A price uncertainty principle and the existence of sequential equilibrium : (I) A numerical example

In three related papers, we consider a pure exchange financial economy, where agents may 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 foresight. The first paper, developed hereafter, illustrates, on a heuristic example, why changing anticipations may alter equilibrium prices and allocations, explain bubbles or crashes on markets at equilibrium, or preclude any perfect price foresight. The second paper shows that correct anticipations need always embed a set of "minimum uncertainty", depending on observed prices and the fundamental characteristics of the economy, and studies the properties of this set. The third paper proves, in the complete model, that the existence of a sequential equilibrium is still characterized by the no-arbitrage condition.