Decision Making and the Temporal Resolution of Uncertainty

Abstract

There exist in the literature many two-period analyses of behavior under uncertainty. (See, for example, Sandmo [1970] and [1971], Rothschild and Stiglitz [1971], Turnovsky [1973] and Epstein [1975, 1978].) These works typically assume that a decision must be made in period 1 subject to uncertainty about the environment that will prevail in period 2. At the start of period 2 the true state of the environment becomes known and perhaps some further decisions are made. The effects on the period 1 decision of the prior uncertainty in expectations are closely examined. Clearly the above framework is inadequate for modelling the more general situation where n >1 decisions are made sequentially and subject to improving information about the eventual state of the world. In this general framework the influence on decisions of the way in which uncertainty is resolved through time represents an interesting area of investigation. This paper undertakes such an investigation in the context of several specific decision problems. For simplicity (see footnote 4), we adopt a minimal extension of the two-period model that makes possible the analysis of the temporal resolution of uncertainty, namely, a three-period model. Thus the decision-making framework considered in this paper may be described as follows: an expected utility maximizing agent faces a three-period planning horizon. He makes decisions in each period. Period 3 decisions are made after all uncertainty has been resolved. In period 1 the decision is made subject to prior expectations about the state of the world that will prevail in period 3. The uncertain future environment is represented by a random variable Z. Before the start of period 2 new information about the ultimate value of Z becomes available. The information is forthcoming through the observation of another random variable Y which in general is correlated with Z. The agent is a Bayesian decision maker and revises his prior probability distribution about Z after observing Y. The amount of additional information about Z provided by Y is a parameter in the model. The objective of the paper is to compare the decisions in period I in two choice problems that differ only with respect to the amount of information provided by Y about Z. Note that in both problems the agent faces the identical prior uncertainty about Z. The difference in the two problems is only in the amount of