Dropping Rational Expectations

We consider a pure-exchange sequential economy, where uncertainty prevails and agents, possibly asymmetrically informed, exchange commodities, on spot markets, and securities of all kinds, on typically incomplete financial markets. Consumers have private characteristics, anticipations and beliefs, and no model to forecast prices. We show that they face an incompressible uncertainty, represented by a so-calles 'minimum uncertainty set', which adds to the exogenous uncertainty, on the state of nature, an uncertainty over the price to prevail, on every spot market. Equilibrium is reached when agents expect the 'true' price as a possible outcome on every spot market, and elect optimal strategies, which clear on all markets. We show this sequential equilibrium exists in standard conditions, when agents' anticipations embed the minimum uncertainty set. This outcome is stronger than Radner's (1979), Duffie-Shaffer's (1985) or De Boisdeffre's (2021), which prove the generic existence of equilibrium when agents make perfect forecasts. From an asymptotic argument, our main theorem is derived from De Boisdeffre's (2007), which characterizes the exitence of equilibria on purely financial markets by a no-arbitrage condition.