  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.
