Eye movement data has been extensively utilized by researchers interested in studying decision-making within the strategic setting of economic games. In this paper, we demonstrate both a deep learning and traditional machine learning classification method which are able to accurately identify a given participant's decision strategy before they commit to an action while playing games. Our approach focuses on creating scanpath images that best capture the dynamics of a participant's gaze behaviour during a given game in a way that is meaningful to the machine learning models. Our results demonstrate a higher classification accuracy compared to traditional methods of analysis applied to the same economic game environments by as much as 18 percentage points. In a broader context, we aim to illustrate the potential for eye-tracking data to create information asymmetries in strategic environments in favour of those who collect and process the data. These information asymmetries could become especially relevant as eye-tracking is expected to become more widespread in user applications, with the seemingly imminent mass adoption of virtual reality systems, and the development of devices with the ability to record eye movement outside of a laboratory setting.