Dropping rational expectations

In [5], we proposed a general equilibrium model, with incomplete financial markets and asymmetric information, where agents forecasted prices privately without rational expectations. Consistently, they anticipated idiosyncratic sets of future prices, and elected probability laws on these sets, that we called beliefs. Under mild conditions, and di¤erently from Hart [1975] and Radner [1979], equilibrium always existed in this model, as long as agents' anticipations precluded arbitrage. The joint determination of equilibrium prices and beliefs is traditionally seen as a rational expectations' problem. Hereafter, we suggest it may be otherwise. We propose to show that agents, whose prior anticipation sets yield an arbitrage, may update their expectations from observing trade opportunities on financial markets. With no price to be observed, they eventually infer smaller arbitrage-free anticipation sets, which cannot be narrowed down any further. Once these sets are attained, equilibrium prices may change if agents change their beliefs, but they will convey the same information.