Overlapping generations are extracting a natural resource over an infinite future. We examine fair allocation of resource and compensations among generations. Fairness is defined by core lower bounds and solidarity upper bounds. The core lower bounds require that all coalition of generations obtains at least what it could achieve by itself. The solidarity upper bounds require that no coalition of generations enjoy a higher welfare that it would achieve nobody else extract the resource. We show that, upon existence, the allocation that satisfies the two fairness criteria is unique. It assigns to each generation its marginal contribution to the preceding generation. We then characterize its dynamics.