This paper provides sufficient conditions for existence of Markovian equilibrium in models with non-paternalistic altruism extending to one generation ahead. When utility is non-separable, we show that each equilibrium savings policy correspondence is increasing everywhere and single-valued, except perhaps on a countable number of points. It is also upper hemi-continuous where it is single valued. When utility is separable, we show that the equilibrium is unique, increasing, and continuous, and we provide an algorithm converging uniformly to the equilibrium.
Morand, Olivier F. and Reffett, Kevin L., "On the Existence and Characterization of Markovian Equilibrium in Models with Simple Non-Paternalistic Altruism" (2002). Economics Working Papers. 200206.