Unique Games and Games Based on Groups

We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that generalize XOR games, and show that when the group is the cyclic group of order 3, then these games correspond to a 3-labelling problem for directed graphs.

Publication Details

Journal
ArXiv.org
Published
2025-06-23
Primary Topic
Computability, Logic, AI Algorithms
Type
article
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article

Unique Games and Games Based on Groups

ArXiv.org
Computability, Logic, AI Algorithms
article

Unique Games and Games Based on Groups

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Abstract

We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that generalize XOR games, and show that when the group is the cyclic group of order 3, then these games correspond to a 3-labelling problem for directed graphs.

ArXiv.org
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Openalex Percentile: Top 48%
Computability, Logic, AI Algorithms
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Unique Games and Games Based on Groups · ArXiv.org (2025) | TGRS Research Map | TGRS