Multi-objective optimization problems and game theory problems have a wide array of applications and because of this there are different types of solutions available. This dissertation explores two areas of optimization and a solution type for each. First, substantial efficiency (SE) as a type of solution to multi-objective optimization problems that extends proper efficiency. Secondly, strong Nash equilibria (SNE) as a type of solution to game theoretic problems that extends Nash equilibria. Substantial efficiency is demonstrated to be a superior solution to the more rudimentary notion of proper efficiency in solving some multi-objective financial market and economic problems. Using this as motivation, a careful examination is given for SE solutions in linear multi-objective optimization problems. Examples are given showing that SE solutions are non-trivial and may not always exist. A method for testing for substantial efficiency is provided. Existence of a SE solution can also be guaranteed in a specific context. Both a topological inspection and recession analysis are provided for the set of SE solutions. A situation where a SNE can be guaranteed is provided. An algorithm is also provided that when convergent will be to a SNE.
|Commitee:||Sirotkin, Gleb, Bello-Cruz, Yunier, Krislock, Nathan|
|School:||Northern Illinois University|
|School Location:||United States -- Illinois|
|Source:||DAI-A 82/3(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Applied Mathematics, Finance|
|Keywords:||Algorithm, Financial market problems, Game theory, Multi-objective optimization, Recession analysis, Variational analysis|
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