We consider an iterated model of agents playing a two-player game on a graph. The agents change their strategies as the game progresses based on anticipated payoffs. Using only the time series of the agents’ strategies, we determine the pairwise mutual information between all agents in the graph, and use these values as a predictors of the graph’s topology. From this, we assess the influence of various model parameters on the effectiveness of mutual information at recovering the actual causal structure. It is found that the degree to which the functional connectivity reflects the actual causal structure of the graph strongly depends on which game is being played and how the agents are changing their strategies. Further, there is evidence that the edge density of the graph may also have some impact on the accuracy of the inferred network. This approach allows us to better connect the dynamics of the systems under study with the difference in their functional and actual connectivity, and has broad implications for the interpretation and application of information-based network inference. The methods and analyses described can be generalized and applied to other types of network models.