Westudy abstract decision problems by introducing an extended dominance relation with respect to a set of alternatives. This extension is in between the traditional dominance relation as formulated by Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944) and the transitive closure of it. Subsequently, stable sets are defined and studied...

In the paradigm of von Neumann and Morgenstern, a representation of a ne preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on a real open...