In this study we analyze a recent controversy within the biomedical world, concerning the evaluation of safety of certain vaccines. This specific struggle took place among experts: the Danish epidemiologist Peter Gotzsche on one side and a respected scientific institution, the Cochrane, on the other. However, given its relevance, the consequences of such a conflict invest a much larger spectrum of actors, last but not least the public itself. Our work is aimed at dissecting a specific aspect happening in this complex scenario: strategy. In other words, we want to highlight the value and the impact of strategic decisions when complex issues, as those analyzed, are at stake. In order to address this we have decided to adopt a game-theoretic approach. Our work will be structured as it follows. First, we will introduce the controversy and the two main actors: Peter Gotzsche and the Cochrane. Second, we will explain why this controversy is important and its value beyond its academic relevance. Third, we will frame the controversy as a game and will provide several models representing different situations, also furnishing an analysis of these distinct scenarios. In the end we will argue why such game-theoretic approach can be useful in dissecting this type of issues.