Financial Market with Learning from Price under Knightian Uncertainty

Following the framework proposed by Vives (2014), we reconsidered the problem of learning from equilibrium prices under Knightian uncertainty or ambiguity. Specifically, we examine the situation in which uninformed traders face Knightian uncertainty regarding the number of informed traders, causing them to infer pessimistic market information from prices. With Knightian uncertainty, equilibrium price acts as a signaling device, informing uninformed traders whether the market is crowded with informed traders. It exhibits a two-regime characteristic, in which uninformed traders endogenously believe there are more (less) informed traders trading in the market when observing usual (unusual) price. Consequently, Knightian uncertainty alone can lead to price overreaction or under-reaction, resulting in higher or lower price. In addition, we find that Knightian uncertainty can partially explain demand (in)elasticity, highlighting the role of ambiguity as a micro-foundation for explaining demand (in)elasticity, as discussed previously by Gabaix and Koijen (2021). Finally, we show that reducing ambiguity may not always increase the expected trading profits of uninformed traders, as the effect of ambiguity levels can be nonlinear and nonmonotonic.