We study economies with Knightian uncertainty about state prices. We introduce an equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such equilibria lead to inefficient allocations; they coincide with Arrow–Debreu equilibria if and only if the values of net trades are ambiguity‐free in mean. In economies without aggregate uncertainty, inefficiencies are generic. Equilibrium allocations under price uncertainty are efficient in a constrained sense that we call uncertainty–neutral efficient. Arrow–Debreu equilibria turn out to be non‐robust with respect to the introduction of Knightian uncertainty.
Short Bio: Frank Riedel studied Mathematics at Freiburg University. He completed a Ph.D. with Hans Föllmer at Humboldt University in Berlin. After postdoc positions in Berkeley and Stanford, he became Professor for Economics at Bonn University. Since 2009, he is Director of the Institute of Mathematical Economics at Bielefeld. Frank Riedel's research focuses recently on applications of model and Knightian uncertainty to financial problems. In particular, he addresses the issue of pricing American Options under Knightian uncertainty in recent Econometrica paper.