Global convergence in an overlapping generations model with two-sided altruism

We study the evolutionary dynamics of an overlapping generations economy with two-sided altruism, where each generation cares about the utilities of its parental generation, its offspring, and its own. We assume that the young and old generations in each period act jointly, as a central planner. We then introduce the concepts of a two-sided altruistic path and a two-sided altruistic stationary path. Then, we go on to prove that the former always converges to the latter, in the two-sided altruistic model. This stationary capital level is higher than the steady-state level in the model with a constant discount factor.