2024 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 (Face-to-face)
Media-enhanced courses: -
Day of week/Period (Classrooms): 3-4 Mon / 3-4 Thu
Class: -
Course Code: IEE.B404
Number of credits: 200
Course offered: 2024
Offered quarter: 4Q
Syllabus updated: Mar 14, 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.

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.