Mathematical Sciences: Cooperative Game Theory

本科生研究体验奖将资助一个由六名学生组成的团队。他们将在首席调查员的监督下工作，并由数学系的几名教员协助。该计划将运行八周，集中讨论合作博弈论的问题。一个训练有素的数学学生只需很短的准备时间就能理解基本概念。在学生到达现场之前，将布置一些初步阅读材料。将向学生介绍几个有充分潜力发展健全研究项目的领域。它们包括价值公理，价值在现实生活成本分配中的应用，一个对策的核仁值计算、多选项投票权指数和拟阵简单对策。该学院将为该项目提供充足的计算支持。将努力让学生参加夏季在俄亥俄州立大学举行的年度博弈论国际会议的一部分。预计还将参观NSF中心，附近罗格斯大学的离散和应用数学高级研究院。最终报告预计将在该计划结束时发布。最有希望的将在必要时进行修订，以提交期刊。

A team of six students will be supported by this Research Experiences for Undergraduates award. They will work under the supervision of the principal investigator, assisted by several faculty members of the mathematics department. The program will run for eight weeks concentrating on problems of cooperative game theory. A well-trained mathematics student can understand the basic concepts with only a short period of preparation. Some preliminary reading will be assigned before the students arrive at the site. Several areas in which there is ample potential for the development of sound research projects will be presented to the students. They include value axiomatics, application of values to real life cost allocations, value computation of the nucleolus of a game and multi-alternative voting power indices and matroidal simple games. Ample computational support for the project will be provided by the college. Efforts will made to have students attend part of the annual international conference on game theory held at Ohio State University during the summer. Visits to the NSF center, the Advanced Research Institute for Discrete and Applied Mathematics at nearby Rutgers University are also expected. Final reports are expected at the end of the program. The most promising will be revised where necessary for journal submission.