Mathematical Sciences: Cooperative Game Theory

六名从事合作博弈论问题数学研究的本科生将获得这一本科生研究经验奖的资助。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，它提供了优秀的应用于现实世界问题的来源，其相对较少的文献是平易近人的，不是高度技术性的。要考虑的主题包括价值公理，该领域的目标是通过一组性质来刻画价值，并确定众所周知的值满足某些性质的博弈类别--这些性质通常是由公平或讨价还价能力的直觉概念推动的。价值的应用是另一个主题，它涉及诸如机场着陆、旅行推销员和其他分配策略的应用。为学生提供的其他课程还包括研究多种可供选择的投票权。指数、拟阵简单对策和对策核仁单纯形计算的复杂性。学校为学生提供了充足的电脑和图书馆设施。每个学生都要根据已完成的研究写一份期末报告。然后，它将被准备用于期刊提交，在专业会议上发表，或用作荣誉论文的基础。将分发一份时事通讯，以保持参与者和顾问之间的联系。

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.