# Game theory

2021/2022
Programme:
Mathematics, First Cycle
Year:
3 year
Semester:
first
Kind:
optional
Group:
B
ECTS:
6
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
3
Seminar
0
Tutorial
3
Lab
0
Content (Syllabus outline)

• Strategic games with preference functions for several players. Nash equilibrium. Best response. Domination. Models of duopoly.
• Strategic games with utility functions for several players. Mixed strategies and lotteries. Mixed Nash equilibrium. Principle of indifference. Domination. Existence of mixed Nash equilibrium.
• Bimatrix games. Principle of indifference. Search of Nash equilibrium. Special bimatrix games. Safety level.
• Matrix games. Minimax Theorem. Solution through linear programming and duality. Special matrix games.
• Bayesian games. Bayesian Nash equilibrium.
• Extensive games. Subgame perfect Nash equilibrium. Stackelberg model of duopoly.
• Extensive games with imperfect information. Behavioral strategy. Kuhn's theorem.
• Cooperative games. Nash bargaining solution. Cooperative games in coalitional form. Imputations. Core. Shapley values
• Combinatorial games. Nim.

T.S. Ferguson: Game Theory. Elektronska knjiga dostopna na http://www.math.ucla.edu/~tom/Game_Theory/Contents.html
M. J. Osborne: An Introduction to Game Theory, Oxford University Press, 2003.
M. J. Osborne, A. Rubinstein: A Course in Game Theory, 10. natis, MIT Press, 2004.
B. von Stengel: Game Theory Basics. Lecture Notes, 2011.

Objectives and competences

The student gets acquainted with basic game theory and its use for modeling different situations, especially in the fields of economics and finance. The theoretic concepts are explained through several examples.

Intended learning outcomes

Knowledge and understanding: The student knows basic problems in Game Theory and understands the meaning of the assumptions in each type of game.
Application: Modeling of conflicting situations arising from the interaction of subjects.
Reflection: Use and weaknesses of the description and exploration of phenomena in everyday life with the help of formal models.
Transferable skills: Ability of precise mathematical description and awareness of its weaknesses.

Learning and teaching methods

Lectures, exercises, homework, consultations

Assessment

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

CABELLO, Sergio, DÍAZ-BÁÑEZ, José Miguel, LANGERMAN, Stefan, SEARA, Carlos, VENTURA, Inma. Facility location problems in the plane based on reverse nearest neighbor queries. European journal of operational research, ISSN 0377-2217. [Print ed.], 2010, vol. 202, iss. 1, str. 99-106. [COBISS-SI-ID 15160921]
CABELLO, Sergio, JAKOVAC, Marko. On the b-chromatic number of regular graphs. Discrete applied mathematics, ISSN 0166-218X. [Print ed.], 2011, vol. 159, iss. 13, str. 1303-1310. [COBISS-SI-ID 15914329]
CABELLO, Sergio, MOHAR, Bojan. Crossing and weighted crossing number of near-planar graphs. V: TOLLIS, Ioannis G. (ur.), PATRIGNANI, Maurizio (ur.). Graph drawing : 16th international symposium, GD 2008, Heraklion, Crete, Greece, September 21-24, 2008 : revised papers, (Lecture notes in computer science, ISSN 0302-9743, 5417). Berlin, Heidelberg: Springer, cop. 2009, str. 38-49. [COBISS-SI-ID 15099225]
KONVALINKA, Matjaž. Skew quantum Murnaghan-Nakayama rule. Journal of algebraic combinatorics, ISSN 0925-9899, 2012, vol. 35, no. 4, str. 519-545. [COBISS-SI-ID 16250713]
KONVALINKA, Matjaž, PAK, Igor. Geometry and complexity of O'Hara's algorithm. Advances in applied mathematics, ISSN 0196-8858, 2009, vol. 42, iss. 2, str. 157-175. [COBISS-SI-ID 15545945]
KONVALINKA, Matjaž. On quantum immanants and the cycle basis of the quantum permutation space. Annals of combinatorics, ISSN 0218-0006, 2012, vol. 16, no. 2, str. 289-304. [COBISS-SI-ID 16310873]