In this paper, we introduce "Integrity Games" (https://integgame.eu/)--a freely available, gamified online teaching tool on academic integrity. In addition, we present results from a randomized controlled experiment measuring the learning outcomes from playing "Integrity Games." "Integrity Games" engages students in reflections on realistic and relevant academic integrity issues that lie in the grey zone between good practice and misconduct. Thereby, it aims to (1) motivate students to learn more about academic integrity, (2) increase their awareness of the grey-zone issues, and (3) increase their awareness of misconduct. To achieve these aims, the tool presents four gamified cases that lead students through an engaging narrative. The experiment to measure learning outcomes was conducted in three European countries, and included N = 257 participants from across natural science, social science and the humanities. We show that the participants enjoyed playing "Integrity Games," and that it increased their sensitivity to grey-zone issues and misconduct. However, the increases identified were similar to those achieved by the participants in the control group reading a non-gamified text. We end by discussing the value of gamification in online academic integrity training in light of these results.