Subgame perfect manipulation of children by overlapping generations of agents with two-sided altruism and endogenous fertility

In this paper we consider an overlapping generations model with endogenous fertility and two-sided altruism and show the limitations of applying commonly used open loop Nash equilibrium in characterizing equilibrium transfers from parents to children in the form of bequest, and transfers from children to parents as voluntary old-age support. Since in our model children are concerned with parents' old-age consumption, agents have incentives to save less for old age and to have more children so as to strategically induce their children to transfer more old-age support. We formulate such strategic behavior within a sequential multi-stage game and use the notion of subgame perfect equilibrium to study the consequences of such strategic manipulations on private intergenerational transfers, fertility and savings decisions, and on Pareto optimality of equilibrium allocation. We then examine the role of social security to correct such strategic distortions.