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- 工学院，物質理工学院，環境・社会理工学院共通科目
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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Industrial Engineering and Economics
- Instructor(s)
- Kawasaki Ryo
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon1-2(W631) Thr1-2(W631)
- Group
- -
- Course number
- IEE.B302
- Credits
- 2
- Academic year
- 2021
- Offered quarter
- 1Q
- Syllabus updated
- 2021/4/5
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
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.
Student learning outcomes
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.
Keywords
Bargaining problem, Nash bargaining solution, games in characteristic function form, core, nucleolus, Shapley value
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This class will be held in lecture form. If time allows, some exercise problems will be explained.
Course schedule/Required learning
| 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 |
Out-of-Class Study Time (Preparation and Review)
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.
Textbook(s)
No designated textbook. Lecture notes will be distributed online (T2SCHOLA).
Reference books, course materials, etc.
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)
Assessment criteria and methods
Grades will be based on homework assignments and the final exam (to be held in the classroom). How the final exam will be conducted may be subject to change in cases of increased infections of COVID-19.
Related courses
- IEE.B201 ： Microeconomics I
- IEE.B202 ： Microeconomics II
- IEE.B205 ： Noncooperative Game Theory
- IEE.B337 ： Mathematical Economics
- IEE.A201 ： Basic Mathematics for Industrial Engineering and Economics
Prerequisites (i.e., required knowledge, skills, courses, etc.)
No prerequisites.
