Tragedy of the Commons and Prisonner's Dilemma

The aim of this note is about the formalization of the problem of open- access natural resourses by the prisonner's dilemma game. The extreme simplification of the metaphor between prisonner's dilemma and the "tragedy of the commons" leads to imagine only two strategies ("cooperation"/"defection" for example), where there is generally a continuum of possible strategies. We are going to demonstrate that what looks like a strong rationality in the case of one alternative (the existence of an equilbrium in dominant strategies), can only subsist in the continuous case under unrealistic hypotheses. Thus, the situation described by the prisonner's dilemma only squares with very particular andnot much plausible yield functions of the resourse.