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8104 Non Cooperative Game Theory: Repeated games



(Theory of Repeated Games)

Term: Spring 2013

Number of credits:  2

Course description



The course has two main parts.


In the first we will develop the tools to study subgame perfect equilibria of repeated games with discounting, beginning with the simple case of perfect monitoring, and concluding with APS.


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


In the second part we will discuss topics.


1.       Credible Government Policies  

2.       Stochastic games

3.       Stability of Nash equilibria;

4.       KM stability, M stability

5.       Stable equilibria in finitely repeated games








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 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.
  4. The classic source for perfect public equilibria is Dilip Abreu, David Pierce, Ennio Stacchetti, ``Toward a Theory of Discounted Repeated Games with Imperfect Monitoring’’, Econometrica, 1990, 5, 1041-1063.
  5. The Mailath and Samuelson Book ``Repeated Games and Reputations: Long-Run Relationships'', Oxford University Press, is mostly focused on reputation, but is another good reference for this part. 


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 second part will be based on chapter 10 of van Damme, and several papers. Stable equilibria are defined in Kohlberg E. and Mertens JF.. (1986) On the strategic stability of equilibria, Econometrica, 54, 5, 1003–1037 and Mertens, J.M., (1989) Stable equilibria: A reformulation. Part I: Definition and basic properties. Mathematics of Operations Research, 4, 575–625.  



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, which 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