Two strains of microorganisms that both use sugar as energy resource, but which may choose between two different pathways of ATP production, are studied from a game-theory point of view. We consider these pathways as distinct strategies to which we assign payoffs that are proportional to the expected steady-state number of individuals sustainable on the basis of these strategies. In a certain parameter range, we find that the payoffs fulfil the conditions for the prisoner's dilemma. Therefore, cooperative behaviour is unlikely to occur, unless additional factors intervene. In fact, the yeast Saccharomyces cerevisiae uses a competitive strategy by fermenting sugars even under aerobic conditions, thus wasting its own resource. The simple quantifiable structure of the model should enable access to an experimentally determined payoff matrix.