This course covers the elementary concepts of cooperative game theory. The topics include the bargaining problem and the Nash bargaining solution, games in characteristic function form, and applications such as voting games, markets, and topics built off of optimization problems.
The objective of this course is for students to first grasp the basic concepts of cooperative game theory and then apply them to problems in economics and industrial engineering. Ideally, the application of the theory should span to a broader range of situations than was possible by only using noncooperative game theory.
By completing this course, students will have the necessary tools to do the following:
1) Build an economic model and to apply cooperative game theory.
2) Calculate the Nash bargaining solution, core, nucleolus, and Shapley value in their respective game models.
3) Think and explain phenomenon in a logical manner.
Bargaining problem, Nash bargaining solution, games in characteristic function form, core, nucleolus, Shapley value
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
---|---|---|---|---|
- | - | ✔ | - | - |
This class will be held in lecture form. If time allows, some exercise problems will be explained.
Course schedule | Required learning | |
---|---|---|
Class 1 | What is cooperative game theory, and how is it different from noncooperative game theory? | Details will be given in each lecture. |
Class 2 | Cooperative games with two players: the Nash bargaining problem | |
Class 3 | Calculating the Nash bargaining solution - Formula and the four axioms | |
Class 4 | Cooperative games with three or more players: games in characteristic function form and the core | |
Class 5 | Mathematical definition of the core and applications | |
Class 6 | Application of the core to cost allocation problems | |
Class 7 | Definition of the nucleolus - Excess vector, acceptable imputations | |
Class 8 | Application of the nucleolus - Cost allocation, bankrupcy problem, Talmud rule, CG consistency | |
Class 9 | Review of Lectures 1 through 8 and midterm exam | |
Class 10 | Definition of the Shapley value and examples | |
Class 11 | Application of the Shapley value - Voting games, Shapley-Shubik voting index, Banzhaf voting index | |
Class 12 | Application of the Shapley value (2) - Cost allocation, Axioms | |
Class 13 | Market with indivisible goods, matching | |
Class 14 | Matching problem - DA algorithm, stability | |
Class 15 | Networks - Pairwise stability, efficiency |
No designated textbook. Lecture notes can be found on the OCW page.
Muto, S. Introduction to Game Theory. Tokyo: Nikkei Publishing Inc., 2001. (Japanese)
Funaki, Y. Exercises in Game Theory. Tokyo: Saiensu-sha Co. Ltd. Publishers, 2004. (Japanese)
Muto, S. Game Theory. Tokyo: Ohmsha, 2011. (Japanese)
Homework (approximately 30%), midterm exam and final exam (approximately 70%)
No prerequisites.