2019 Advanced Cooperative Game Theory

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Academic unit or major
Graduate major in Industrial Engineering and Economics
Instructor(s)
Fukuda Emiko 
Course component(s)
Lecture
Day/Period(Room No.)
-
Group
-
Course number
IEE.B404
Credits
2
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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, nucleolus, Shapley value, matching problems, stable set

Competencies that will be developed

Intercultural skills Communication skills Specialist 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/Required learning

  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

Textbook(s)

No textbook. Lecture notes can be found on the OCW-i site.

Reference books, course materials, etc.

Muto, S. Game Theory. Tokyo: Ohmsha, 2011. (Japanese)

Assessment criteria and methods

Homework (30%), Final 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 (i.e., required knowledge, skills, courses, etc.)

Knowledge of undergraduate level cooperative game theory is required.

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