Mathematical Sciences: Cooperative Game Theory

数学科学：合作博弈论

• 批准号: 9000874
• 负责人: David Housman
• 金额: $ 2.4万
• 依托单位: Drew University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-03-15 至 1991-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000874&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cooperative; Game; Theory

Six undergraduates engaged in mathematical research on problems in cooperative game theory will be supported by this Research Experiences for Undergraduates award. Cooperative game theory is a good field for facilitating undergraduate discovery. It is not normally included in the traditional undergraduate curriculum, it provides a source of excellent applications to real world problems and its relatively small body of literature is approachable and not highly technical. Topics to be considered include value axiomatics, an area whose goals are to characterize values by sets of properties and to determine the classes of games on which well-known values satisfy certain properties - properties usually prompted by intuitive notions of fairness or bargaining power. Applications of values is another theme which involves applications such as airport landings, traveling salesman and other assignment strategies. Other topics for students include studies of multi-alternative voting power. Indices, matroidal simple games and the complexity of simplex calculations of the nucleolus of a game. Ample computer and library facilities are available for the students. Each student will write a final report based upon the research completed. It will then be prepared for journal submission, presentation at a professional meeting or used as a basis for an honors thesis. A newsletter will be circulated to maintain contact between participants and advisors.

6名从事合作博弈论问题数学研究的本科生将获得本本科生研究经验奖。合作博弈论是促进大学生发现的一个很好的领域。它通常不包括在传统的本科课程中，它为解决现实世界的问题提供了一个优秀的应用来源，它相对较少的文献是平易近人的，而不是高度技术性的。要考虑的主题包括价值公理，这一领域的目标是通过一系列属性来描述价值，并确定已知价值满足某些属性的游戏类别-这些属性通常由公平或议价能力的直觉概念引起。价值的应用是另一个主题，涉及应用，如机场着陆，旅行推销员和其他分配策略。学生的其他课题还包括对多选项投票权的研究。指数、矩阵简单对策和单纯形对策的复杂性计算的一个核仁。有充足的电脑和图书馆设施供学生使用。每个学生将根据完成的研究写一份最终报告。然后准备提交期刊，在专业会议上展示或用作荣誉论文的基础。将分发一份通讯，以保持与会者和顾问之间的联系。