme Renault, et al.	Mathematical Foundations of Game Theory	2019	Springer	English
D. Cvetković, S. Simić	Diskretna matematika-matematika za kompjuterske nauke	1987	Naučna knjiga	Serbian language
Michael H. Albert, Richard J. Nowakowski, et al.	Lessons in Play: An Introduction to Combinatorial Game Theory	2019	A K Peters	English
John Maynard Smith	Evolution and the Theory of Games	1982	Cambridge University Press	English
J. Beck	Foundations of positional games	1996		English
Saul Stahl	A Gentle Introduction to Game Theory	1998	American Mathematical Society	English
Vladimir Mazalov	Mathematical Game Theory and Applications	2014	Wiley	English
Tatjana Grbić	Skripta iz matematičke teorije igara	2011		Serbian language