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8004 Repeated Games: Theory and Applications



(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



First part


  1. 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.
  2. Another good book, at a lower level, is the chapter in Game Theory, Fudenberg and Tirole, MIT Press.
  3. The book MS is also a good reference for this part.
  4. 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


  1. For the topic of Credible Government Policies chapters 15 and 21 of the Lindquist and Sargent, Recursive Macroeconomic Theory, MIT Press, are sufficient
  2. 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:

  1.    A Mid-Term Exam at the beginning of the fourth week, and
  2.    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. 

  • The first homework is here. It is due on April 15.


       The midterm exam is on April 18th, Thursday

                                                Final Exam

    The last day of class in the fourth mini is May 10. The final exam is on May 9th