Airports are attractive targets for terrorists, as they are designed to accommodate and process large amounts of people, resulting in a high concentration of potential victims. A popular method to mitigate the risk of terrorist attacks is through security patrols, but resources are often limited. Game theory is commonly used as a methodology to find optimal patrol routes for security agents such that security risks are minimized. However, game-theoretic models suffer from payoff uncertainty and often rely solely on expert assessment to estimate game payoffs. Experts cannot incorporate all aspects of a terrorist attack in their assessment. For instance, attacker behavior, which contributes to the game payoff rewards, is hard to estimate precisely. To address this shortcoming, we proposed a novel empirical game theory approach in which payoffs are estimated using agent-based modeling. Using this approach, we simulated different attacker and defender strategies in an agent-based model to estimate game-theoretic payoffs, while a security game was used to find optimal security patrols. We performed a case study at a regional airport, and show that the optimal security patrol is non-deterministic and gives special emphasis to high-impact areas, such as the security checkpoint. The found security patrol routes are an improvement over previously found security strategies of the same case study.