Equilibrium resource management with altruistic overlapping generations

We imbed a classic fishery model, where the optimal policy follows a Most Rapid Approach Path to a steady state, into an overlapping generations setting. The current generation discounts future generations׳ utility flows at a rate possibly different from the pure rate of time preference used to discount their own utility flows. The resulting model has non-constant discount rates, leading to time inconsistency. The unique Markov Perfect equilibrium to this model has a striking feature: provided that the current generation has some concern for the not-yet born, the equilibrium policy does not depend on the degree of that concern.