Author ORCID Identifier

https://orcid.org/0000-0001-9783-4957

Date Available

1-1-2025

Year of Publication

2025

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Engineering

Department/School/Program

Computer Science

Advisor

Dr. Judy Goldsmith

Abstract

Tiered coalition formation games (TCFGs) have been proposed for modeling the ordering of power in intransitive structures. Furthering our understanding of the usefulness of this concept requires a close examination of this game and its variants, as well as the delineation between stability concepts and methods of finding stable outcomes. Derived from a simulation of the performance of characters in the games Pokémon Red and Blue Versions, we present an approximation of its power structure found via machine learning. We compare our findings to the community consensus ranking presented on a fan-run website, and further comment on the stability of that consensus ranking. Elsewhere, we conduct a theoretical investigation of TCFGs and especially the tier-restricted variant, k-tiered coalition formation games (k-TCFGs). We analyze the complexity of finding a Nash stable outcome and seek answers to whether there is always a core stable outcome.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2024.541

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