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 discussion, group work, lectures and working on exercise problems. 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.
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.
games in normal form, games in extensive form, option form, graph models, simple games, games in characteristic function form, committees
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Each mathematical model is dealt with over two or three classes.
In the first class, the students examine examples of decision making situations which can be described by the mathematical model, first individually, second in pairs, then in groups of four, and finally with the class as a whole. Then a lecture on the mathematical model is presented, and the students work on exercise problems. At the end of the class, each student writes and submits a “summary report” on what he/she learned through individual observation, other students’ ideas, the lecture, and exercise problems.
In the following class(es), as in the first class, the students learn analysis methods applicable to the mathematical model through discussion, group work, lectures, and working on exercise problems, then write and submit “summary reports.”
|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||State the definition of games in characteristic function form.|
|Class 13||Games in characteristic function form (2): Core, Shapley value and nucleolus||Analyze games in characteristic function form using core, Shapley value and nucleolus, then explain the results.|
|Class 14||Committees : Definition, stable alternatives||State the definition of committees. Analyze committees by using stable alternatives, then explain the results.|
|Class 15||Poster presentation||Give a poster presentation as a group based on Background Report, Model Report, and Analysis Report.|
Course materials are posted on OCW-i and/or provided during the classes.
Students are encouraged to actively participate in discussion, group work and working on exercise problems during classes. 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.
Assessment will be based on: “summary reports” written during each class (30% in total); three reports (10% each; total 30%); making a poster (20%); and one presentation (20%).
Prospective students should be familiar with mathematical expression and analysis, and have interests in various social problems. Students must have successfully completed “Trans-disciplinary Exercise in Social and Human Sciences S1A (Basics of Logic and Set Theory)” and “Trans-disciplinary Exercise in Social and Human Sciences S1B (Basics of Metric, Convergence and Continuity)” or have equivalent knowledge.
Takehiro Inohara, inostaff[at]shs.ens.titech.ac.jp
This course consists of the content of science.