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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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Published: Swansea University, Wales, UK 2024
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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first_indexed 2024-07-18T11:44:00Z
last_indexed 2024-07-18T11:44:00Z
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spelling v2 67150 2024-07-18 Computable Analysis and Game Theory: From Foundations to Applications 48d905c96d1bad1a0081a07096a6f911 TONICHA CROOK TONICHA CROOK true false 2024-07-18 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). E-Thesis Swansea University, Wales, UK Game Theory, Computable Analysis, Hypergames, Cybersecurity, Machine Learning 3 7 2024 2024-07-03 10.23889/SUThesis.67150 A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information. COLLEGE NANME COLLEGE CODE Swansea University Pauly, A Doctoral Ph.D AIMLAC CDT AIMLAC CDT 2024-07-18T12:48:18.3287550 2024-07-18T12:37:35.2097171 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science TONICHA CROOK 1 67150__30927__8a941012a9b14641bf638f8dc93992a4.pdf 2024_Crook_T.final.67150.pdf 2024-07-18T12:42:51.2892619 Output 2159333 application/pdf E-Thesis – open access true Copyright: The Author, Tonicha Crook, 2024 true eng
title Computable Analysis and Game Theory: From Foundations to Applications
spellingShingle Computable Analysis and Game Theory: From Foundations to Applications
TONICHA CROOK
title_short Computable Analysis and Game Theory: From Foundations to Applications
title_full Computable Analysis and Game Theory: From Foundations to Applications
title_fullStr Computable Analysis and Game Theory: From Foundations to Applications
title_full_unstemmed Computable Analysis and Game Theory: From Foundations to Applications
title_sort Computable Analysis and Game Theory: From Foundations to Applications
author_id_str_mv 48d905c96d1bad1a0081a07096a6f911
author_id_fullname_str_mv 48d905c96d1bad1a0081a07096a6f911_***_TONICHA CROOK
author TONICHA CROOK
author2 TONICHA CROOK
format E-Thesis
publishDate 2024
institution Swansea University
doi_str_mv 10.23889/SUThesis.67150
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description 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).
published_date 2024-07-03T12:48:17Z
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score 11.017776

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