Nest-monotonic two-stage acts and exponential probability capacities

Abstract

This paper examines conditions for Choquet expected utility (CEU) to satisfy both the reduction of two-stage acts and the recursion axioms, which are taken for granted in economics. A key idea of this paper is to consider nest-monotonic two-stage acts, which share their rankings of states with those of their reduced onestage acts. Our main theorem shows that the axioms, one of which is restricted to nest-monotonic two-stage acts, and consequentialism are satisfied if and only if the preference is exponential CEU, which is such that the probability capacity is an exponential transformation of a probability measure. This result indicates that within a specified range of decision problems, exponential CEU is the only form of CEU that derives indifference to the timing of information resolution. Furthermore, the relation between first-and second-stage exponential CEU is characterized both by the f * -Bayesian updating rule and by comonotonic dynamic consistency. Conditions to establish the law of iterated expectation for CEU are also discussed.