Add to ORKGWe consider risk sharing among individuals in a one-period setting under uncertainty, that will result in payoffs to be shared among the members. We start with optimal risk sharing in an Arrow-Debreu economy, or equivalently, in a Borch-style reinsurance market. From the results of this model we can infer how risk is optimally distributed between individuals according to their preferences and initial endowments, under some idealized conditions. A main message in this theory is the mutuality principle, of interest related to the economic effects of pandemics. From this we point out some elements of a more general theory of syndicates, where in addition, the group of people is to make a common decision under uncertainty. We extend to a compet...