Before revision: We consider the market of n financial agents who aim to increase their expected utilities by sharing their random incomes . Given the  optimal sharing rules, we address the situation where agents do not share their true random endowments, but instead they report as endowments the random quantities that maximize their expected utility when the sharing rules are applied.
After revision: We consider the market of n financial agents who aim to increase their utilities by efficiently sharing their random incomes . Given the optimal sharing rules, we address the situation where agents do not share their true random endowments, but instead they report as endowments the random quantities that maximize their expected utility when the sharing rules are applied.