Mathematical Sciences: Cooperative Game Theory

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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.