This article delves into the complex world of quantum games in multi-agent settings, proposing a model wherein agents utilize gradient-based strategies to optimize local rewards. A learning model is introduced to focus on the learning efficacy of agents in various games and the impact of quantum circuit noise on the performance of the algorithm. The research uncovers a non-trivial relationship between quantum circuit noise and algorithm performance. While generally an increase in quantum noise leads to performance decline, we show that low noise can unexpectedly enhance performance in games with large numbers of agents under some specific circumstances. This insight not only bears theoretical interest, but also might have practical implications given the inherent limitations of contemporary noisy intermediate-scale quantum (NISQ) computers. The results presented in this paper offer new perspectives on quantum games and enrich our understanding of the interplay between multi-agent learning and quantum computation. Both challenges and opportunities are highlighted, suggesting promising directions for future research in the intersection of quantum computing, game theory and reinforcement learning.
Keywords: game theory; quantum computing; reinforcement learning.