Before revision:  Given the endogenously derived optimal sharing rules, we address the situation where agentsdo not reveal their true endowments, but instead they report as endowments the random quantities that maximize their utilities when the sharing rulesare applied. Under mean-variance preferences, it is shown that each agent should share only a fraction of his true endowment and report that he is exposed to some endowment he does not possess.
After revision:  The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent's set of strategic choices consists of the security payoffs and the pricing kernel that are consistent with the optimal-sharing rules; while in the incomplete setting, agents respond via demand functions on a vector of given tradeable securities. It is shown that each agent should share only a fraction of his true endowment and report that he is exposed to some endowment he does not possess.