Publication Date


Document Type


First Advisor

Deng, Sien

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences


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.


151 pages




Northern Illinois University

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