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.

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