Learned Convention and Subgame Perfect Equilibrium in an Overlapping Generations Model with Two-Sided Altruism

This paper considers an overlapping generations model of endogenous fertility, savings and intergenerational transfers. While subgame perfect equilibrium notion is more relevent to analyze individual incentives in this set-up, due to computational complexity and lack of an appropriate equilibrium selection theory, most previous studies employed the open-loop Nash equilibrium. This paper introduces a unifying notion of equilibrium in which behaviors are guided by best responses, given a fixed convention and bounded rational expectations about other agents' behaviors. The paper provides an evolutionary process for convention based on learning. When the process converges, the limiting equilibrium is shown to be a subgame perfect equilibrium. This procedure provides a rationale for equilibrium selection and a method to compute subgame perfect equilibrium locally. Using this procedure, the paper studies the effect of a social security program on local subgame perfect equilibrium level of intergenerational transfers, fertility rate and welfare of a representative agent