Dynamic choice and nonexpected utility

This paper explores how some widely studied classes of nonexpected utility models could be used in dynamic choice situations. A new "sequential consistency" condition is introduced for single-stage and two-stage decision problems. Sequential consistency requires that if a decision maker has committed to a family of models (e.g., the rank dependent family, or the betweenness family) then he use the same family throughout. The conditions are presented under which dynamic consistency, consequentialism, and sequential consistency can be simultaneously preserved for a nonexpected utility maximizer. Each of the conditions is relevant in prescriptive decision making. We allow for cases where the exact sequence of decisions and events, and thus the dynamic structure of the decision problem, is relevant to the decision maker. In spite of this added flexibility of our analysis, our results show that nonexpected utility models can only be used in a considerably restrictive way in dynamic choice. A puzzling implication is that, for the currently most popular decision models (rank-dependent and betweenness), a departure from expected utility can only be made in either the first stage or the last stage of a decision tree. The results suggest either a development of new nonexpected utility models or a return to expected utility.