GAM, combining games and agent-based models, shows potential for investigating complex social phenomena. Games offer engaging environments generating insights into social dynamics, perceptions, and behaviours, while agent-based models support the analysis of complexity. Games and agent-based models share the important ability both to input and output qualitative and quantitative data. Currently, there is no overview of GAM approaches. In a systematic literature review, we identified six research design types in empirical studies to date. The functional range of these design types is wide, with diverse application domains involving analogue, digital, and hybrid games. This makes GAM a highly versatile approach, appealing to researchers in both natural and social sciences, along with the gaming community itself. To consolidate the GAM field, we propose recording the design and implementation of studies that combine games and agent-based models by using a dedicated documentation scheme.