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Computable Analysis and Game Theory: From Foundations to Applications / TONICHA CROOK
Swansea University Author: TONICHA CROOK
DOI (Published version): 10.23889/SUThesis.67150
Abstract
This body of research showcases several facets of the intersection between computer science and game theory. On the foundational side, we explore the obstructions to the computability of Nash equilibria in the setting of computable analysis. In particular, we study the Weihrauch degree of the proble...
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Swansea University, Wales, UK
2024
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| Institution: | Swansea University |
| Degree level: | Doctoral |
| Degree name: | Ph.D |
| Supervisor: | Pauly, A |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa67150 |
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| Abstract: |
This body of research showcases several facets of the intersection between computer science and game theory. On the foundational side, we explore the obstructions to the computability of Nash equilibria in the setting of computable analysis. In particular, we study the Weihrauch degree of the problem of finding a Nash equilibrium for a multiplayer game in normal form. We conclude that the Weihrauch degree Nash for multiplayer games lies between AoUC∗[0,1] and AoUC⋄[0,1] (Theorem 5.3). As a slight detour, we also explore the demarcation between computable and non-computable computational problems pertaining to the verification of machine learning. We demonstrate that many verification questions are computable without the need to specify a machine learning framework (Section 7.2). As well as looking into the theory of learners, robustness and sparisty of training data. On the application side, we study the use of Hypergames in Cybersecurity. We look into cybersecurity AND/OR attack graphs and how we could turn them into a hypergame (8.1). Hyper Nash equilibria is not an ideal solution for these games, however, we propose a regret-minimisation based solution concept. In Section 8.2, we survey the area of Hypergames and their connection to cybersecurity, showing that even if there is a small overlap, the reach is limited. We suggest new research directions such as adaptive games, generalisation and transferability (Section 8.3). |
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| Item Description: |
A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information. |
| Keywords: |
Game Theory, Computable Analysis, Hypergames, Cybersecurity, Machine Learning |
| College: |
Faculty of Science and Engineering |
| Funders: |
AIMLAC CDT |