Recent years have seen an explosion in the diversity of partner control mechanisms hypothesised to stabilise cooperative behaviour among unrelated individuals. Game theory suggests numerous strategies, each with specific decision rules that allow cooperators to control a non-contributing partner. This diversity of hypothetical strategies seems likely to reflect diversity in the types of intraspecific cooperation and interspecific mutualism that exist in nature. It is therefore important to provide a framework that explains similarities and differences between the various hypothetical strategies and that predicts how key parameters that describe the natural history of natural systems favour different control mechanisms. We develop a novel unifying framework for pairwise interactions between unrelated individuals, in which we link specific control mechanisms to specific game structures. The latter are defined by unique combinations of the states of five parameters that describe investment, aspects of the payoff matrix, the number of interactions and partner choice. We find that specific control mechanisms potentially have utility in a limited number of game structures; conversely, each game structure may typically offer a few competing control mechanisms. Our framework offers theoreticians specific problems that await mathematical exploration, while at the same time offering empiricists guidelines for evaluating the game structure and corresponding control mechanisms in their systems.