UNIVERSITY OF MILAN – BICOCCA
FACULTY OF ECONOMICS
ADVANCED GAME THEORY (2009/10)
Prof. Mario Gilli
PURPOSE:
This course is an introduction to advanced topics in game theory. Its objective is to equip
the students with tools which are essential to study economics of information and of
strategic behaviour and for setting up and solving a wide range of economic problems.
COURSE DESCRIPTION:
The course consists in the first 32 hours of Game Theory plus other 8 hours, totalizing 40
hours (5 CFU).
We begin reviewing game representations. First a game tree is defined, as well as
information sets and pure, mixed and behavioral strategies, perfect recall and Kuhn’s
theorem. Then we consider Strategic form games and the relation among different ways of
modelling strategic Interaction. Thus existence and properties of solutions and of Nash
equilibria are discussed.
Next Nash equilibria in extensive form games are analysed and refinements proposed.
Refinements of Nash equilibria will be discussed considering applications to bargaining,
signalling and oligopoly models.
Finally we turn to the analysis of dynamic games, covering finitely and infinitely repeated
games, the folk theorem for repeated games, subgame perfection, and punishment
strategies.
STRUCTURE:
The lectures will illustrate the main concepts through formal definitions and examples, with
a particular attention to the calculus of solutions, some theorems without proof will be
discussed in the lectures. There will be problem sets and homework. You are encouraged
to form small group to solve homework. The homework will be quite difficult: you are not
expected to be able to answer all the questions correctly. Homework are difficult because
they are aimed to improve your understanding of the subtle problems of game theory.
Because of this characteristics they are done home and in groups so to incentivize
discussions and readings among students and talks with the teacher. Clearly this means
that they are not a good forecast of the exercises of the final exam, which will be a lot
simpler.
Your course grade will be based on the homework and on the final exam. Good class
participation can improve your evaluation. I expect you to come to class prepared to
respond intelligently to questions about the readings and assignments.
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Textbooks:
1. Jurgen Eichberger, Game Theory for Economists, Academic Press,1993.
2. Martin Osborne and Ariel Rubinstein, A Course in Game Theory, MIT Press,
1994.
3. Lecture notes.
OFFICE HOURS:
Wednesday 1.30-2.30 p.m. or contact Gilli by email mario.gilli@unimib.it
EXAMINATION:
The examination consists of two parts: two homework and a written individual
examination.
• HOMEWORK: the homework will consist in questions, that you have to
solve in one or two weeks working in a group. The marks count for 50% of
the final mark in Advanced Game Theory. Students that will not be able to
follow the lectures can substitute the homework with a written paper.
• FINAL EXAM: the final exam will count for 50% of the final mark and it will
consist in two questions in one hour and half.
• I STRONGLY SUGGEST THE STUDENTS TO TAKE THE EXAM
IMMEDIATELY AFTER THE COURSE (December 3rd 2009).
On the website of the course (http://dipeco.economia.unimib.it) you will find
• all the information relevant for the course
• all the slides of the lectures.
Moreover it would be extremely useful if you enrol yourself at the following website:
http://dipeco.economia.unimib.it/dbs/game/index.asp.
putting your name, surname and mail address.
LECTURES:
The lectures are on Monday from 9.00 to 10.30 am in room U7/12 and
Thursday from 9.00 to 10.30 am in room U6/20.
CONTENTS:
E = Eichberger, Game Theory for Economists;
O&R = Osborne and Rubinstein, A Course in Game Theory,
O&R1 = Martin Osborne and Ariel Rubinstein, Bargaining and Markets.
DETAILLED TIMETABLE OF THE LECTURES
L1
L2
L3
Topic of the lecture
Models of Games
- Extensive Form Games-1
Models of Games
- Extensive Form Games-2
Models of Games
- Strategic Forms Games
Day
Chapters
28/9/2009
E, chapter 1
O&R chapters 6 &11
E, chapter 1
O&R chapters 6 &11
1/10/2009
5/10/2009
E, chapter 5
2
L4
Models of Games
- Incomplete Information
8/10/2009
HW1
L5
HOMEWORK 1
Solutions for Games in
Strategic Form:
- Dominance
- Bayesian rationality
Nash Equilibria in strategic
and in extensive form
games
- Nash Theorem
- Properties
- Calculations
12/10/2009
12/10/2009
L6
E, chapter 2
O&R chapter 4
E, chapter4
O&R chapter 2
15/10/2009
E, chapter 4
O&R chapter 2
Equilibria in extensive form
games
Sequential rationality in
imperfect information
games
19/10/2009
E, chapter 6
O&R chapter 12
E, chapter 6
O&R chapter 12
Refinements of Sequential
Equilibria - 1
Refinements of Sequential
Equilibria - 2
26/10/2009
HW2
R HW1
L11
L12
HOMEWORK 2
RETURN OF HW1
CORRECTION OF HW1
Sequential Equilibria and
signalling games - 1
2/11/2009
2/11/2009
2/11/2009
5/11/2009
L13
Sequential Equilibria and
signalling games - 2
Bargaining Theory – 1
9/11/2009
L7
L8
L9
L10
L14
L15
Bargaining Theory - 2
R HW2 RETURN OF HW2
L16
CORRECTION OF HW2
22/10/2009
29/10/2009
E, chapter 7
O&R chapter 12
E, chapter 7
O&R chapter 12
E, chapter 7
Notes
12/11/2009
E, chapter 7
Notes
E, chapter ???
16/11/2009
19/11/2009
19/11/2009
E, Chapter ???
RETURN OF HW2
CORRECTION OF HW2
END OF GAME THEORY COURSE
L17
23/11/2009
L18
Repeated Games:
- the Folk Theorem
Finitely Repeated Games
L19
SUMMING UP
30/11/2009
L20
Final exam
26/11/2009
E, chapter 8
O&R chapter 8
E, chapter 8
O&R chapter 8
3/12/2009
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