Non Cooperative Game Theory and Information Economics

Fall - 2007

Game Theory tries to understand how rational individuals interact and to predict the result of this interaction. A better name would be interactive decision theory because it tries to understand the decision process of individuals that are involved in a situation where the actions of each one affect the welfare of the others, and who are conscious of this fact. This means that the interaction takes place not only at the level of the actions but at the level of the reasoning as well: players need to put themselves in the shoes of the others in order to try to predict their behavior.

Game theory can be seen as a part of mathematics that is tailored to satisfy the needs of the social sciences.

By the end of the course you will be ackwainted with some of the central models of game theory, such as bargaining models, auctions, and the formalization of knowledge.

Course Organization

• Prerequisites

  603.


 
• Lectures

  The class meets on Tuesdays and Thursdays, 2:10-3:25. Attendance to the lectures is not compulsory but is very important. You are strongly encouraged to actively participate in class discussions and to ask questions during lectures, since a portion of your grade depends on class participation.


 
• Office Hours and Staff
   
  • Lecturer: Oscar Volij
  • Office Hours: By appointment.
    You are strongly encouraged to come to office hours. This is the best way for the student to clarify ideas and the best way for the professor to grasp the students' level of understanding. Past experience shows that students who come to office hours perform better than those who do not come.
  • Teaching Assitant: Oscar Volij
  
   
• Reading Material

  You are encouraged to read any textbook in Game Theory that you may find. No book is required. If you want to buy one, I would recommend Martin J. Osborne and Ariel Rubinstein, A Course in Game Theory , MIT Press. It is a very serious and formal book, where no single word is redundant. Another recommended books are Drew Fudenberg and Jean Tirole, Game Theory, MIT Press, and Ken Binmore's Playing for Real: A text on Game Theory, Oxford University Press.

• Homework

  Homework consists of questions and problems on the material covered in class. The assignments are not compulsory.

• Exams

  There will be two in-class exams. The first one on October 11, and the second one on November 27. The exam are closed book. Absence from an exam can be excused only for emergency reasons.

• Class Participation

  It is important that you show your interest in the course. The best way to do so is by asking questions and participating in class discussions. Your feedback is also very valuable. Please do not hesitate to provide comments and constructive criticism on the course organization.

• The Final Grade

  Your final grade will be computed as follows:

  • First exam:40%
  • Second exam: 40%
  • Problem sets: 10%
  • Class Participation: 10%

• Outline of Topics
   
  • Cooperative Bargaining
    • The Nash Bargaining Solution.
  • Extensive games with perfect information
    • Nash equilibrium.
    • Subgame perfect equilibrium.
    • Rubinstein's altenating offers game.
  • Common Knowledge
    • Alternative definitions.
    • Agreeing to disagree.
    • Common Knowledge of Rationality and Correlated Equilibrium.
  • Auctions
    • Standard Auctions.
    • Revenue Equivalence.
  • Bibliography
     
    • Nash, John (1950), The Bargaining Problem, Econometrica 28, 155--162.
    • Rubinstein, Ariel (1982), Perfect Equilibrium in a Bargaining Model, Econometrica 50, 97--110.
    • Aumann, Robert J. (1976), Agreeing to Disagree, Annals of Statistics 4, 1236--1239.
    • Monderer, Dov and Dov Samet (1989), Approximating Common Knowledge with Common Beliefs, Games and Economic Behavior 1, 170--190.
    • Aumann, Robert J. (1987), Correlated Equilibrium as an Expression of Bayesian Rationality, Econometrica 55, 1--18.
    • Aumann, Robert J. (1974), Subjectivity and Correlation in Randomized Strategies, Journal of Mathematical Economics 1, 67-96.
    • Nielsen, T., A. Brnadenburger, J. Geanakoplos, R. Mc Kelvey, and T. Page (1990), Common Knowledge of an Aggregate of Expectations, Econometrica 58, 1235-1239.
    • Krishna, Vijay (2002), Auction Theory, Academic Press.