In this paper we study the optimal conversion policy set by a society composed of a sequence of non-overlapping imperfectly altruistic generations. We show that society can be equivalently viewed as a sequence of hyperbolic discounting agents. Under uncertainty about future pay-offs we determine, as solution to an intergenerational non-cooperative dynamic game, the optimal timing of irreversible conversion. We show that under both naive and sophisticated beliefs about future time-inconsistency, the option value attached to the conversion decision is eroded and earlier conversion occurs. This determines a drastic bias toward the current generation gratification, which affects the intergenerational allocation of benefits and costs from deforestation.