Time Continuity and Nonadditive Expected Utility

Assume that a decision maker assesses the worth of the lottery Xn for each n. Assume also that for each n, Xn is preferred to Y . Now, consider the situation where Xn converges, in some sense, to the lottery X. If X is preferred to Y , then the preference order is referred to as time continuous (Gilboa [7]). Information consisting of probabilities of some (but maybe not all) events induces an integral with respect to a probability specified on a sub–algebra (PSA) (Lehrer [10]). The decision maker evaluates the alternatives utilizing only the available information and completely ignoring unavailable information. The paper studies time continuity for two preference functionals: the Choquet integral and the integral with respect to a PSA. The integral with respect to PSA is determined by the structures of the available information. By relating it to the Choquet integral, we characterize the structure of available information that would yield time continuity. JEL classification: D81.