Game characterizations and lower cones in the Weihrauch degrees

Nobrega, Hugo; Pauly, Arno

doi:10.23638/lmcs-15(3:11)2019

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Connections To Proof Theory1

Wadge Games1

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Cited by 3 publications

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“…Open Question 18 (Nobrega & P. [35]). What is the Weihrauch degree of obtaining a point of discontinuity of a function from a Player I winning strategy in the Wadge game for it?…”

Section: Connections To Proof Theorymentioning

confidence: 99%

An update on Weihrauch complexity, and some open questions

Pauly¹

2020

Preprint

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“…Open Question 18 (Nobrega & P. [35]). What is the Weihrauch degree of obtaining a point of discontinuity of a function from a Player I winning strategy in the Wadge game for it?…”

Section: Connections To Proof Theorymentioning

confidence: 99%

An update on Weihrauch complexity, and some open questions

Pauly¹

2020

Preprint

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“…A Wadge game is defined as a two-player game with perfect information, where player one selects a natural number and player two responds by either choosing a natural number or passing [114]. For generalised Wadge games, when the lower cone forms a transparent cylinder, they characterise a lower cone within the Weihrauch degrees.…”

Section: Wadge Gamesmentioning

confidence: 99%

Computable Analysis and Game Theory: From Foundations to Applications

Crook

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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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Sequential Discontinuity and First-Order Problems

Pauly,

Soldà

2024

Twenty Years of Theoretical and Practical Synergies

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Game characterizations and lower cones in the Weihrauch degrees

Cited by 3 publications

References 0 publications

An update on Weihrauch complexity, and some open questions

An update on Weihrauch complexity, and some open questions

Computable Analysis and Game Theory: From Foundations to Applications

Sequential Discontinuity and First-Order Problems

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