Before revision:  An assumption of "smallness" type - imposed through the new notion of "closeness to Pareto optimality" - is shown to be sufficient for existence and uniqueness  . Central role in our analysis is played by a fully-coupled nonlinear system of quadratic BSDEs.
After revision:  An assumption of "smallness" type - imposed through the new notion of "closeness to Pareto optimality" - is shown to be sufficient for existence and uniqueness . In particular, this assumption encapsulates settings with small endowments, small time-horizon, or a large population of weakly heterogeneous agents . Central role in our analysis is played by a fully-coupled nonlinear system of quadratic BSDEs.