Saving for an uncertain future.

T he units that are subject to selection pressure in evolutionary biology are ‘‘strategies,’’ which are conditional actions (for example, do P if X occurs; otherwise do Q). In contrast, the units in economics (they are called ‘‘people’’) select strategies from available menus so as to further their projects and purposes. If evolutionary dynamics involves mindless competition among strategies, economic dynamics involves the ways in which people revise their beliefs (and so, their strategies) in light of what they know and what they observe. However, even though the two are different, a remarkable body of work that began with a publication by John Nash (1) has shown that evolutionary and economic dynamics are embedded in a common analytical framework, namely, multiagent decision theory, commonly known as the theory of games (2, 3). A necessary preliminary in any game theoretic exercise is the analysis of a decision unit (DU) that inhabits an environment in which there are no other DUs. The problem before the analyst is to predict what the DU would choose under a given set of circumstances. The common tool to use there is optimization theory (4, 5). A classic problem is to analyze how the DU trades off present against future consumptions, which is the concern of Arrow and Levin (6) in this issue of PNAS. For example, squirrels collect food for winter. Because that requires energy they face tradeoffs between current and future consumption. The question arises: what collection size would maximize inclusive fitness? Similarly, people save a portion of their wealth, not only for their own future consumption but also for their offspring and, by recursion, the offspring of their offspring, the offspring of their offspring’s offspring, and so on, down the generations. If the DU’s objective is to maximize the sum of the expected present values of his dynasty’s utilities and if a person’s utility is an increasing function of his consumption level, how much of his wealth should the DU consume? We assume that the DU has inherited a certain amount of wealth from his parents. Consider first the case where he faces no future uncertainty. Even on intuitive grounds it is clear that the DU’s optimal consumption-to-wealth ratio would depend on four factors: (i) the numbers of his descendents, (ii) the extent to which people prefer early consumption to delayed consumption because of an impatience to consume, (iii) the functional dependence of utility on consumption, and (iv) the rate of return on saving (e.g., market interest rates). The precise way in which those four factors play their part has been known for a long time (7–10). From that work it can be shown, for example, that if the rate of return on saving was suddenly to increase (e.g., because of a technological innovation), or if the rate of growth in the size of his dynasty was suddenly to increase (e.g., owing to an