A price uncertainty principle and the existence of sequential equilibrium

We consider a pure exchange financial economy, where agents observe private information signals, form private anticipations and face an "exogenous uncertainty" on the future state, and an "endogenous uncertainty", on the future prices. At a sequential equilibrium, all agents expect the "true" price as a possible outcome, and elect optimal strategies, which clear on all markets at every time period. This concept differs from both traditional ones of temporary equilibrium and sequential equilibrium with perfect price foresight. We display on an example a continuum of sequential equilibria, varying with agents' anticipations. We show, when anticipations are private or prone to change, that "correct" price forecasts need always embed a set of "minimum uncertainty", which only depends on the fundamentals of the economy and current period prices. When anticipations are so correct, we prove the existence of a sequential equilibrium is still characterized by the no-arbitrage condition