The perfect foresight assumption revisited: the existence of sequential equilibrium with price uncertainty

Our earlier papers had extended to asymmetric information some classical existence theorems of general equilibrium theory, under the standard assumption that agents had perfect foresights, that is, they knew at the outset which price would prevail tomorrow on each spot market. Yet, observation suggests that agents more often trade with an un-precise knowledge of future prices. Hereafter, we let agents anticipate, in each random state, an idiosyncratic set of plausible prices, called price expectations, which overlap across agents on each spot market. A state equilibrium is reached when agents have expectations, which include "true" spot prices, and make decisions at the first period, which are optimal within the budget set and clear on all markets ex post. In an earlier model with finitely many expectations, we showed the existence of this so-called "correct foresights equilibrium" was characterized by the no-arbitrage condition of finance. We now extend this result to the case of infinite price expectations' sets and continuous probability distributions