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.
@article{arxiv.2506.18644,
title = {Unique Games and Games Based on Groups},
author = {Rupert H. Levene and Vern I. Paulsen},
journal= {arXiv preprint arXiv:2506.18644},
year = {2025}
}