Sequential equilibrium without rational expectations of prices: an existence proof

We consider a pure exchange economy, where consumers may exchange commodities, on spot markets, and securities, on purely financial markets, and be asymmetrically informed. Agents have private characteristics, anticipations and beliefs, and no model to forecast prices. Therefore, they face an incompressible uncertainty, represented by a "minimum uncertainty set", which typically adds to the 'exogenous uncertainty', on tomorrow's state of nature, an 'endogenous uncertainty' on spot prices, which depend on agents' private beliefs. At equilibrium, all consumers expect the 'true' price in each realizable state as a possible outcome, and elect optimal strategies, ex ante, which clear on all markets, ex post. We show that equilibrium exists under standard conditions, as long as agents' prior anticipations, which may be refined from observing markets, embed the minimum uncertainty set.