Unique Games and Games Based on Groups

Rupert H. Levene; Vern I. Paulsen

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arXiv · 2506.18644

Unique Games and Games Based on Groups

Rupert H. Levene·Vern I. Paulsen

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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.

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Rupert H. Levene, Vern I. Paulsen. 2025-06-23. Unique Games and Games Based on Groups. https://arxiv.org/abs/2506.18644

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