2019　Cooperative Game Theory

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Undergraduate major in Industrial Engineering and Economics
Instructor(s)
Kawasaki Ryo
Course component(s)
Lecture
Day/Period(Room No.)
Mon1-2(W934)  Thr1-2(W934)
Group
-
Course number
IEE.B302
Credits
2
2019
Offered quarter
1Q
Syllabus updated
2019/3/20
Lecture notes updated
2019/5/29
Language used
Japanese
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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.

Keywords

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

Competencies that will be developed

Intercultural skills Communication skills Specialist 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 Review of Lectures 1 through 8 and midterm exam
Class 10 Definition of the Shapley value and examples
Class 11 Application of the Shapley value - Voting games, Shapley-Shubik voting index, Banzhaf voting index
Class 12 Application of the Shapley value (2) - Cost allocation, Axioms
Class 13 Market with indivisible goods, matching
Class 14 Matching problem - DA algorithm, stability
Class 15 Networks - Pairwise stability, efficiency

Textbook(s)

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

Homework (approximately 30%), midterm exam and final exam (approximately 70%)

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.