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2016　Cooperative Game Theory

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Academic unit or major
Undergraduate major in Industrial Engineering and Economics
Instructor(s)
Kawasaki Ryo 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Mon5-6(W931)  Thr5-6(W931)  
Group
-
Course number
IEE.B302
Credits
2
Academic year
2016
Offered quarter
2Q
Syllabus updated
2016/4/27
Lecture notes updated
2016/7/26
Language used
Japanese
Access Index

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

✔ 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 Review of Lectures 1 through 9 and midterm exam
Class 11 Application of the Shapley value (1) - Cost allocation
Class 12 Application of the Shapley value - Voting games, Shapley-Shubik voting index, Banzhaf voting index
Class 13 Application of the core (1) - Market with indivisible goods, matching
Class 14 Application of the core (2) - Matching problem, DA algorithm
Class 15 Application of the core (3) - Networks, cost allocation, stability

Textbook(s)

Muto, S. Introduction to Game Theory. Tokyo: Nikkei Publishing Inc., 2001. (Japanese)

Reference books, course materials, etc.

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 (approximately 25%) and final exam (approximately 45%)

Related courses

  • IEE.B201 ： Microeconomics I
  • IEE.B202 ： Microeconomics II
  • IEE.B205 ： Noncooperartive 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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