A Dynamic Model of Altruistically-Motivated Transfers

This paper studies an environment with two infinitely-lived altruistic agents whose only sources of income are a risk-free return on savings and voluntary transfers from the other player. We study the Markov-perfect equilibrium of a continuous-game (differential game). On the technical side, we address shortcomings of Markov-perfect equilibrium and standard control theory by introducing a refinement we term limit-consistency, in which we study a sequence of discrete-time games converging to the differential game. The concept allows us to deal with discontinuities in policies and regions where measure-valued controls are used. We find that as in the well-known two-period model of altruism savings decisions are not Pareto-efficient. Agents do not want to induce the other person to overconsume on their expense, a phenomenon known as the Samaritan's dilemma (Buchanan, 1975). Our model exhibits what we call the dynamic Samaritan's dilemma: distortions are present long before the "last" period. A stark difference to the two-period model is that the donor's savings decision is also distorted. Transfers only flow when the recipient's borrowing constraint binds, which is in line with stylized facts from the empirical literature.