BTW, genes are an example of an agent that arguably has a reversed time-discounting function. Genes "care" about their eventual, "equilibrium" level in the population. This is a tricky example, though, because genes only "care" about the future retrospectively; the more-numerous genes that "didn't care", disappeared. But the body as a whole can be seen as maximizing the proportion of the population that will contain its genes in the distant future. (Believing this is relevant to theories of aging that attempt to explain the Gompertz curve.)