This paper is concerned with the issue: Does there exist a social security program which can be maintained period after period? To address this issue, the paper considers dynamic allocation in an altruistic overlapping generations economy. The altruism is intergenerational, nonpaternalistic, and two-sided. Lt is assumed that generations coexisting in the same period agree on a social welfare Function, which evaluates the consumption of various generations, and play a game against those living in different periods. A perfect equilibrium of this game is shown to exist and its properties are examined. (C) 1997 Academic Press.