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
✔ Specialist skills | Intercultural skills | Communication 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 | Definition of the Shapley value and examples | |
Class 10 | Application of the Shapley value - Voting games, Shapley-Shubik voting index, Banzhaf voting index | |
Class 11 | Application of the Shapley value (2) - Cost allocation, Axioms | |
Class 12 | Market with indivisible goods, matching | |
Class 13 | Matching problem - DA algorithm, stability | |
Class 14 | Matching Problem - Coincidence and conflict |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
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)
Grades will be based on homework assignments etc.
No prerequisites.