Professor ALDO RUSTICHINI

arust@econ.umn.edu

**Course: **ECON 8004 MICROECONOMIC THEORY

(Theory of
Repeated Games)

**Term**: Spring 2013

# Number of credits: 2

**Course description**

In
the course we will develop the tools to study subgame perfect equilibria of
repeated games with discounting. This is the theory of strategic interaction
between players that meet repeatedly over time, and either do so infinitely
many times, or they do not know for sure when their interaction will stop. We
will focus on the case of perfect monitoring in which strategies are observed
in every period. In the first part we will study the theory, in the second we
will consider two important applications.

**First
part: theory**

1.
Reminder
on Extensive Form games: Behavioral and Mixed Strategies

2.
Definition
of Repeated Game with discounting

3.
Nash
and Sub-game Perfect Equilibria of repeated games

4.
Feasible
and Incentive compatible set of payoffs

5.
Nash
equilibria of repeated games: characterization

6.
Nash
operator: main properties

7.
One
stage deviation property

8.
Subgame
Perfect equilibria: characterization

9.
Subgame
Perfect operator: main properties

10.
Simple
strategy profiles

11.
Folk
Theorem

12.
Repeated
games with imperfect public monitoring

**Second
part: extension and applications.**

1.
Credible
Government Policies

2.
Reputation

**References**

** **

**First
part**

- A good source for the
first part of the first part is
*Stability
and Perfection of Nash Equilibria*, Eric van Damme, Springer Verlag: chapters
2, 6, are prerequisites, and have been covered in the 8103, chapter 8
develops the theory of repeated games.
- Another good book, at a
lower level, is the chapter in
*Game
Theory*, Fudenberg and Tirole, MIT Press.
- The book MS is also a good
reference for this part.
- The simple strategy
profiles and the One stage deviation principle are presented in the
original paper of Dilip Abreu, ``On the Theory of Infinitely Repeated
Games with Discounting’’,
*Econometrica*,
1988, 2, 383-396.

** **

**Second part**

- For the topic of Credible
Government Policies chapters 15 and 21 of the Lindquist and Sargent,
*Recursive Macroeconomic Theory*, MIT
Press, are sufficient
- The Mailath and Samuelson
Book Reputation is mostly focused on reputation, so it is the ideal reference
for this second part. Of course we will cover only a small fraction of the
book.

**Home works, Exams
and Grades**

** **

Home-works are going to be assigned on a regular basis, and
the solution discussed in class or in the recitation hour.

There is going to be:

- A Mid-Term Exam at the beginning of the fourth week,
and
- A Final Exam. The final Exam may include material from
the entire course.

Grades
are based on weights of 30 per cent to Homeworks, 30 per cent to Midterm and 40
per cent on the Final.