Game Theory
(3 Lecture, 1 Practical)
(MAT.759UF / MAT.760UF)

E. Dragoti-Çela
Department of Discrete Mathematics
• Time and place (lecture),

Time and place (practical),

• Start: Monday, March 5, 08:15-10:00, seminar room AE06, Steyrergasse 30, ground floor

• Registration
• via TUGonline

• Contents
• This is an introductory course in game theory. The first and main part of the course will deal with the analysis of games focussing on strategies and equilibria. In particular we will discuss strategic form games like two-person zero-sum games, zero-sum games in graphs and general sum games. We will consider the dominance, security and stability of strategies. A very important concept is the Nash equilibrium of which we will discuss the existence and in some special cases also its computation. We will also introduce some games in extensive form and the concepts of perfect and imperfect information. Further we will discuss some routing games and the concepts of selfish routing and the price of anarchy. The second part of the course will deal with the design of games and mechanisms. In particular we will discuss cooperative games, fair division and auctions. Besides the discussion of the theory will also consider examples of game theory models of real and toy applications and analyse their solutions. The goal of the course is to make the students familiar with some of the fundamental concepts and methods in the above mentioned areas of game theory.

The titles of the main chapters (including keywords) are:

• Two-person zero-sum games (the minimax theorem, the technique if domination, Nash equilibria, the von Neumann Minimax Theorem.)
• Zero-sum games on graphs (hide and seek games, pursuit-evasor games)
• General-sum games (more than two players, Nash-equilibria, the Nash Theorem, infinite strategy spaces)
• Games in extensive form (perfect and imperfect information, Bayesian games)
• The price of anarchy (selfish routing, network formation games)
• Cooperative games (transferable utility, the core, Shapley value, Shapley's Theorem)

• and as time allows

• Auctions (the bidder model, auctions with a reserve price, the Bayes-Nash equilibrium, a two-bidder special case, the multibidder case)

• Literature
• The main sources of literature are

• Grading of the practical is based on a point system.
The are three possibilities to collect points:

• Solve practical exercises announced periodically as working sheets and claim that you would be ready to present the solution during the practical units.
At the beginning of any practical the students should announce what exercises thay have solved and would be ready to present. The instructor will then ask one of the candidates to do the presentation.
• Presentation of solutions in the classroom.
• Written practical exam.

The total number P of points collected by a student results as

P=(1)/(3) * ((k)/(k_a)) + (1)/(3)*(t)/(t_a)) + (1)/(60) (p),

where

k     is the overall number of exercises solved by the student according to what he/she has announced during the term,

k_a   is the overall number of releases exercises during the term,

t_a   is the overall number of exercises presented by the student during the term,

t     is the overall number of points credited to the student for presentations during the term ,

p     is the overall number of points credited to the student for the written exam (between 0 und 20),

From points P to grades (among 1,2,3,4,5 sorted from the best to the worse, 5 beeing the only negative grade) :
0.00 <= P < 0.50   5
0.50 <= P < 0.65   4
0.65 <= P < 0.80   3
0.80 <= P < 0.90   2
0.90 <= P               1

The written practical exam: The practical unit has to be evaluated by a continuous assessment, therefore there will only be two dates for the written exam: the first date will be at the end of the summer term and the second date at the beginning of the following winter term.
Students who whish to improve their grade obtained after the first date can have a second try and make use of the second date. In this case only the points collected during the later exam will count, the points of the first try will be ignored. The dates of the written exam will be announced on time.
The registration for the written exam should be done electronically via TUG-online.

The lecture will be graded in terms of a written and an oral exam.
The dates for this exam will be announced on time and will be settled in agreement with the students. The first date will be at the end of the summer term.

There will be up to three dates per term, if needed; they will be announced via TUGonline;
The registration for the exams should be done via TUGonline.

The usage of notices, scripts, records, books or electronic equipment what so ever is not allowed at the written exams.

• Exercise sheets (pdf)

cela@opt.math.tu-graz.ac.at.

Last update: June 2018