2025 (Current Year) Faculty Courses School of Engineering Department of Industrial Engineering and Economics Graduate major in Industrial Engineering and Economics
Advanced Cooperative Game Theory
- Academic unit or major
- Graduate major in Industrial Engineering and Economics
- Instructor(s)
- Emiko Fukuda
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- IEE.B404
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 4Q
- Syllabus updated
- Mar 19, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
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, stable set, bargaining set, nucleolus, Shapley value, NTU games, matching problems
Competencies
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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 (1) - Core, dominance core, convex games | |
| Class 5 | Shapley value - Marginal contribution, permutation, axioms, potential | |
| Class 6 | Voting games - Power indices | |
| Class 7 | Review of Lectures 1-6, midterm evaluation | |
| Class 8 | Core (2) - Core, Convex games, Balanced games, Bondareva-Shapley Theorem | |
| Class 9 | Stable set - Relationship between the core | |
| Class 10 | Bargaining set - Objection, counter-objection | |
| Class 11 | Nucleolus - Kernel, nonemptiness and uniqueness of the nucleolus | |
| 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 |
Study advice (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 will be uploaded online (T2SCHOLA).
Reference books, course materials, etc.
Muto, S. Game Theory. Tokyo: Ohmsha, 2011. (Japanese)
Nakayama, M., Y. Funaki, and S. Muto. Cooperative Game Theory. Tokyo: Keisoshobo, 2008. (Japanese)
Chakravarty, S. R., M. Mitra, and P. Sarkar. A Course on Cooperative Game Theory. Cambridge University Press, 2015.
Peleg, B. and P. Sudholter, Introduction to the Theory of Cooperative Games, 2nd ed., Springer-Verlag, 2008.
Evaluation methods and criteria
Homework (30%), Exam (70%)
Related courses
- IEE.B401 ： Advanced Microeconomics
- IEE.B402 ： Advanced Macroeconomics
- IEE.B403 ： Advanced Noncooperative Game Theory
- IEE.B431 ： Advanced Topics in Microeconomics
- IEE.B433 ： Advanced Topics in Mathematical Economics
Prerequisites
Knowledge of undergraduate level cooperative game theory is strongly required.