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Abstract Repeated small dynamic networks are integral to studies in evolutionary game theory, where networked public goods games offer novel insights into human behaviours. Building on these findings, it is necessary to develop a statistical model that effectively captures dependencies across multiple small dynamic networks. While separable temporal exponential-family random graph models (STERGMs) have demonstrated success in modelling a large single dynamic network, their application to multiple small dynamic networks with less than 10 actors, remains unexplored. In this study, we extend the STERGM framework to accommodate multiple small dynamic networks, offering an approach to analysing such systems. Taking advantage of the small network sizes, our proposed approach improves accuracy in statistical inference through direct computation, unlike conventional approaches that rely on Markov Chain Monte Carlo methods. We demonstrate the validity of this framework through the analysis of a networked public goods experiment into individual decision-making about cooperation and defection. The resulting statistical inference uncovers insights into the dynamics of social dilemmas, showcasing the effectiveness, and robustness of this modelling and approach.