シラバス参照

講義概要/Course Information

2024/07/19 現在

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	2024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	W4-508
公開E-mail /e-mail	stakahashi@uec.ac.jp
授業関連Webページ /Course website	Google Classroom
更新日 /Last update	2024/03/07 10:20:14	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 cooperative games. Cooperative game theory, the mathematics of analyzing the distribution of gains in forms of collective action such as cooperation, collusion, and conspiracy, will be explained with examples. The objective of this course is to provide an in-depth understanding of the concept of cooperative games and to gain knowledge about modeling social phenomena.
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, Mathematical optimization, 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: 1. 中山幹夫，船木由喜彦，武藤滋夫：協力ゲーム理論， 勁草書房，2008. 2. 船木由喜彦，武藤滋夫，中山幹夫(編著)，ゲーム理論 アプリケーションブック，東洋経済新報社，2013． 3. J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, 1st ed., Princeton University Press, 1944. (2nd ed., 1947, 3rd ed., 1953.). 4. B. Peleg and P. Sudh\:{o}lter, Introduction to the Theory of Cooperative Games, 2nd ed., Springer-Verlag, 2008. (1st ed., 2003.) 5.Satya R. Chakravarty, Manipushpak Mitra, Palash Sarkar, A Course on Cooperative Game Theory, Cambridge University Press, 2018.
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）	The class is type （Ca）: the English slide and the Japanese oral explain. Lecture 1：Guidance, Introduction to cooperative game Lecture 2：Basic of cooperative game theory, Characteristic function, Allocation Lecture 3：Core Lecture 4：Stable set, Relationship between core and stable set Lecture 5：Bargaining set Lecture 6：Kernel Lecture 7：Nucleolus Lecture 8：Shapley value Lecture 9：Convex game Lecture 10： NTU game 1 (Pure exchanging economy model) Lecture 11：NTU game 2 (Solution concepts) Lecture 12： Strategic form of cooperative games 1 (Reduction game) Lecture 13 : Strategic form of cooperative games 2 (Strong Nash equilibrium) Lecture 14 : Application of the cooperative game Lecture 15 : Summary
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
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：Reports and Exercises. (b) Evaluation criteria：To be able to understand fundamental mathematical models and solutions for the cooperative game. To be able to solve about 70% of the exercises.
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	This lecture uses basic linear algebra and set theory
キーワード /Keywords	Cooperative game, Core, Shapley value, Polyhedron