Purpose - The purpose of this paper is to investigate the state of the art in static and dynamic games (or inter-firm relationships). This research area has changed significantly over the last 25 years through the development of phenomena such as the supply chain and the progressive overcoming of monopolistic and oligopolistic frameworks. By exploring the state of the art in inter-firm relationships, this paper aims to identify the most suitable research methods to be used by future research in this domain and to highlight the major areas under investigation. Design/methodology/approach - This research adopts both qualitative and quantitative approaches. The qualitative approach describes the technical differences between static and dynamic methods and gives evidence of their appropriateness when applied to a game. Quantitative analysis transforms some of the information extracted from the qualitative analysis into categorical variables in order to obtain an indication of the major issues still to be addressed. Findings - The resulting findings identify the extent of the use of static and dynamic modelling in previous research and how their use has changed over time, what resolution methods need to be applied when investigating inter-firm relationship, what features influence this decision and what research areas still remain unexplored. Originality/value - The existing literature on the modelling of static and dynamic games lacks an exhaustive review. Several contributions investigate the literature on inter-firms relationships and review numerous issues, but focus only on static or dynamic modelling. This paper fills this gap by reviewing a number of theoretical papers. © Emerald Group Publishing Limited.