KTH Mathematics  

Mathematical Statistics

SF2972 Game Theory, 7.5 university credits, period 3, 2013


  • Lecturers: Jörgen Weibull (jorgen.weibull@hhs.se), Mark Voorneveld (mark.voorneveld@hhs.se) and Jonas Sjöstrand (jonass@kth.se).
  • Examiner: Boualem Djehiche (boualem@math.kth.se)

Course main content

  • Games in normal form:
    • Pure and mixed strategies
    • Nash equilibrium
    • Dominance and rationalizability
    • Perfect and proper equilibrium
  • Games in extensive form:
    • Pure, mixed, and behavioral strategies, Kuhn's theorem
    • Perfect information: Nash equilibrium, subgame perfect equilibrium
    • Imperfect information: sequential and perfect Bayesian equilibrium
  • On Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2012: matching and market design
  • Combinatorial game theory:
    • Impartial games: nim, nimber, Sprague-Grundy's theorem
    • Partizan games: Hackenbush, Conway's abstract theory, surreal numbers


All lectures begin quarter past, so 10-12 means 10.15-12.00. Room 3721 is on floor 7 at the department of mathematics, KTH. To find the other rooms, please consult the Classroom Search Engine.
Date Time Place Lecturer Contents
Lecture 1 Jan 22 10-12 3733 Jörgen Introduction and simple examples
Lecture 2 Jan 24 10-12 3721 Jörgen Nash equilibrium
Lecture 3 Jan 29 10-12 E2 Jörgen Finite games in normal form, part I
Lecture 4 Jan 31 10-12 3721 Jörgen Finite games in normal form, part II
Lecture 5 Feb 5 10-12 E2 Mark Games in extensive form
Lecture 6 Feb 7 8-10 3721 Mark Games in extensive form
Seminar 1 Feb 8 15-17 E33 Jörgen Problem set 1, its solutions, and an extra problem set
Lecture 7 Feb 12 10-12 E33 Mark Games in extensive form
Lecture 8 Feb 14 8-10 3721 Mark Introduction to matching problems
Seminar 2 Feb 18 10-12 3721 Mark Short solutions
Lecture 9 Feb 19 10-12 E31 Jonas impartial games
Lecture 10 Feb 21 13-15 3721 Jonas ONAG Ch. 7 and 0, pages 71-80 and 3-14
Lecture 11 Feb 26 10-12 E51 Jonas ONAG Ch. 1 and 2, pages 15-18, 23-24
Lecture 12 Feb 28 13-15 E52 Jonas ONAG Ch. 8, pages 81,86-89
Lecture 13 Mar 5 10-12 E33 Jonas ONAG Ch. 10, pages 109-112
Lecture 14 Mar 7 13-15 3721 Jonas ONAG Ch. 9, pages 97-108, and Ch. 16, page 205
Seminar 3 Mar 12 10-12 D3 Jonas Problem set 3
Written exam Mar 15 8.00-13.00 M1
Re-exam Jun 3 14.00-19.00 ?

Required readings

Jörgen's part of the course:
Chapter 1 (except 1.3.4-1.3.5)
Section 2.1
Chapter 3
Chapter 4
Chapter 5 (except 5.3)
Chapter 6 (except 6.5-6.7)
Chapter 13 (except 13.7)

Marks's part of the course: a reading guide.

Jonas's part of the course: a checklist.


In addition to the written exam there will be three seminars with corresponding problem sets. At each seminar, you should

  • be there in time,
  • bring your written solutions to the problem set, and
  • be prepared to present your solutions in class.
Your solutions do not have to be absolutely correct, and we will not look deeply into them nor provide any written feedback. However, we will check that you have made a serious attempt to solve all the problems. The same goes for your presentations in class. Though the solutions should be handed in individually, cooperation is strongly encouraged when you solve the problems.

To pass the course you must pass all three seminars and the written exam.

The written exam will be divided in two: part A on classical game theory and part B on combinatorial game theory. Part A will be scored from 0 to 20 credits and part B from 0 to 15 credits, so the maximal number of credits you can get is 35. The required number of credits for the different grades are as follows.

grade FxEDCBA
required credit sum 171821242730

No aids will be permitted during the exam.


  • Hans Peters, Game Theory: a Multi-Leveled Approach, Springer 2008.
  • J. H. Conway, On Numbers and Games, A.K. Peters, Ltd., 2001, 2nd ed., (1st Ed., Academic Press, New York, 1976)
We also recommend the four books
  • E. R. Berlekamp, J. H. Conway, R. K. Guy, Winning Ways for Your Mathematical Plays, A.K. Peters, Ltd., 2001, 2nd ed., Vol. 1-4, (1st ed., Academic Press, New York, 1982)
though it is possible to follow the course without them. An electronic version is freely available to KTH students (at KTHB).

Old exams

Old exams are available from the main course page. Note that the content and the design of the course are not exactly the same as in 2011.

To Mathematical Statistics
To Mathematical Statistics Courses
Published by: Jonas Sjöstrand
Updated: 22/1-2013