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.
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.
Bargaining problems, Nash bargaining solution, TU games, core, balanced games, nucleolus, Shapley value, matching problems, stable set
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
This course will be held in lecture form. If time allows, some exercise problems will be explained.
|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|
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 textbook. Lecture notes can be found on the OCW-i site.
Muto, S. Game Theory. Tokyo: Ohmsha, 2011. (Japanese)
Homework (30%), Final exam (70%)
Knowledge of undergraduate level cooperative game theory is required.