### 2020　Advanced Cooperative Game Theory

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Graduate major in Industrial Engineering and Economics
Instructor(s)
Fukuda Emiko
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Mon3-4(Zoom)  Thr3-4(Zoom)
Group
-
Course number
IEE.B404
Credits
2
2020
Offered quarter
4Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

This course covers advanced topics in cooperative game theory. These topics include (1) bargaining problems, (2) TU games, (3) market with indivisible goods, (4) matching theory.

In recent years, game theory has been extensively used in theoretical economics. This course is intended to provide students with knowledge of cooperative game theory for application to complex economic systems.

### Student learning outcomes

By taking this course, students will have developed the following skills:
1) Build an economic model using advanced cooperative game theory.
2) Calculate bargaining solutions, core, etc. of cooperative games.
3) Think logically and explain complex social phenomenon using game theory.
4) Read technical papers in academic journals that use cooperative game theory.

### Keywords

Bargaining problems, Nash bargaining solution, TU games, core, balanced games, nucleolus, Shapley value, matching problems, stable set

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

This course 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 Brief overview of cooperative game theory, two-player bargaining problem (1) - Bargaining problem, Nash bargaining solution Details will be given in each lecture.
Class 2 Bargaining problem (2) - Proof of Nash's theorem, Kalai-Smorodinsky bargaining solution
Class 3 Transferable Utility (TU) Game - Characteristic function, superadditivity, strategic equivalence, imputation
Class 4 Core - Convex games, Balanced games, Bondareva-Shapley Theorem
Class 5 Stable set - Relationship between the core
Class 6 Bargaining set - Objection, counter-objection
Class 7 Nucleolus (2) - Nonemptiness and uniqueness of the nucleolus
Class 8 Review of Lectures 1-7, midterm evaluation
Class 9 Shapley value (1) - Marginal contribution, permutation, axioms
Class 10 Shapley value (2) - Potential
Class 11 Voting games - Power indices
Class 12 Market with indivisible goods and assignment games (1) - NTU-games, core, competitive equilibrium
Class 13 Market with indivisible goods and assignment games (1) - Assignment games, core, top trading cycles (TTC)
Class 14 Matching theory - Stable matching, optimality

### 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 textbook. Lecture notes can be found on the OCW-i site.

### Reference books, course materials, etc.

Muto, S. Game Theory. Tokyo: Ohmsha, 2011. (Japanese)

### Assessment criteria and methods

Homework (30%), Final exam (70%)