Print

2022　Graduate Methodologies in Cognition, Mathematics and Information S1

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Graduate major in Social and Human Sciences
Instructor(s)
Inohara Takehiro 
Class Format
Lecture    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Fri3-4()  
Group
-
Course number
SHS.M461
Credits
2
Academic year
2022
Offered quarter
1-2Q
Syllabus updated
2022/3/16
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

[IMPORTANT]
If you would like to take this course, please send an email to the professor in charge, in advance.

The subject of the email should be "Wishing to attend Graduate Methodologies in CMI-S1", and write a) the name of this course , b) your name, c) your student number, and d) the email address you would like to register in the body of the email.

- - - - - - -
The theme of this course is “Decision Making Models.” This course deals with mathematical methods for modeling and analyzing competitive or social decision making situations through lectures, discussion, working on exercise problems and group work. Specifically, this course gives definitions, examples and analysis methods of “games in normal form,” “games in extensive form,” “option form,” “graph models,” “simple games,” “games in characteristic function form,” and “committees.” These are mathematical models for describing and analyzing decision making situations, which the students are expected to understand upon completion of this course.

This course aims to cultivate the students’ abilities to: select an appropriate mathematical model for describing and analyzing a focal decision making situation; describe a real-world decision making situation by a mathematical model; analyze the mathematical model and draw some insights on the situation from the results of the mathematical analysis; and convey the mathematical analysis results to others concisely.

Student learning outcomes

Upon completion of this course, students should be able to:
1) State the definitions of mathematical models using examples of decision making situations described by the mathematical models;
2) Apply analysis methods to examples of decision making situations described by the mathematical models, and explain the analysis results to others;
3) Select an appropriate mathematical model and describe a real-world decision making situation; and
4) Apply analysis methods to a real-world decision making situation described by a mathematical model, and explain others the analysis results and some insights on the situation drawn from the results.

Keywords

games in normal form, games in extensive form, option form, graph models, simple games, games in characteristic function form, committees

Competencies that will be developed

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

Class flow

Each mathematical model is dealt with over two or three classes.

First, a lecture on the definitions of basic concepts and analysis methods is presented. Then, the students examine the contents of the lecture, and work on exercises. After the class, each student writes and submits a “summary report” on what he/she learned through individual observation, other students' ideas, the lecture, and exercises.

Students also work in a group of two or three; each group writes three reports on the background and the detail of a real-world decision making situation (Background Report), on the model of the situation (Model Report) and on the analysis results of the situation (Analysis Report). Moreover, each group is prepares one poster based on these three reports and gives a poster presentation as a group at the end of the second quarter.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Games in normal form (1): Definition State the definition of games in normal form.
Class 2 Games in normal form (2): Dominant strategy equilibrium and Nash equilibrium Analyze games in normal form using dominant strategy equilibrium and Nash equilibrium, then explain the results.
Class 3 Games in extensive form (1): Definition State the definition of games in extensive form.
Class 4 Games in extensive form (2): Backward induction and subgame perfect equilibrium Analyze games in extensive form using backward induction and subgame perfect equilibrium, then explain the results.
Class 5 Option form (1): Definition State the definition of option form.
Class 6 Option form (2): Stability concepts Analyze option form using stability concepts, then explain the results.
Class 7 Graph models (1): Definition State the definition of graph models.
Class 8 Graph models (2): Transition time analysis Analyze graph models using transition time analysis, then explain the results.
Class 9 Simple games and weighted majority games (1): Definition State the definition of simple games and weighted majority games.
Class 10 Simple games and weighted majority games (2): Dictator, veto, unanimity, properness and symmetry Analyze simple games and weighted majority games using dictator, veto, unanimity, properness and symmetry, then explain the results.
Class 11 Simple games and weighted majority games (3): Power indices and coalition power comparison Analyze simple games and weighted majority games using power indices and coalition power comparison, then explain the result.
Class 12 Games in characteristic function form (1): Definition, Core, Shapley value and nucleolus State the definition of games in characteristic function form. Analyze games in characteristic function form using core, Shapley value and nucleolus, then explain the results.
Class 13 Committees : Definition, stable alternatives State the definition of committees. Analyze committees by using stable alternatives, then explain the results.
Class 14 Poster presentation Give a poster presentation as a group based on Background Report, Model Report, and Analysis Report.

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.

Textbook(s)

None specified.

Reference books, course materials, etc.

Course materials will be provided via T2SCHOLA and other means.

Assessment criteria and methods

Students are encouraged to actively participate in discussion, group work and working on exercise problems during classes.

Assessment will be based on: “summary reports” for each class (30% in total); three reports (10% each; total 30%); making a poster (20%); and one presentation (20%).

Related courses

  • SHS.M442 ： Graduate Lecture in Cognition, Mathematics and Information S1B
  • SHS.M443 ： Graduate Lecture in Cognition, Mathematics and Information F1A
  • SHS.M444 ： Graduate Lecture in Cognition, Mathematics and Information F1B
  • SHS.M462 ： Graduate Methodologies in Cognition, Mathematics and Information F1
  • SHS.M441 ： Graduate Lecture in Cognition, Mathematics and Information S1A

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

Prospective students should be familiar with mathematical expression and analysis, and have interests in various social problems.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Prof. Takehiro Inohara, inostaff[at]shs.ens.titech.ac.jp

When inquiring by emails, include the course title in the subject, and your student ID and name in the body of the email.

Office hours

Make an appointment by email.

Other

This course consists of the content of science.

Page Top