Pareto optimal allocations and optimal risk sharing for coherent or convex risk measures as well as for insurance prices have been studied widely in the literature. In particular, Pareto optimal allocations have been characterized by applying inf-convolution of risk measures and convex...

We provide priority-constrained versions of the ordinal efficiency welfare theorem for school choice lotteries. Moreover, we show that a constrained version of a cardinal second welfare theorem fails to hold, but can be restored for a relaxed notion of equilibrium with priority-specific prices

In this paper we show that in a pure exchange economy where social weights and total resources are fixed there is no possibility to improve the social welfare by means of efficient reallocations of the resources. However, if social weights are not fixed but can be selected from a particular set,...