This paper studies general equilibrium theory, for both complete and incomplete markets, under Knightian uncertainty. Noting that the preference represented by Knightian uncertainty induces a set of complete preferences, we set ourselves the task of inquiring the relationship between an equilibrium under Knightian uncertainty and its counterpart under the induced complete preferences. It is shown that they are actually equivalent. The importance of this result is due to its applications, among which the existence of equilibria under Knightian uncertainty and their computation follow at once from the existing knowledge on general equilibrium theory under complete preferences. Moreover, by means of that equivalence, we are in a position to investigate the problem of efficiency and indeterminacy of equilibria under Knightian uncertainty.