シラバス参照
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シラバス参照
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| 講義概要/Course Information |
| 科目基礎情報/General Information |
| 授業科目名 /Course title (Japanese) |
ゲームの数理 | ||
|---|---|---|---|
| 英文授業科目名 /Course title (English) |
Mathematical Models in Games | ||
| 科目番号 /Code |
|||
| 開講年度 /Academic year |
2022年度 | 開講年次 /Year offered |
全学年 |
| 開講学期 /Semester(s) offered |
前学期 | 開講コース・課程 /Faculty offering the course |
博士前期課程、博士後期課程 |
| 授業の方法 /Teaching method |
講義 | 単位数 /Credits |
2 |
| 科目区分 /Category |
大学院専門教育科目 - 専門科目Ⅱ | ||
| 開講類・専攻 /Cluster/Department |
情報・ネットワーク工学専攻 | ||
| 担当教員名 /Lecturer(s) |
高橋 里司 | ||
| 居室 /Office |
西4号館508 | ||
| 公開E-mail |
stakahashi@uec.ac.jp | ||
| 授業関連Webページ /Course website |
Google Classroom | ||
| 更新日 /Last update |
2022/03/18 16:50:36 | 更新状況 /Update status |
公開中 /now open to public |
| 講義情報/Course Description |
| 主題および 達成目標（2,000文字以内） /Themes and goals（up to 2,000 letters） |
This lecture provides several mathematical models in games. This year, we will treat ratings and rankings of games. Rating and ranking is an optimization problem, called a linear-ordering problem, which is very simple but full of various paradoxes. In sports games, ratings are used not only to express the strength and characteristics of teams, but also to set gambling multipliers. On the other hand, the ranking issue has been integrated into the social system as a voting issue, and has been studied and discussed before its application to sports. In this lecture, the world of rating and ranking as a political science will be treated. The objectives of this course are (1) to understand and be able to program rating and ranking models, and (2) to understand the impossibility theorem in social choice theory. |
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| 前もって履修 しておくべき科目（1,000文字以内） /Prerequisites（up to 1,000 letters） |
None |
| 前もって履修しておくこ とが望ましい科目（1,000文字以内） /Recommended prerequisites and preparation（up to 1,000 letters） |
Linear algebra, Logic, Discrete Mathematics |
| 教科書等（1,000文字以内） /Course textbooks and materials（up to 1,000 letters） |
Preparing slides and text. Supplemental documents are given if necessary. The following is reference: Preparing slides and text. Supplemental documents are given if necessary. The following is reference: 1. A. N. Langville and C. D. Meyer: Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton Univ. Press, 2012. 2. A. N. Langville and C. D. Meyer: Who's #1?: The Science of Rating and Ranking, Princeton Univ. Press, 2012. 3. 坂井 豊貴: 社会的選択理論への招待, 日本評論社，2013. 4. K. J. Arrow: 社会的選択と個人的評価, 勁草書房, 2013. |
| 授業内容と その進め方（2,000文字以内） /Course outline and weekly schedule（up to 2,000 letters） |
Lecture Type : English Type II (Ca) This class uses the English slide and the Japanese oral explain. Lecture 1：Guidance, Introduction to rating, ranking, social choice theory Lecture 2：Least squares model : Massey and Colley's method Lecture 3：Long-term model: Keener's method Lecture 4：Elo rating: regression toward the mean Lecture 5：Markov and PageRank method Lecture 6：OD rating method and re-ordering Lecture 7：Point spread Lecture 8：Summary of 1st half Lecture 9：Ranking aggregation: social choice theory Lecture 10 : Borda and Condorcet method Lecture 11：Social welfare function Lecture 12：Kemeny's method Lecture 13 : Gibbard–Satterthwaite theorem Lecture 14 : Arrow's impossible theorem Lecture 15 : Summary of 2nd half |
| 実務経験を活かした 授業内容 (実務経験内容も含む) /Course content utilizing practical experience |
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| 授業時間外の学習 （予習・復習等）（1,000文字以内） /Preparation and review outside class（up to 1,000 letters） |
To understand deeply by solving the exercises distributed during the lecture. |
| 成績評価方法 および評価基準 （最低達成基準を含む） （1,000文字以内） /Evaluation and grading （up to 1,000 letters） |
(a) Evaluation method：Weekly exercises (25%) and Reports (75%). (b) Evaluation criteria：Understand the models covered in the lecture and be able to fit actual data and perform calculations. Understand and be able to explain the proof of Arrow's impossibility theorem |
| オフィスアワー： 授業相談（1,000文字以内） /Office hours（up to 1,000 letters） |
Emails and classroom streams at any time. Also it is able to come my office W4-508 with appointment． |
| 学生へのメッセージ（1,000文字以内） /Message for students（up to 1,000 letters） |
This class is planning to hold a lecture where you can learn about the fun of mathematical modeling and the wide range of applications, using games as the theme. |
| その他 /Others |
None |
| キーワード /Keywords |
Rating, Ranking, Social choice theory, Eigenvalue problem, linear-ordering problem, impossible theorem |