KTH Mathematics  

Mathematical Statistics

SF2972 Game Theory, 7.5 university credits, period 3, 2015


  • 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
  • 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. To find the rooms, please consult the KTH place finder.
Date Time Place Lecturer Contents
Lecture 1 Thu Jan 22 13-15 B24 Jörgen Introduction and simple examples
Lecture 2 Mon Jan 26 13-15 M37 Jörgen Nash equilibrium
Lecture 3 Tue Jan 27 13-15 M37 Jörgen Finite games in normal form, part I
Lecture 4 Thu Jan 29 13-15 M37 Jörgen Finite games in normal form, part II
Lecture 5 Mon Feb 2 8-10 M37 Mark Games in extensive form I
Seminar 1 Wed Feb 4 15-17 B21 Jörgen Problem set 1 and solutions
Lecture 6 Thu Feb 5 13-15 B24 Mark Games in extensive form II
Lecture 7 Mon Feb 9 8-10 M37 Mark Games in extensive form III
Lecture 8 Wed Feb 11 13-15 M37 Mark Games in extensive form IV
Seminar 2 Mon Feb 16 8-10 M37 Mark (The problems are found in the lecture notes above.) Solutions
Lecture 9 Tue Feb 17 15-17 M37 Jonas Informal introduction, Chap. 0-3 (except 1.1, 1.5, 1.7, 2.2, 2.3, 3.4) in LIP
Lecture 10 Fri Feb 20 10-12 M23 Jonas Algebra of games, Chap. 4 (except 4.3) in LIP, Sec. 1-4 in the compendium
Lecture 11 Thu Feb 26 10-12 B24 Jonas Simplifying games, Sec. 4.3 in LIP, Sec. 5 in the compendium
Lecture 12 Fri Feb 27 10-12 M37 Jonas Numbers and Hackenbush, Sec. 5.1, 6.4 in LIP, Sec. 6 in the compendium
Lecture 13 Thu Mar 5 13-15 B24 Jonas Thermography, Sec. 8.1-8.3 in LIP, Sec. 8-9 in the compendium
Lecture 14 Fri Mar 6 10-12 M37 Jonas Impartial games, Sec. 7.1-7.4 in LIP, Sec. 9 in the compendium
Seminar 3 Mon Mar 9 13-15 M37 Jonas Problem set 3
Written exam Thu Mar 19 8.00-13.00 M24, M33

Required readings for Jörgen's part of the course

Chapters 1-4
Chapter 5 (except 5.3)
Chapter 6 (except 6.5-6.7)
Chapter 13 (except 13.6-13.8)

Recommended problems in Lessons in play

  • Chapter 1: 8
  • Chapter 2: 10
  • Chapter 3: 2,3
  • Chapter 4: 1,3
  • Chapter 5: 3,11,15
  • Chapter 6: 6
  • Chapter 7: 11
  • Chapter 8: 2,6


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.
  • Michael H. Albert, Richard J. Nowakowski and David Wolf, Lessons in Play: An Introduction to Combinatorial Game Theory, A.K. Peters, Ltd., 2007
  • Combinatorial game theory, a concise text by Jonas.
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 changed from 2011 to 2013.

To Mathematical Statistics
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Published by: Jonas Sjöstrand
Updated: 23/1-2015