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2024　Noncooperative Game Theory

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Academic unit or major
Undergraduate major in Industrial Engineering and Economics
Instructor(s)
Fukuda Emiko 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon5-6(W8E-101)  Thr5-6(W8E-101)  
Group
-
Course number
IEE.B205
Credits
2
Academic year
2024
Offered quarter
2Q
Syllabus updated
2024/3/14
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

This course covers the elementary topics in non-cooperative game theory. These topics include (1) games in strategic form, dominated strategies, Nash equilibrium; (2) games in extensive form and subgame-perfect equilibrium; (3) repeated games and the Folk Theorem; and (4) evolutionary game theory.

In everyday life, people interact with each other. Game theory is a mathematical tool used in analyzing the interaction among rational decision makers. Its applications range throughout many topics in economics and management, and by applying this theory, additional insights may emerge. The objective of this course is for students to be able to apply the theory when examining topics of their interest in economics and industrial engineering.

Student learning outcomes

By taking this course, students will have attained the following skills:
1) Build an economic model using non-cooperative game theory.
2) Calculate Nash equilibria, subgame-perfect equilibria, etc. of games given in strategic form and extensive form.
3) Think logically and explain social phenomenon using game theory.

Keywords

Games in strategic form, Nash equilibrium, games in extensive form, subgame-perfect equilibrium, Bayesian games, Perfect Bayesian equilibrium, evolutionary game theory

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 Games in strategic form (1) - Definition of a game, game in (bi)matrix form, dominated strategies Understand the dominance relationship of strategies.
Class 2 Games in strategic form (2) - Best response, Nash equilibrium, mixed-strategy Nash equilibrium Understand the definition of Nash equilibrium and the properties of mixed-strategy Nash equilibria.
Class 3 Games in strategic form (3) - Rationalizable strategies, strategic form games with more than 2 players Understand the definitions and concepts of domination, weak domination, and rationalizability.
Class 4 Games in strategic form (4) - Zero-sum games, Minimax Theorem, applications (e.g. duopoly) Derive Cournot equilibrium and Bertrand equilibrium. Understand the saddle point of zero sum games.
Class 5 Games in extensive form (1) - Game tree, information set, subgame,subgame-perfect equilibrium, games with perfect information, backwards induction Understand the definition of an extensive form game and a subgame perfect equilibrium.
Class 6 Games in extensive form (2) - Chain store paradox, new-entry game, Stackelberg model Understand the chain store paradox. Derive equilibrium of Stackelberg games.
Class 7 Games in extensive form (3) - Behavioral strategies and mixed strategies, beliefs, weak perfect Bayesian equilibrium Understand the relationship between behavioral and mixed strategies. Understand the definitions of belief and weak perfect Bayesian equilibrium.
Class 8 Review of Lectures 1-7, midterm exam
Class 9 Repeated games (1) - Finitely repeated games, component games, strategies in repeated games Understand the definitions of strategy and utility in repeated games. Understand the properties of subgame perfect equilibria in finitely repeated games.
Class 10 Repeated games (2) - Infinitely repeated games, Folk Theorem Understand the definition of a trigger strategy in an infinitely repeated game. Find the conditions under which the trigger strategy is a Nash equilibrium. Understand the Folk Theorem.
Class 11 Games with incomplete information (1) - Incomplete information, Bayesian games, types, Bayesian-Nash equilibrium Understand the definitions of Bayesian game, Bayesian Nash equilibrium, and strategy-proofness.
Class 12 Games with incomplete information (2) - Weak perfect Bayesian equilibrium, belief, consistency, sequential rationality Formulate an incomplete information game with sequential moves. Find weakly complete Bayesian equilibrium.
Class 13 Games with incomplete information (3) - Adverse selection, signaling, screening Understand signaling games, separating equilibrium, and pooling equilibrium.
Class 14 Evolutionary game theory - Basic concepts, evolutionary stable strategies (ESS), applications Understand the definition and properties of evolutionary stable strategies.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparation and review (including assignments) for each class.

Textbook(s)

No designated textbook. Lecture notes will be distributed online (T2SCHOLA).

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)
Greve, T. Non-Cooperative Game Theory. Tokyo: Chisen-shokan, 2011. (Japanese)

Assessment criteria and methods

Homework (approximately 30%), Midterm exam and Final exam (approximately 35% each).

Related courses

  • IEE.B201 ： Microeconomics I
  • IEE.B202 ： Microeconomics II
  • IEE.B206 ： Experimental Economics
  • IEE.B302 ： Cooperative Game Theory
  • IEE.A201 ： Basic Mathematics for Industrial Engineering and Economics

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

No prerequisites.

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