2020 Cooperative Game Theory

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Academic unit or major
Undergraduate major in Industrial Engineering and Economics
Kawasaki Ryo 
Course component(s)
Mode of instruction
Day/Period(Room No.)
Mon1-2(W934)  Thr1-2(W934)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course covers the elementary concepts of cooperative game theory. The topics include the bargaining problem and the Nash bargaining solution, games in characteristic function form, and applications such as voting games, markets, and topics built off of optimization problems.

The objective of this course is for students to first grasp the basic concepts of cooperative game theory and then apply them to problems in economics and industrial engineering. Ideally, the application of the theory should span to a broader range of situations than was possible by only using noncooperative game theory.

Student learning outcomes

By completing this course, students will have the necessary tools to do the following:
1) Build an economic model and to apply cooperative game theory.
2) Calculate the Nash bargaining solution, core, nucleolus, and Shapley value in their respective game models.
3) Think and explain phenomenon in a logical manner.


Bargaining problem, Nash bargaining solution, games in characteristic function form, core, nucleolus, Shapley value

Competencies that will be developed

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

Class flow

This class 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 What is cooperative game theory, and how is it different from noncooperative game theory? Details will be given in each lecture.
Class 2 Cooperative games with two players: the Nash bargaining problem
Class 3 Calculating the Nash bargaining solution - Formula and the four axioms
Class 4 Cooperative games with three or more players: games in characteristic function form and the core
Class 5 Mathematical definition of the core and applications
Class 6 Application of the core to cost allocation problems
Class 7 Definition of the nucleolus - Excess vector, acceptable imputations
Class 8 Application of the nucleolus - Cost allocation, bankrupcy problem, Talmud rule, CG consistency
Class 9 Definition of the Shapley value and examples
Class 10 Application of the Shapley value - Voting games, Shapley-Shubik voting index, Banzhaf voting index
Class 11 Application of the Shapley value (2) - Cost allocation, Axioms
Class 12 Market with indivisible goods, matching
Class 13 Matching problem - DA algorithm, stability
Class 14 Matching Problem - Coincidence and conflict

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.


No designated textbook. Lecture notes can be found on the OCW page.

Reference books, course materials, etc.

Muto, S. Introduction to Game Theory. Tokyo: Nikkei Publishing Inc., 2001. (Japanese)
Funaki, Y. Exercises in Game Theory. Tokyo: Saiensu-sha Co. Ltd. Publishers, 2004. (Japanese)
Muto, S. Game Theory. Tokyo: Ohmsha, 2011. (Japanese)

Assessment criteria and methods

Grades will be based on homework assignments etc.

Related courses

  • IEE.B201 : Microeconomics I
  • IEE.B202 : Microeconomics II
  • IEE.B205 : Noncooperative Game Theory
  • IEE.B337 : Mathematical Economics
  • IEE.A201 : Basic Mathematics for Industrial Engineering and Economics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites.

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