A no-trade theorem under Knightian uncertainty with general preferences

This paper derives a no-trade theorem under Knightian uncertainty, which generalizes the theorem of Milgrom and Stokey (1982, Journal of Economic Theory 26, 17) by allowing general preference relations. It is shown that the no-trade theorem holds true as long as agents' preferences are dynamically consistent in the sense of Machina and Schmeidler (1991, Econometrica 60, 745), and satisfies the so-called piece-wise monotonicity axiom. A preference satisfying the piece-wise monotonicity axiom does not necessarily imply the additive utility representation, nor is necessarily based on beliefs.