A wide variety of mechanisms, such as alert triggers and auditing routines, have been developed to notify administrators about types of suspicious activities in the daily use of large databases of personal and sensitive information. However, such mechanisms are limited in that: 1) the volume of such alerts is often substantially greater than the auditing capabilities of budget-constrained organizations and 2) strategic attackers may disguise their actions or carefully choose which records they touch, thus evading auditing routines. To address these problems, we introduce a novel approach to database auditing that explicitly accounts for adversarial behavior by 1) prioritizing the order in which types of alerts are investigated and 2) providing an upper bound on how much budget to allocate for auditing each alert type. We model the interaction between a database auditor and potential attackers as a Stackelberg game in which the auditor chooses an auditing policy and attackers choose which records in a database to target. We further introduce an efficient approach that combines linear programming, column generation, and heuristic search to derive an auditing policy, in the form of a mixed strategy. We assess the performance of the policy selection method using a publicly available credit card application dataset, the results of which indicate that our method produces high-quality database audit policies, significantly outperforming baselines that are not based in a game theoretic framing.