A dynamic model of altruistically-motivated transfers

This paper studies a dynamic Markovian game of two infinitely-lived altruistic agents without commitment. Players can save, consume and give transfers to each other. We identify a continuum of equilibria in which imperfectly-altruistic agents act as if they were a perfectly-altruistic dynasty which is less patient than the two agents themselves. In such equilibria, the poor agent receives transfers until both effectively pool their wealth and tragedy-of-the-commons-type inefficiencies occur. We also provide a sharp characterization of strategic interactions in consumption and transfer behavior. This provides new insights relative to existing two-period models. It allows us to differentiate between the Samaritan's dilemma - e.g. a child runs down its assets inefficiently fast in anticipation of transfers - and what we refer to as the Prodigal-Son dilemma - e.g. parents do not leave an early bequest, anticipating a child's profligate behavior.