### 2021　Cooperative Game Theory

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Undergraduate major in Industrial Engineering and Economics
Instructor(s)
Kawasaki Ryo
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Mon1-2(W631)  Thr1-2(W631)
Group
-
Course number
IEE.B302
Credits
2
2021
Offered quarter
1Q
Syllabus updated
2021/4/5
Lecture notes updated
-
Language used
Japanese
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### 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.