Sharing individual-level pandemic data is essential for accelerating the understanding of a disease. For example, COVID-19 data have been widely collected to support public health surveillance and research. In the United States, these data are typically de-identified before publication to protect the privacy of the corresponding individuals. However, current data publishing approaches for this type of data, such as those adopted by the U.S. Centers for Disease Control and Prevention (CDC), have not flexed over time to account for the dynamic nature of infection rates. Thus, the policies generated by these strategies have the potential to both raise privacy risks or overprotect the data and impair the data utility (or usability). To optimize the tradeoff between privacy risk and data utility, we introduce a game theoretic model that adaptively generates policies for the publication of individual-level COVID-19 data according to infection dynamics. We model the data publishing process as a two-player Stackelberg game between a data publisher and a data recipient and then search for the best strategy for the publisher. In this game, we consider 1) average performance of predicting future case counts; and 2) mutual information between the original data and the released data. We use COVID-19 case data from Vanderbilt University Medical Center from March 2020 to December 2021 to demonstrate the effectiveness of the new model. The results indicate that the game theoretic model outperforms all state-of-the-art baseline approaches, including those adopted by CDC, while maintaining low privacy risk. We further perform an extensive sensitivity analyses to show that our findings are robust to order-of-magnitude parameter fluctuations.