In this paper, we navigate the intricate domain of reviewer rewards in open-access academic publishing, leveraging the precision of mathematics and the strategic acumen of game theory. We conceptualize the prevailing voucher-based reviewer reward system as a two-player game, subsequently identifying potential shortcomings that may incline reviewers towards binary decisions. To address this issue, we propose and mathematically formalize an alternative reward system with the objective of mitigating this bias and promoting more comprehensive reviews. We engage in a detailed investigation of the properties and outcomes of both systems, employing rigorous game-theoretical analysis and deep reinforcement learning simulations. Our results underscore a noteworthy divergence between the two systems, with our proposed system demonstrating a more balanced decision distribution and enhanced stability. This research not only augments the mathematical understanding of reviewer reward systems, but it also provides valuable insights for the formulation of policies within journal review system. Our contribution to the mathematical community lies in providing a game-theoretical perspective to a real-world problem and in the application of deep reinforcement learning to simulate and understand this complex system.

翻译：本文以数学的严谨性和博弈论的策略智慧，探索开放获取学术出版中审稿人奖励这一复杂领域。我们将当前基于代金券的审稿人奖励系统概念化为双人博弈，随后识别出可能促使审稿人倾向于二元决策的潜在缺陷。为解决该问题，我们提出并数学形式化了一种替代性奖励系统，旨在减轻这种偏差并促进更全面的审稿。我们通过严格的博弈论分析和深度强化学习仿真，对两种系统的属性及结果进行了详细研究。结果揭示了两种系统间显著的分歧，我们提出的系统展现出更均衡的决策分布和更强的稳定性。本研究不仅加深了对审稿人奖励系统的数学理解，也为期刊审稿系统的政策制定提供了宝贵见解。我们为数学界的贡献在于：为现实问题提供博弈论视角，并应用深度强化学习来模拟和理解这一复杂系统。