We study economies in which agents face Knightian uncertainty

about state prices. Knightian uncertainty leads naturally to nonlinear

expectations. We introduce a corresponding equilibrium concept

with sublinear prices and prove that equilibria exist under weak conditions.

In general, such equilibria lead to Pareto inefficient allocations;

the equilibria coincide with Arrow-Debreu equilibria only if the

values of net trades are ambiguity-free in the mean. In economies

without aggregate uncertainty, inefficiencies are generic. We introduce

a constrained efficiency concept, uncertainty-neutral efficiency;

equilibrium allocations under price uncertainty are efficient in this constrained

sense. Arrow-Debreu equilibria turn out to be non-robust

with respect to the introduction of Knightian uncertainty.