Flexibility and Uncertainty

Abstract

The preserving of flexibility when faced with uncertainty is a neglected aspect of behaviour under risk. Yet it is an important factor in decisions to hold liquid assets or delay irreversible investment. This paper formalizes the notion of flexibility in a sequential decision context, and relates its value to the amount of information an agent expects to receive. A rudimentary money demand model is developed embodying these ideas, and the history of flexibility as an economic concept is traced. Choices are frequently made between alternatives that imply different degrees of future commitment-between a short-term investment that leaves future options open, for example, and a long-term one that, by its very nature, forecloses those options. The relative attractiveness of the two depends on their probability distributions of payoffs over time. A basic consideration in this choice is the recognition that beliefs about the risks governing these payoffs may change. Current doubts may be partially resolved in the near future. This prospect decreases the attractiveness of the longer term commitment, in that one is able to respond less fully to new information, and, even if it does not directly affect the risks associated with shorter term choices, enhances their appeal. This paper formalizes the above remarks by establishing connections between the following two (partial) orderings: The first is an ordering based on variability of beliefs. One set of beliefs is more variable than another if more final risk is resolved at an intermediate stage. The more one expects to learn by an intermediate period, relative to what one knows today, the more variation one is anticipating in beliefs about the final outcome. The second is an ordering of current actions, or positions, based on flexibility. One position is more flexible than another if it leaves available a larger set of future positions at any given level of cost. These two orderings are incorporated in a simple sequential decision model to suggest the following behavioural principle: The more variable are a decision-maker's beliefs, the more flexible is the position he will choose. This principle potentially applies whenever (i) there will be opportunities to act after further information is received, and (ii) current actions influence either the attractiveness or availability of different future actions.