Publication Date

2020

Document Type

Dissertation/Thesis

First Advisor

Deng, Sien

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

Abstract

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.

Extent

151 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

Download

Share

COinS