Topics in game theory

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M5
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

The lecturer choose some important topics in game theory, for example:
Bimatrix games. Number of equilibria, efficient methods for finding equilibria, stability.
Combinatorial games. Games on graphs.
Repeated games.
Bargaining, auctions.
Applications of game theory in social sciences.
Decision theory. Social choice theory.
Evolutionary game theory.
Experimental game theory.
Differential games.

Readings

A. Fraenkel: Combinatorial Games, Electron. J. Combinatorics, DS2, zadnja dopolnitev, 2006.
D. Fudenberg, J. Tirole: Game Theory, MIT Press, Cambridge MA, 1991.
P. Morris: Introduction to Game Theory, Springer, New York, 1994.
M. J. Osborne: An Introduction to Game Theory, Oxford University Press, Oxford, 2004.
M. J. Osborne, A. Rubinstein: A Course in Game Theory, 10. natis, MIT Press, Cambridge MA, 2004.

Objectives and competences

The student gains a deeper knowledge of some areas of game theory, including recent results.

Intended learning outcomes

Knowledge and understanding:
The student gains a deeper understanding of the chosen area of game theory. He or she learns the newest results in the field and their applications.
Application:
Modelling in situations with a potential for conflict, finding the solution using formal methods.
Reflection:
Applications and shortcomings of descriptions and study of everyday life with the help of formal models.
Transferable skills:
Ability to set up a rigorous mathematical framework and understand its shortcomings. Ability to study modern scientific papers and monographs independently.

Learning and teaching methods

Lectures, usage of distance learning techniques, exercises, homeworks, consultations, seminars

Assessment

Type (examination, oral, coursework, project):
seminar work
written or oral exam
Grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Matjaž Konvalinka:
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, PAK, Igor. Triangulations of Cayley and Tutte polytopes. Advances in mathematics, ISSN 0001-8708, 2013, vol. 245, str. 1-33. [COBISS-SI-ID 16706905]
DOLŽAN, David, KONVALINKA, Matjaž, OBLAK, Polona. Diameters of connected components of commuting graphs. The electronic journal of linear algebra, ISSN 1081-3810, 2013, vol. 26, str. 433-445. [COBISS-SI-ID 16707161]
Sergio Cabello:
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 number and weighted crossing number of near-planar graphs. Algorithmica, ISSN 0178-4617, 2011, vol. 60, no. 3, str. 484-504. [COBISS-SI-ID 15261785]