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Nov 27, 2024
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MATH 486 - Game Theory (3 units)
Extensive form games; Nash, perfect equilibrium; matrix/bimatrix games; minmax theorem; TU/NTU solutions; marriage, college admissions, and housewrapping games; core; Shapley value; power indices.
Recommended Preparation: MATH 330.
Units of Lecture: 3
Student Learning Outcomes:
Upon completion of this course:
1. Students will be able to model real world problems from the social and biological sciences as cooperative or noncooperative games, and to choose appropriate solution concepts to analyze them.
2. Students will be able to solve strategic form matrix and bimatrix games for both minimax solution and Nash equilibria, use backward induction for finding perfect Nash equilibria in perfect-information extensive form games, find the TU solution for bimatrix games, run the Deferred Acceptance Procedure and Top Trading Cycle algorithms for ordinal preference games, and solve for the core and Shapley Value for n-player TU games.
3. Students will be able to demonstrate an understanding of the underlying theory behind the models, including the minimax theorem, Shapley-Bondareva theorem, Nash’s theorem, the Folk Theorem for repeated games, and the relationship between some of these and linear programming.
4. Students will be able to demonstrate an understanding of some of the subtleties of game theoretic modelling, such as the role and modelling of information, the advantages and disadvantages of modelling using strategic vs extensive form, the difference between cooperative and noncooperative games, and the implications of the “TU-assumption” for cooperative games.
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