Mathematical Sciences: Cooperative Game Theory

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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.