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
|Intercultural skills||Communication skills||Specialist 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||Nucleolus (1) - Excess vector, lexicographic ordering|
|Class 6||Nucleolus (2) - Nonemptiness, uniqueness|
|Class 7||Shapley value (1) - Marginal contribution, permutation, axioms|
|Class 8||Shapley value (2) - Potential, restricted domain|
|Class 9||Other solution concepts - Bargaining set, kernel|
|Class 10||Market with indivisible goods and assignment games (1) - Definition of assignment games, core|
|Class 11||Market with indivisible goods and assignment games (1) - Competitive equilibrium and the core|
|Class 12||Matching theory (1) - Stable matching, optimality|
|Class 13||Matching theory (2) - Extensions|
|Class 14||Barter model (1) - NTU games, core, competitive equilibrium, top trading cycles (TTC)|
|Class 15||Barter model (2) - Stable allocation, strong core|
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.